Diff of the two buildlogs: -- --- b1/build.log 2020-06-20 21:24:07.823830980 +0000 +++ b2/build.log 2020-06-20 21:34:27.787557267 +0000 @@ -1,6 +1,6 @@ I: pbuilder: network access will be disabled during build -I: Current time: Fri Jul 23 15:45:00 -12 2021 -I: pbuilder-time-stamp: 1627098300 +I: Current time: Sun Jun 21 11:24:11 +14 2020 +I: pbuilder-time-stamp: 1592688251 I: Building the build Environment I: extracting base tarball [/var/cache/pbuilder/buster-reproducible-base.tgz] I: copying local configuration @@ -18,7 +18,7 @@ I: Extracting source gpgv: unknown type of key resource 'trustedkeys.kbx' gpgv: keyblock resource '/root/.gnupg/trustedkeys.kbx': General error -gpgv: Signature made Thu Jan 3 23:08:20 2019 -12 +gpgv: Signature made Sat Jan 5 01:08:20 2019 +14 gpgv: using RSA key 3F464391498FE874BDB5D98F2124AA1983785C90 gpgv: Can't check signature: No public key dpkg-source: warning: failed to verify signature on ./octave-queueing_1.2.6-5.dsc @@ -32,138 +32,172 @@ dpkg-source: info: applying texinfo-absolute-path.patch I: Not using root during the build. I: Installing the build-deps -I: user script /srv/workspace/pbuilder/50668/tmp/hooks/D02_print_environment starting +I: user script /srv/workspace/pbuilder/19078/tmp/hooks/D01_modify_environment starting +debug: Running on profitbricks-build2-i386. +I: Changing host+domainname to test build reproducibility +I: Adding a custom variable just for the fun of it... +I: Changing /bin/sh to bash +Removing 'diversion of /bin/sh to /bin/sh.distrib by dash' +Adding 'diversion of /bin/sh to /bin/sh.distrib by bash' +Removing 'diversion of /usr/share/man/man1/sh.1.gz to /usr/share/man/man1/sh.distrib.1.gz by dash' +Adding 'diversion of /usr/share/man/man1/sh.1.gz to /usr/share/man/man1/sh.distrib.1.gz by bash' +I: Setting pbuilder2's login shell to /bin/bash +I: Setting pbuilder2's GECOS to second user,second room,second work-phone,second home-phone,second other +I: user script /srv/workspace/pbuilder/19078/tmp/hooks/D01_modify_environment finished +I: user script /srv/workspace/pbuilder/19078/tmp/hooks/D02_print_environment starting I: set - BUILDDIR='/build' - BUILDUSERGECOS='first user,first room,first work-phone,first home-phone,first other' - BUILDUSERNAME='pbuilder1' - BUILD_ARCH='i386' - DEBIAN_FRONTEND='noninteractive' - DEB_BUILD_OPTIONS='buildinfo=+all reproducible=+all parallel=18' - DISTRIBUTION='' - HOME='/root' - HOST_ARCH='i386' + BASH=/bin/sh + BASHOPTS=checkwinsize:cmdhist:complete_fullquote:extquote:force_fignore:globasciiranges:hostcomplete:interactive_comments:progcomp:promptvars:sourcepath + BASH_ALIASES=() + BASH_ARGC=() + BASH_ARGV=() + BASH_CMDS=() + BASH_LINENO=([0]="12" [1]="0") + BASH_SOURCE=([0]="/tmp/hooks/D02_print_environment" [1]="/tmp/hooks/D02_print_environment") + BASH_VERSINFO=([0]="5" [1]="0" [2]="3" [3]="1" [4]="release" [5]="i686-pc-linux-gnu") + BASH_VERSION='5.0.3(1)-release' + BUILDDIR=/build + BUILDUSERGECOS='second user,second room,second work-phone,second home-phone,second other' + BUILDUSERNAME=pbuilder2 + BUILD_ARCH=i386 + DEBIAN_FRONTEND=noninteractive + DEB_BUILD_OPTIONS='buildinfo=+all reproducible=+all parallel=10' + DIRSTACK=() + DISTRIBUTION= + EUID=0 + FUNCNAME=([0]="Echo" [1]="main") + GROUPS=() + HOME=/root + HOSTNAME=i-capture-the-hostname + HOSTTYPE=i686 + HOST_ARCH=i386 IFS=' ' - INVOCATION_ID='ecbda4b07da64c6d8ff2d6eff5875d74' - LANG='C' - LANGUAGE='en_US:en' - LC_ALL='C' - LD_LIBRARY_PATH='/usr/lib/libeatmydata' - LD_PRELOAD='libeatmydata.so' - MAIL='/var/mail/root' - OPTIND='1' - PATH='/usr/sbin:/usr/bin:/sbin:/bin:/usr/games' - PBCURRENTCOMMANDLINEOPERATION='build' - PBUILDER_OPERATION='build' - PBUILDER_PKGDATADIR='/usr/share/pbuilder' - PBUILDER_PKGLIBDIR='/usr/lib/pbuilder' - PBUILDER_SYSCONFDIR='/etc' - PPID='50668' - PS1='# ' - PS2='> ' + INVOCATION_ID=ccf8ecb116d8477084fb1770c1986e6a + LANG=C + LANGUAGE=de_CH:de + LC_ALL=C + LD_LIBRARY_PATH=/usr/lib/libeatmydata + LD_PRELOAD=libeatmydata.so + MACHTYPE=i686-pc-linux-gnu + MAIL=/var/mail/root + OPTERR=1 + OPTIND=1 + OSTYPE=linux-gnu + PATH=/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/i/capture/the/path + PBCURRENTCOMMANDLINEOPERATION=build + PBUILDER_OPERATION=build + PBUILDER_PKGDATADIR=/usr/share/pbuilder + PBUILDER_PKGLIBDIR=/usr/lib/pbuilder + PBUILDER_SYSCONFDIR=/etc + PIPESTATUS=([0]="0") + POSIXLY_CORRECT=y + PPID=19078 PS4='+ ' - PWD='/' - SHELL='/bin/bash' - SHLVL='2' - SUDO_COMMAND='/usr/bin/timeout -k 18.1h 18h /usr/bin/ionice -c 3 /usr/bin/nice /usr/sbin/pbuilder --build --configfile /srv/reproducible-results/rbuild-debian/tmp.RltQsfhCVf/pbuilderrc_PwjB --hookdir /etc/pbuilder/first-build-hooks --debbuildopts -b --basetgz /var/cache/pbuilder/buster-reproducible-base.tgz --buildresult /srv/reproducible-results/rbuild-debian/tmp.RltQsfhCVf/b1 --logfile b1/build.log octave-queueing_1.2.6-5.dsc' - SUDO_GID='112' - SUDO_UID='107' - SUDO_USER='jenkins' - TERM='unknown' - TZ='/usr/share/zoneinfo/Etc/GMT+12' - USER='root' - _='/usr/bin/systemd-run' - http_proxy='http://85.184.249.68:3128' + PWD=/ + SHELL=/bin/bash + SHELLOPTS=braceexpand:errexit:hashall:interactive-comments:posix + SHLVL=3 + SUDO_COMMAND='/usr/bin/timeout -k 24.1h 24h /usr/bin/ionice -c 3 /usr/bin/nice -n 11 /usr/bin/unshare --uts -- /usr/sbin/pbuilder --build --configfile /srv/reproducible-results/rbuild-debian/tmp.RltQsfhCVf/pbuilderrc_SdFU --hookdir /etc/pbuilder/rebuild-hooks --debbuildopts -b --basetgz /var/cache/pbuilder/buster-reproducible-base.tgz --buildresult /srv/reproducible-results/rbuild-debian/tmp.RltQsfhCVf/b2 --logfile b2/build.log octave-queueing_1.2.6-5.dsc' + SUDO_GID=112 + SUDO_UID=107 + SUDO_USER=jenkins + TERM=unknown + TZ=/usr/share/zoneinfo/Etc/GMT-14 + UID=0 + USER=root + _='I: set' + http_proxy=http://78.137.99.97:3128 I: uname -a - Linux profitbricks-build6-i386 4.19.0-9-amd64 #1 SMP Debian 4.19.118-2+deb10u1 (2020-06-07) x86_64 GNU/Linux + Linux i-capture-the-hostname 4.19.0-9-686-pae #1 SMP Debian 4.19.118-2+deb10u1 (2020-06-07) i686 GNU/Linux I: ls -l /bin total 5476 - -rwxr-xr-x 1 root root 1302248 Apr 17 2019 bash - -rwxr-xr-x 3 root root 38280 Jul 10 2019 bunzip2 - -rwxr-xr-x 3 root root 38280 Jul 10 2019 bzcat - lrwxrwxrwx 1 root root 6 Jul 10 2019 bzcmp -> bzdiff - -rwxr-xr-x 1 root root 2227 Jul 10 2019 bzdiff - lrwxrwxrwx 1 root root 6 Jul 10 2019 bzegrep -> bzgrep - -rwxr-xr-x 1 root root 4877 Jun 24 2019 bzexe - lrwxrwxrwx 1 root root 6 Jul 10 2019 bzfgrep -> bzgrep - -rwxr-xr-x 1 root root 3641 Jul 10 2019 bzgrep - -rwxr-xr-x 3 root root 38280 Jul 10 2019 bzip2 - -rwxr-xr-x 1 root root 17768 Jul 10 2019 bzip2recover - lrwxrwxrwx 1 root root 6 Jul 10 2019 bzless -> bzmore - -rwxr-xr-x 1 root root 1297 Jul 10 2019 bzmore - -rwxr-xr-x 1 root root 38692 Feb 28 2019 cat - -rwxr-xr-x 1 root root 75588 Feb 28 2019 chgrp - -rwxr-xr-x 1 root root 63268 Feb 28 2019 chmod - -rwxr-xr-x 1 root root 75588 Feb 28 2019 chown - -rwxr-xr-x 1 root root 153732 Feb 28 2019 cp - -rwxr-xr-x 1 root root 132820 Jan 17 2019 dash - -rwxr-xr-x 1 root root 120676 Feb 28 2019 date - -rwxr-xr-x 1 root root 92040 Feb 28 2019 dd - -rwxr-xr-x 1 root root 100620 Feb 28 2019 df - -rwxr-xr-x 1 root root 149736 Feb 28 2019 dir - -rwxr-xr-x 1 root root 79412 Jan 9 2019 dmesg - lrwxrwxrwx 1 root root 8 Sep 26 2018 dnsdomainname -> hostname - lrwxrwxrwx 1 root root 8 Sep 26 2018 domainname -> hostname - -rwxr-xr-x 1 root root 34532 Feb 28 2019 echo - -rwxr-xr-x 1 root root 28 Jan 7 2019 egrep - -rwxr-xr-x 1 root root 34532 Feb 28 2019 false - -rwxr-xr-x 1 root root 28 Jan 7 2019 fgrep - -rwxr-xr-x 1 root root 67700 Jan 9 2019 findmnt - -rwsr-xr-x 1 root root 30112 Apr 22 2020 fusermount - -rwxr-xr-x 1 root root 206392 Jan 7 2019 grep - -rwxr-xr-x 2 root root 2345 Jan 5 2019 gunzip - -rwxr-xr-x 1 root root 6375 Jan 5 2019 gzexe - -rwxr-xr-x 1 root root 100952 Jan 5 2019 gzip - -rwxr-xr-x 1 root root 21916 Sep 26 2018 hostname - -rwxr-xr-x 1 root root 79752 Feb 28 2019 ln - -rwxr-xr-x 1 root root 55400 Jul 26 2018 login - -rwxr-xr-x 1 root root 149736 Feb 28 2019 ls - -rwxr-xr-x 1 root root 112032 Jan 9 2019 lsblk - -rwxr-xr-x 1 root root 87972 Feb 28 2019 mkdir - -rwxr-xr-x 1 root root 79748 Feb 28 2019 mknod - -rwxr-xr-x 1 root root 46916 Feb 28 2019 mktemp - -rwxr-xr-x 1 root root 42348 Jan 9 2019 more - -rwsr-xr-x 1 root root 50592 Jan 9 2019 mount - -rwxr-xr-x 1 root root 13724 Jan 9 2019 mountpoint - -rwxr-xr-x 1 root root 157832 Feb 28 2019 mv - lrwxrwxrwx 1 root root 8 Sep 26 2018 nisdomainname -> hostname - lrwxrwxrwx 1 root root 14 Feb 14 2019 pidof -> /sbin/killall5 - -rwxr-xr-x 1 root root 38660 Feb 28 2019 pwd - lrwxrwxrwx 1 root root 4 Apr 17 2019 rbash -> bash - -rwxr-xr-x 1 root root 46852 Feb 28 2019 readlink - -rwxr-xr-x 1 root root 75588 Feb 28 2019 rm - -rwxr-xr-x 1 root root 42756 Feb 28 2019 rmdir - -rwxr-xr-x 1 root root 22276 Jan 21 2019 run-parts - -rwxr-xr-x 1 root root 125036 Dec 22 2018 sed - lrwxrwxrwx 1 root root 4 Jul 23 02:47 sh -> dash - -rwxr-xr-x 1 root root 34532 Feb 28 2019 sleep - -rwxr-xr-x 1 root root 79652 Feb 28 2019 stty - -rwsr-xr-x 1 root root 71072 Jan 9 2019 su - -rwxr-xr-x 1 root root 34564 Feb 28 2019 sync - -rwxr-xr-x 1 root root 504024 Apr 23 2019 tar - -rwxr-xr-x 1 root root 13860 Jan 21 2019 tempfile - -rwxr-xr-x 1 root root 104292 Feb 28 2019 touch - -rwxr-xr-x 1 root root 34532 Feb 28 2019 true - -rwxr-xr-x 1 root root 17768 Apr 22 2020 ulockmgr_server - -rwsr-xr-x 1 root root 30108 Jan 9 2019 umount - -rwxr-xr-x 1 root root 34532 Feb 28 2019 uname - -rwxr-xr-x 2 root root 2345 Jan 5 2019 uncompress - -rwxr-xr-x 1 root root 149736 Feb 28 2019 vdir - -rwxr-xr-x 1 root root 34208 Jan 9 2019 wdctl - -rwxr-xr-x 1 root root 946 Jan 21 2019 which - lrwxrwxrwx 1 root root 8 Sep 26 2018 ypdomainname -> hostname - -rwxr-xr-x 1 root root 1983 Jan 5 2019 zcat - -rwxr-xr-x 1 root root 1677 Jan 5 2019 zcmp - -rwxr-xr-x 1 root root 5879 Jan 5 2019 zdiff - -rwxr-xr-x 1 root root 29 Jan 5 2019 zegrep - -rwxr-xr-x 1 root root 29 Jan 5 2019 zfgrep - -rwxr-xr-x 1 root root 2080 Jan 5 2019 zforce - -rwxr-xr-x 1 root root 7584 Jan 5 2019 zgrep - -rwxr-xr-x 1 root root 2205 Jan 5 2019 zless - -rwxr-xr-x 1 root root 1841 Jan 5 2019 zmore - -rwxr-xr-x 1 root root 4552 Jan 5 2019 znew -I: user script /srv/workspace/pbuilder/50668/tmp/hooks/D02_print_environment finished + -rwxr-xr-x 1 root root 1302248 Apr 18 2019 bash + -rwxr-xr-x 3 root root 38280 Jul 11 2019 bunzip2 + -rwxr-xr-x 3 root root 38280 Jul 11 2019 bzcat + lrwxrwxrwx 1 root root 6 Jul 11 2019 bzcmp -> bzdiff + -rwxr-xr-x 1 root root 2227 Jul 11 2019 bzdiff + lrwxrwxrwx 1 root root 6 Jul 11 2019 bzegrep -> bzgrep + -rwxr-xr-x 1 root root 4877 Jun 25 2019 bzexe + lrwxrwxrwx 1 root root 6 Jul 11 2019 bzfgrep -> bzgrep + -rwxr-xr-x 1 root root 3641 Jul 11 2019 bzgrep + -rwxr-xr-x 3 root root 38280 Jul 11 2019 bzip2 + -rwxr-xr-x 1 root root 17768 Jul 11 2019 bzip2recover + lrwxrwxrwx 1 root root 6 Jul 11 2019 bzless -> bzmore + -rwxr-xr-x 1 root root 1297 Jul 11 2019 bzmore + -rwxr-xr-x 1 root root 38692 Mar 1 2019 cat + -rwxr-xr-x 1 root root 75588 Mar 1 2019 chgrp + -rwxr-xr-x 1 root root 63268 Mar 1 2019 chmod + -rwxr-xr-x 1 root root 75588 Mar 1 2019 chown + -rwxr-xr-x 1 root root 153732 Mar 1 2019 cp + -rwxr-xr-x 1 root root 132820 Jan 18 2019 dash + -rwxr-xr-x 1 root root 120676 Mar 1 2019 date + -rwxr-xr-x 1 root root 92040 Mar 1 2019 dd + -rwxr-xr-x 1 root root 100620 Mar 1 2019 df + -rwxr-xr-x 1 root root 149736 Mar 1 2019 dir + -rwxr-xr-x 1 root root 79412 Jan 10 2019 dmesg + lrwxrwxrwx 1 root root 8 Sep 27 2018 dnsdomainname -> hostname + lrwxrwxrwx 1 root root 8 Sep 27 2018 domainname -> hostname + -rwxr-xr-x 1 root root 34532 Mar 1 2019 echo + -rwxr-xr-x 1 root root 28 Jan 8 2019 egrep + -rwxr-xr-x 1 root root 34532 Mar 1 2019 false + -rwxr-xr-x 1 root root 28 Jan 8 2019 fgrep + -rwxr-xr-x 1 root root 67700 Jan 10 2019 findmnt + -rwsr-xr-x 1 root root 30112 Apr 23 09:38 fusermount + -rwxr-xr-x 1 root root 206392 Jan 8 2019 grep + -rwxr-xr-x 2 root root 2345 Jan 6 2019 gunzip + -rwxr-xr-x 1 root root 6375 Jan 6 2019 gzexe + -rwxr-xr-x 1 root root 100952 Jan 6 2019 gzip + -rwxr-xr-x 1 root root 21916 Sep 27 2018 hostname + -rwxr-xr-x 1 root root 79752 Mar 1 2019 ln + -rwxr-xr-x 1 root root 55400 Jul 27 2018 login + -rwxr-xr-x 1 root root 149736 Mar 1 2019 ls + -rwxr-xr-x 1 root root 112032 Jan 10 2019 lsblk + -rwxr-xr-x 1 root root 87972 Mar 1 2019 mkdir + -rwxr-xr-x 1 root root 79748 Mar 1 2019 mknod + -rwxr-xr-x 1 root root 46916 Mar 1 2019 mktemp + -rwxr-xr-x 1 root root 42348 Jan 10 2019 more + -rwsr-xr-x 1 root root 50592 Jan 10 2019 mount + -rwxr-xr-x 1 root root 13724 Jan 10 2019 mountpoint + -rwxr-xr-x 1 root root 157832 Mar 1 2019 mv + lrwxrwxrwx 1 root root 8 Sep 27 2018 nisdomainname -> hostname + lrwxrwxrwx 1 root root 14 Feb 15 2019 pidof -> /sbin/killall5 + -rwxr-xr-x 1 root root 38660 Mar 1 2019 pwd + lrwxrwxrwx 1 root root 4 Apr 18 2019 rbash -> bash + -rwxr-xr-x 1 root root 46852 Mar 1 2019 readlink + -rwxr-xr-x 1 root root 75588 Mar 1 2019 rm + -rwxr-xr-x 1 root root 42756 Mar 1 2019 rmdir + -rwxr-xr-x 1 root root 22276 Jan 22 2019 run-parts + -rwxr-xr-x 1 root root 125036 Dec 23 2018 sed + lrwxrwxrwx 1 root root 4 Jun 21 11:26 sh -> bash + lrwxrwxrwx 1 root root 4 Jun 19 22:45 sh.distrib -> dash + -rwxr-xr-x 1 root root 34532 Mar 1 2019 sleep + -rwxr-xr-x 1 root root 79652 Mar 1 2019 stty + -rwsr-xr-x 1 root root 71072 Jan 10 2019 su + -rwxr-xr-x 1 root root 34564 Mar 1 2019 sync + -rwxr-xr-x 1 root root 504024 Apr 24 2019 tar + -rwxr-xr-x 1 root root 13860 Jan 22 2019 tempfile + -rwxr-xr-x 1 root root 104292 Mar 1 2019 touch + -rwxr-xr-x 1 root root 34532 Mar 1 2019 true + -rwxr-xr-x 1 root root 17768 Apr 23 09:38 ulockmgr_server + -rwsr-xr-x 1 root root 30108 Jan 10 2019 umount + -rwxr-xr-x 1 root root 34532 Mar 1 2019 uname + -rwxr-xr-x 2 root root 2345 Jan 6 2019 uncompress + -rwxr-xr-x 1 root root 149736 Mar 1 2019 vdir + -rwxr-xr-x 1 root root 34208 Jan 10 2019 wdctl + -rwxr-xr-x 1 root root 946 Jan 22 2019 which + lrwxrwxrwx 1 root root 8 Sep 27 2018 ypdomainname -> hostname + -rwxr-xr-x 1 root root 1983 Jan 6 2019 zcat + -rwxr-xr-x 1 root root 1677 Jan 6 2019 zcmp + -rwxr-xr-x 1 root root 5879 Jan 6 2019 zdiff + -rwxr-xr-x 1 root root 29 Jan 6 2019 zegrep + -rwxr-xr-x 1 root root 29 Jan 6 2019 zfgrep + -rwxr-xr-x 1 root root 2080 Jan 6 2019 zforce + -rwxr-xr-x 1 root root 7584 Jan 6 2019 zgrep + -rwxr-xr-x 1 root root 2205 Jan 6 2019 zless + -rwxr-xr-x 1 root root 1841 Jan 6 2019 zmore + -rwxr-xr-x 1 root root 4552 Jan 6 2019 znew +I: user script /srv/workspace/pbuilder/19078/tmp/hooks/D02_print_environment finished -> Attempting to satisfy build-dependencies -> Creating pbuilder-satisfydepends-dummy package Package: pbuilder-satisfydepends-dummy @@ -608,7 +642,7 @@ Get: 393 http://deb.debian.org/debian buster/main i386 texlive all 2018.20190227-2 [32.6 kB] Get: 394 http://deb.debian.org/debian buster/main i386 texlive-font-utils all 2018.20190227-2 [1746 kB] Get: 395 http://deb.debian.org/debian buster/main i386 texlive-plain-generic all 2018.20190227-2 [24.3 MB] -Fetched 234 MB in 4s (58.3 MB/s) +Fetched 234 MB in 1min 10s (3344 kB/s) debconf: delaying package configuration, since apt-utils is not installed Selecting previously unselected package libbsd0:i386. (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 19234 files and directories currently installed.) @@ -2250,7 +2284,7 @@ Building tag database... -> Finished parsing the build-deps I: Building the package -I: Running cd /build/octave-queueing-1.2.6/ && env PATH="/usr/sbin:/usr/bin:/sbin:/bin:/usr/games" HOME="/nonexistent/first-build" dpkg-buildpackage -us -uc -b +I: Running cd /build/octave-queueing-1.2.6/ && env PATH="/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/i/capture/the/path" HOME="/nonexistent/second-build" dpkg-buildpackage -us -uc -b dpkg-buildpackage: info: source package octave-queueing dpkg-buildpackage: info: source version 1.2.6-5 dpkg-buildpackage: info: source distribution unstable @@ -2337,7 +2371,7 @@ 0 0.2 0.4 0.6 0.8 1 Class 1 population mix -error: writing file '/nonexistent/first-build/.octave_hist': No such file or directory +error: writing file '/nonexistent/second-build/.octave_hist': No such file or directory error: ignoring const execution_exception& while preparing to exit for i in web.eps power.eps ; do sed -i -e "s:/Title (.*):/Title ($i):" $i ; done convert -density 100 -background white -flatten web.eps web.png @@ -2561,150 +2595,67 @@ dh_octave_check -O--buildsystem=octave Checking package... Checking m files ... -[inst/qnmminf.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnmminf.m -***** test - fail( "qnmminf( [1 2], [1 2 3] )", "incompatible size"); - fail( "qnmminf( [-1 -1], [1 1] )", ">0" ); -warning: qnmminf is deprecated. Please use qsmminf instead -1 test, 1 passed, 0 known failure, 0 skipped -[inst/dtmc_is_irreducible.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmc_is_irreducible.m +[inst/qncsvisits.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncsvisits.m ***** test - P = [0 .5 0; 0 0 0]; - fail( "dtmc_is_irresudible(P)" ); + P = [-1 0; 0 0]; + fail( "qncsvisits(P)", "invalid" ); + P = [1 0; 0.5 0]; + fail( "qncsvisits(P)", "invalid" ); + P = [1 2 3; 1 2 3]; + fail( "qncsvisits(P)", "square" ); + P = [0 1; 1 0]; + fail( "qncsvisits(P,0)", "range" ); + fail( "qncsvisits(P,3)", "range" ); ***** test - P = [0 1 0; 0 .5 .5; 0 1 0]; - [r s] = dtmc_is_irreducible(P); - assert( r == 0 ); - assert( max(s), 2 ); - assert( min(s), 1 ); -warning: dtmc_is_irreducible is deprecated. Please use dtmcisir instead + + ## Closed, single class network + + P = [0 0.3 0.7; 1 0 0; 1 0 0]; + V = qncsvisits(P); + assert( V*P,V,1e-5 ); + assert( V, [1 0.3 0.7], 1e-5 ); ***** test - P = [.5 .5 0; .2 .3 .5; 0 .2 .8]; - [r s] = dtmc_is_irreducible(P); - assert( r == 1 ); - assert( max(s), 1 ); - assert( min(s), 1 ); + + ## Test tolerance of the qncsvisits() function. + ## This test builds transition probability matrices and tries + ## to compute the visit counts on them. + + for k=[5, 10, 20, 50] + P = reshape(1:k^2, k, k); + P = P ./ repmat(sum(P,2),1,k); + V = qncsvisits(P); + assert( V*P, V, 1e-5 ); + endfor +***** demo + P = [0 0.3 0.7; ... + 1 0 0 ; ... + 1 0 0 ]; + V = qncsvisits(P) 3 tests, 3 passed, 0 known failure, 0 skipped -[inst/dtmc_taexps.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmc_taexps.m -***** test - P = dtmc_bd([1 1 1 1], [0 0 0 0]); - p0 = [1 0 0 0 0]; - L = dtmc_taexps(P,p0); - assert( L, [.25 .25 .25 .25 0], 10*eps ); -warning: dtmc_bd is deprecated. Please use dtmcbd instead -warning: dtmc_taexps is deprecated. Please use dtmctaexps instead -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qnopen.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnopen.m +[inst/qnclosedsinglemvaapprox.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnclosedsinglemvaapprox.m ***** test - # Example 34.1 p. 572 - lambda = 3; - V = [16 7 8]; - S = [0.01 0.02 0.03]; - [U R Q X] = qnopen( lambda, S, V ); - assert( R, [0.0192 0.0345 0.107], 1e-2 ); - assert( U, [0.48 0.42 0.72], 1e-2 ); + fail( "qnclosedsinglemvaapprox()", "Invalid" ); + fail( "qnclosedsinglemvaapprox( 10, [1 2], [1 2 3] )", "S, V and m" ); + fail( "qnclosedsinglemvaapprox( 10, [-1 1], [1 1] )", ">= 0" ); + fail( "qnclosedsinglemvaapprox( 10, [1 2], [1 2], [1 2] )", "supports"); + fail( "qnclosedsinglemvaapprox( 10, [1 2], [1 2], [1 1], 0, -1)", "tol"); +warning: qnclosedsinglemvaapprox is deprecated. Please use qncsmvaap instead ***** test - V = [1 1; 1 1]; - S = [1 3; 2 4]; - lambda = [3/19 2/19]; - [U R Q] = qnopen(lambda, S, diag( lambda / sum(lambda) ) * V); - assert( U(1,1), 3/19, 1e-6 ); - assert( U(2,1), 4/19, 1e-6 ); - assert( R(1,1), 19/12, 1e-6 ); - assert( R(1,2), 57/2, 1e-6 ); - assert( Q(1,1), .25, 1e-6 ); + # Example p. 117 Lazowska et al. + S = [0.605 2.1 1.35]; + V = [1 1 1]; + N = 3; + Z = 15; + m = 1; + [U R Q X] = qnclosedsinglemvaapprox(N, S, V, m, Z); + Rs = dot(V,R); + Xs = N/(Z+Rs); + assert( Q, [0.0973 0.4021 0.2359], 1e-3 ); + assert( Xs, 0.1510, 1e-3 ); + assert( Rs, 4.87, 1e-3 ); 2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qsmmmk.m] ->>>>> /build/octave-queueing-1.2.6/inst/qsmmmk.m -***** test - lambda = mu = m = 1; - k = 10; - [U R Q X p0] = qsmmmk(lambda,mu,m,k); - assert( Q, k/2, 1e-7 ); - assert( U, 1-p0, 1e-7 ); -***** test - lambda = [1 0.8 2 9.2 0.01]; - mu = lambda + 0.17; - k = 12; - [U1 R1 Q1 X1] = qsmm1k(lambda,mu,k); - [U2 R2 Q2 X2] = qsmmmk(lambda,mu,1,k); - assert( U1, U2, 1e-5 ); - assert( R1, R2, 1e-5 ); - assert( Q1, Q2, 1e-5 ); - assert( X1, X2, 1e-5 ); - #assert( [U1 R1 Q1 X1], [U2 R2 Q2 X2], 1e-5 ); -***** test - lambda = 0.9; - mu = 0.75; - k = 10; - [U1 R1 Q1 X1 p01] = qsmmmk(lambda,mu,1,k); - [U2 R2 Q2 X2 p02] = qsmm1k(lambda,mu,k); - assert( [U1 R1 Q1 X1 p01], [U2 R2 Q2 X2 p02], 1e-5 ); -***** test - lambda = 0.8; - mu = 0.85; - m = 3; - k = 5; - [U1 R1 Q1 X1 p0] = qsmmmk( lambda, mu, m, k ); - birth = lambda*ones(1,k); - death = [ mu*linspace(1,m,m) mu*m*ones(1,k-m) ]; - q = ctmc(ctmcbd( birth, death )); - U2 = dot( q, min( 0:k, m )/m ); - assert( U1, U2, 1e-4 ); - Q2 = dot( [0:k], q ); - assert( Q1, Q2, 1e-4 ); - assert( p0, q(1), 1e-4 ); -***** test - # This test comes from an example I found on the web - lambda = 40; - mu = 30; - m = 3; - k = 7; - [U R Q X p0] = qsmmmk( lambda, mu, m, k ); - assert( p0, 0.255037, 1e-6 ); - assert( R, 0.036517, 1e-6 ); -***** test - # This test comes from an example I found on the web - lambda = 50; - mu = 10; - m = 4; - k = 6; - [U R Q X p0 pk] = qsmmmk( lambda, mu, m, k ); - assert( pk, 0.293543, 1e-6 ); -***** test - # This test comes from an example I found on the web - lambda = 3; - mu = 2; - m = 2; - k = 5; - [U R Q X p0 pk] = qsmmmk( lambda, mu, m, k ); - assert( p0, 0.179334, 1e-6 ); - assert( pk, 0.085113, 1e-6 ); - assert( Q, 2.00595, 1e-5 ); - assert( R-1/mu, 0.230857, 1e-6 ); # waiting time in the queue -7 tests, 7 passed, 0 known failure, 0 skipped -[inst/dtmcisir.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmcisir.m -***** test - P = [0 .5 0; 0 0 0]; - fail( "dtmcisir(P)" ); -***** test - P = [0 1 0; 0 .5 .5; 0 1 0]; - [r s] = dtmcisir(P); - assert( r == 0 ); - assert( max(s), 2 ); - assert( min(s), 1 ); -***** test - P = [.5 .5 0; .2 .3 .5; 0 .2 .8]; - [r s] = dtmcisir(P); - assert( r == 1 ); - assert( max(s), 1 ); - assert( min(s), 1 ); -3 tests, 3 passed, 0 known failure, 0 skipped [inst/ctmcchkQ.m] >>>>> /build/octave-queueing-1.2.6/inst/ctmcchkQ.m ***** test @@ -2738,175 +2689,109 @@ assert( result, 0 ); assert( index(err, "infinitesimal") > 0 ); 5 tests, 5 passed, 0 known failure, 0 skipped -[inst/qncmvisits.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncmvisits.m +[inst/dtmc_exps.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmc_exps.m ***** test - - ## Closed, multiclass network - - C = 2; K = 3; - P = zeros(C,K,C,K); - P(1,1,1,2) = 1; - P(1,2,1,1) = 1; - P(2,1,2,3) = 1; - P(2,3,2,1) = 1; - V = qncmvisits(P); - for c=1:C - for k=1:K - assert(V(c,k), sum(sum(V .* P(:,:,c,k))), 1e-5); - endfor - endfor + P = dtmc_bd([1 1 1 1], [0 0 0 0]); + L = dtmc_exps(P,[1 0 0 0 0]); + t = dtmc_mtta(P,[1 0 0 0 0]); + assert( L, [1 1 1 1 0] ); + assert( sum(L), t ); +warning: dtmc_bd is deprecated. Please use dtmcbd instead +warning: dtmc_exps is deprecated. Please use dtmcexps instead +warning: dtmc_mtta is deprecated. Please use dtmcmtta instead ***** test - - ## Test multiclass network. Example from Schwetman (figure 7, page 9 of - ## http://docs.lib.purdue.edu/cstech/259/ - ## "Testing network-of-queues software, technical report CSD-TR 330, - ## Purdue University). - - C = 2; K = 4; - P = zeros(C,K,C,K); - # class 1 routing - P(1,1,1,1) = .05; - P(1,1,1,2) = .45; - P(1,1,1,3) = .5; - P(1,2,1,1) = 1; - P(1,3,1,1) = 1; - # class 2 routing - P(2,1,2,1) = .01; - P(2,1,2,3) = .5; - P(2,1,2,4) = .49; - P(2,3,2,1) = 1; - P(2,4,2,1) = 1; - V = qncmvisits(P); - for c=1:C - for i=1:K - assert(V(c,i), sum(sum(V .* P(:,:,c,i))), 1e-5); - endfor - endfor + P = dtmc_bd(linspace(0.1,0.4,5),linspace(0.4,0.1,5)); + p0 = [1 0 0 0 0 0]; + L = dtmc_exps(P,0,p0); + assert( L, p0 ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qnammm.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnammm.m ***** test - - ## Network with class switching. - ## This is example in figure 9 of - ## Schwetman, "Implementing the Mean Value Analysis - ## Algorithm fort the solution of Queueing Network Models", Technical - ## Report CSD-TR-355, Department of Computer Science, Purdue Univrsity, - ## Feb 15, 1982, http://docs.lib.purdue.edu/cstech/286/ - - C = 2; K = 3; - S = [.01 .07 .10; ... - .05 0.7 .10 ]; - P = zeros(C,K,C,K); - P(1,1,1,2) = .7; - P(1,1,1,3) = .2; - P(1,1,2,1) = .1; - P(2,1,2,2) = .3; - P(2,1,2,3) = .5; - P(2,1,1,1) = .2; - P(1,2,1,1) = P(1,3,1,1) = 1; - P(2,2,2,1) = P(2,3,2,1) = 1; - N = [3 0]; - V = qncmvisits(P); - VV = [10 7 2; 5 1.5 2.5]; # result given in Schwetman; our function computes something different, but that's ok since visit counts are actually ratios - assert( V ./ repmat(V(:,1),1,K), VV ./ repmat(VV(:,1),1,K), 1e-5 ); + [U R Q X] = qnammm( 73,[10,15,20,20,25] ); + assert( U, 0.81, 1e-2 ); + assert( Q, 6.5278, 1e-4 ); +warning: qnammm is deprecated. Please use qsammm instead +1 test, 1 passed, 0 known failure, 0 skipped +[inst/erlangb.m] +>>>>> /build/octave-queueing-1.2.6/inst/erlangb.m ***** test - - ## two disjoint classes: must produce two disjoing chains - - C = 2; K = 3; - P = zeros(C,K,C,K); - P(1,1,1,2) = 1; - P(1,2,1,1) = 1; - P(2,1,2,3) = 1; - P(2,3,2,1) = 1; - [nc r] = qncmvisits(P); - assert( r(1) != r(2) ); + fail("erlangb(1, -1)", "positive"); + fail("erlangb(-1, 1)", "positive"); + fail("erlangb(1, 0)", "positive"); + fail("erlangb(0, 1)", "positive"); + fail("erlangb('foo',1)", "positive"); + fail("erlangb(1,'bar')", "positive"); + fail("erlangb([1 1],[1 1 1])","common size"); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/qncmbsb.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncmbsb.m ***** test - - ## two classes, one chain - - C = 2; K = 3; - P = zeros(C,K,C,K); - P(1,1,1,2) = .5; - P(1,2,2,1) = 1; - P(2,1,2,3) = .5; - P(2,3,1,1) = 1; - [nc r] = qncmvisits(P); - assert( r(1) == r(2) ); + fail("qncmbsb([],[])", "nonempty"); + fail("qncmbsb([1 0], [1 2 3])", "2 rows"); + fail("qncmbsb([1 0], [1 2 3; 4 5 -1])", "nonnegative"); + fail("qncmbsb([1 2], [1 2 3; 4 5 6], [1 2 3])", "2 x 3"); + fail("qncmbsb([1 2], [1 2 3; 4 5 6], [1 2 3; 4 5 -1])", "nonnegative"); + fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1])", "3 elements"); + fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 2])", "not supported"); + fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 2 3])", "2 elements"); + fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 -2])", "nonnegative"); + fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 0])", "only supports"); ***** test - - ## a "Moebius strip". Note that this configuration is invalid, and - ## therefore our algorithm must raise an error. This is because this - ## network has two chains, but both chains contain both classes - - C = 2; K = 2; - P = zeros(C,K,C,K); - P(1,1,2,2) = 1; - P(2,2,1,1) = 1; - P(2,1,1,2) = 1; - P(1,2,2,1) = 1; - fail( "qncmvisits(P)", "different"); + [Xl Xu Rl Ru] = qncmbsb([0 0], [1 2 3; 1 2 3]); + assert( all(Xl(:) == 0) ); + assert( all(Xu(:) == 0) ); + assert( all(Rl(:) == 0) ); + assert( all(Ru(:) == 0) ); +***** demo + S = [10 7 5 4; ... + 5 2 4 6]; + NN=20; + Xl = Xu = Rl = Ru = Xmva = Rmva = zeros(NN,2); + for n=1:NN + N=[n,10]; + [a b c d] = qncmbsb(N,S); + Xl(n,:) = a; Xu(n,:) = b; Rl(n,:) = c; Ru(n,:) = d; + [U R Q X] = qncmmva(N,S,ones(size(S))); + Xmva(n,:) = X(:,1)'; Rmva(n,:) = sum(R,2)'; + endfor + subplot(2,2,1); + plot(1:NN,Xl(:,1), 1:NN,Xu(:,1), 1:NN,Xmva(:,1),";MVA;", "linewidth", 2); + title("Class 1 throughput"); legend("boxoff"); + subplot(2,2,2); + plot(1:NN,Xl(:,2), 1:NN,Xu(:,2), 1:NN,Xmva(:,2),";MVA;", "linewidth", 2); + title("Class 2 throughput"); legend("boxoff"); + subplot(2,2,3); + plot(1:NN,Rl(:,1), 1:NN,Ru(:,1), 1:NN,Rmva(:,1),";MVA;", "linewidth", 2); + title("Class 1 response time"); legend("location", "northwest"); legend("boxoff"); + subplot(2,2,4); + plot(1:NN,Rl(:,2), 1:NN,Ru(:,2), 1:NN,Rmva(:,2),";MVA;", "linewidth", 2); + title("Class 2 response time"); legend("location", "northwest"); legend("boxoff"); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/dtmcchkP.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmcchkP.m ***** test - - ## Network with two classes representing independent chains. - ## This is example in figure 8 of - ## Schwetman, "Implementing the Mean Value Analysis - ## Algorithm fort the solution of Queueing Network Models", Technical - ## Report CSD-TR-355, Department of Computer Science, Purdue Univrsity, - ## Feb 15, 1982, http://docs.lib.purdue.edu/cstech/286/ - - C = 2; K = 2; - P = zeros(C,K,C,K); - P(1,1,1,3) = P(1,3,1,1) = 1; - P(2,2,2,3) = P(2,3,2,2) = 1; - V = qncmvisits(P,[1,2]); - assert( V, [1 0 1; 0 1 1], 1e-5 ); + [r err] = dtmcchkP( [1 1 1; 1 1 1] ); + assert( r, 0 ); + assert( index(err, "square") > 0 ); ***** test - C = 2; - K = 3; - P = zeros(C,K,C,K); - P(1,1,1,2) = 1; - P(1,2,1,3) = 1; - P(1,3,2,2) = 1; - P(2,2,1,1) = 1; - [V ch] = qncmvisits(P); - assert( ch, [1 1] ); + [r err] = dtmcchkP( [1 0 0; 0 0.5 0; 0 0 0] ); + assert( r, 0 ); + assert( index(err, "stochastic") > 0 ); ***** test - C = 2; - K = 3; - P = zeros(C,K,C,K); - P(1,1,1,2) = 1; - P(1,2,1,3) = 1; - P(1,3,2,2) = 1; - P(2,2,2,1) = 1; - P(2,1,1,2) = 1; - [V ch] = qncmvisits(P); - assert( ch, [1 1] ); -9 tests, 9 passed, 0 known failure, 0 skipped -[inst/qnclosedmultimvaapprox.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnclosedmultimvaapprox.m + P = [0 1; 1 0]; + assert( dtmcchkP(P), 2 ); ***** test - S = [ 1 3 3; 2 4 3]; - V = [ 1 1 3; 1 1 3]; - N = [ 1 1 ]; - m = [1 ; 1 ]; - Z = [2 2 2]; - fail( "qnclosedmultimvaapprox(N,S,V,m,Z)", "m must be" ); - m = [1 ; 1 ; 1]; - fail( "qnclosedmultimvaapprox(N,S,V,m,Z)", "Z must be" ); -warning: qqnclosedmultimvaapprox is deprecated. Please use qncmmvaap instead + P = dtmcbd( linspace(0.1,0.4,10), linspace(0.4,0.1,10) ); + assert( dtmcchkP(P), rows(P) ); ***** test - S = [ 1 3; 2 4]; - V = [ 1 1; 1 1]; - N = [ 1 1 ]; - m = ones(1,2); - [U R Q X] = qnclosedmultimvaapprox(N,S,V,m); - assert( Q, [ .192 .808; .248 .752 ], 1e-3 ); - Xc = ( X(:,1)./V(:,1) )'; - assert( Xc, [ .154 .104 ], 1e-3 ); - # Compute the (overall) class-c system response time - R_c = N ./ Xc; - assert( R_c, [ 6.508 9.614 ], 5e-3 ); -2 tests, 2 passed, 0 known failure, 0 skipped + N = 1000; + P = reshape( 1:N^2, N, N ); + P(1:N+1:end) = 0; + P = P ./ repmat(sum(P,2),1,N); + assert( dtmcchkP(P), N ); +5 tests, 5 passed, 0 known failure, 0 skipped [inst/qsmm1k.m] >>>>> /build/octave-queueing-1.2.6/inst/qsmm1k.m ***** test @@ -2930,256 +2815,92 @@ assert( Q1, Q2, 1e-4 ); warning: ctmc_bd is deprecated. Please use ctmcbd instead 2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qncmmvaap.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncmmvaap.m -***** test - S = [ 1 3 3; 2 4 3]; - V = [ 1 1 3; 1 1 3]; - N = [ 1 1 ]; - m = [1 ; 1 ]; - Z = [2 2 2]; - fail( "qncmmvaap(N,S,V,m,Z)", "m must be" ); - m = [1 ; 1 ; 1]; - fail( "qncmmvaap(N,S,V,m,Z)", "Z must be" ); -***** test - S = [ 1 3; 2 4]; - V = [ 1 1; 1 1]; - N = [ 1 1 ]; - m = ones(1,2); - [U R Q X] = qncmmvaap(N,S,V,m); - assert( Q, [ .192 .808; .248 .752 ], 1e-3 ); - Xc = ( X(:,1)./V(:,1) )'; - assert( Xc, [ .154 .104 ], 1e-3 ); - # Compute the (overall) class-c system response time - R_c = N ./ Xc; - assert( R_c, [ 6.508 9.614 ], 5e-3 ); -***** demo - S = [ 1, 1, 1, 1; 2, 1, 3, 1; 4, 2, 3, 3 ]; - V = ones(3,4); - N = [10 5 1]; - m = [1 0 1 1]; - [U R Q X] = qncmmvaap(N,S,V,m); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qsmm1.m] ->>>>> /build/octave-queueing-1.2.6/inst/qsmm1.m -***** test - fail( "qsmm1(10,5)", "not ergodic" ); - fail( "qsmm1([2 2], [1 1 1])", "incompatible size"); +[inst/qncscmva.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncscmva.m ***** test - [U R Q X P0] = qsmm1(0, 1); - assert( U, 0 ); - assert( R, 1 ); - assert( Q, 0 ); - assert( X, 0 ); - assert( P0, 1 ); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qnosvisits.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnosvisits.m + N=5; + S = [1 0.3 0.8 0.9]; + V = [1 1 1 1]; + [U1 R1 Q1 X1] = qncscmva( N, S(1:3), repmat(S(4),1,N), V ); + [U2 R2 Q2 X2] = qncsmva(N, S, V); + assert( X1, X2, 1e-5 ); + assert( U1, U2, 1e-5 ); + assert( R1, R2, 1e-5 ); + assert( Q1, Q2, 1e-5 ); ***** test - fail( "qnosvisits([0 .5; .5 0],[0 -1])", "contains negative" ); - fail( "qnosvisits([1 1 1; 1 1 1], [1 1])", "square" ); + N=5; + S = [1 1 1 1 1; ... + 1 1 1 1 1; ... + 1 1 1 1 1; ... + 1 1/2 1/3 1/4 1/5]; + V = [1 1 1 1]; + [U1 R1 Q1 X1] = qncscmva( N, S(1:3,1), S(4,:), V ); + [U2 R2 Q2 X2] = qncsmvald(N, S, V); + assert( U1, U2, 1e-5 ); + assert( R1, R2, 1e-5 ); + assert( Q1, Q2, 1e-5 ); + assert( X1, X2, 1e-5 ); ***** test - - ## Open, single class network - - P = [0 0.2 0.5; 1 0 0; 1 0 0]; - lambda = [ 0.1 0.3 0.2 ]; - V = qnosvisits(P,lambda); - assert( V*P+lambda/sum(lambda),V,1e-5 ); -***** demo - p = 0.3; - lambda = 1.2 - P = [0 0.3 0.5; ... - 1 0 0 ; ... - 1 0 0 ]; - V = qnosvisits(P,[1.2 0 0]) + N=5; + S = [1 1 1 1 1; ... + 1 1 1 1 1; ... + 1 1 1 1 1; ... + 1 1/2 1/3 1/4 1/5]; + V = [1 2 1 1]; + Z = 3; + [U1 R1 Q1 X1] = qncscmva( N, S(1:3,1), S(4,:), V, Z ); + [U2 R2 Q2 X2] = qncsmvald(N, S, V, Z); + assert( U1, U2, 1e-5 ); + assert( R1, R2, 1e-5 ); + assert( Q1, Q2, 1e-5 ); + assert( X1, X2, 1e-5 ); ***** demo - P = [ 0 0.4 0.6 0; ... - 0.2 0 0.2 0.6; ... - 0 0 0 1; ... - 0 0 0 0 ]; - lambda = [0.1 0 0 0.3]; - V = qnosvisits(P,lambda); - S = [2 1 2 1.8]; - m = [3 1 1 2]; - [U R Q X] = qnos( sum(lambda), S, V, m ) -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/ctmc_bd.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmc_bd.m + maxN = 90; # Max population size + Rmva = Rconv = Rcmva = zeros(1,maxN); # Results + S = 4; Z = 10; m = 8; + old = warning("query","qn:numerical-instability"); + warning("off","qn:numerical-instability"); + for N=1:maxN + [U R] = qncsmva(N,S,1,m,Z); # Use MVA + Rmva(N) = R(1); + [U R] = qncsconv(N,[S Z],[1 1],[m -1]); # Use Convolution + Rconv(N) = R(1); + if ( N > m ) + Scmva = S ./ min(1:N,m); + else + Scmva = S ./ (1:N); + endif + [U R] = qncscmva(N,[],Scmva,1,Z); # Use CMVA + Rcmva(N) = R(1); + endfor + warning(old.state,"qn:numerical-instability"); + plot(1:maxN, Rmva, ";MVA;", ... + 1:maxN, Rconv, ";Convolution;", ... + 1:maxN, Rcmva, ";CNVA;", "linewidth",2); + xlabel("Population size (N)"); + ylabel("Response Time"); + ax=axis(); ax(3) = 0; ax(4) = 40; axis(ax); + legend("location","northwest"); legend("boxoff"); +3 tests, 3 passed, 0 known failure, 0 skipped +[inst/engset.m] +>>>>> /build/octave-queueing-1.2.6/inst/engset.m +***** test + fail("erlangb(1, -1)", "positive"); + fail("erlangb(-1, 1)", "positive"); + fail("erlangb(1, 0)", "positive"); + fail("erlangb(0, 1)", "positive"); + fail("erlangb('foo',1)", "positive"); + fail("erlangb(1,'bar')", "positive"); + fail("erlangb([1 1],[1 1 1])","common size"); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/ctmcbd.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmcbd.m ***** test birth = [ 1 1 1 ]; death = [ 2 2 2 ]; - Q = ctmc_bd( birth, death ); + Q = ctmcbd( birth, death ); assert( ctmc(Q), [ 8/15 4/15 2/15 1/15 ], 1e-5 ); 1 test, 1 passed, 0 known failure, 0 skipped -[inst/qncsmvald.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncsmvald.m -***** test - N = 0; - S = [1 2; 3 4; 5 6; 7 8]; - V = [1 1 1 4]; - [U R Q X] = qncsmvald(N, S, V); - assert( U, 0*V ); - assert( R, 0*V ); - assert( Q, 0*V ); - assert( X, 0*V ); -***** test - # Exsample 3.42 p. 577 Jain - V = [ 16 10 5 ]; - N = 20; - S = [ 0.125 0.3 0.2 ]; - Sld = repmat( S', 1, N ); - Z = 4; - [U1 R1 Q1 X1] = qncsmvald(N,Sld,V,Z); - [U2 R2 Q2 X2] = qncsmva(N,S,V,ones(1,3),Z); - assert( U1, U2, 1e-3 ); - assert( R1, R2, 1e-3 ); - assert( Q1, Q2, 1e-3 ); - assert( X1, X2, 1e-3 ); -***** test - # Example 8.7 p. 349 Bolch et al. - N = 3; - Sld = 1 ./ [ 2 4 4; ... - 1.667 1.667 1.667; ... - 1.25 1.25 1.25; ... - 1 2 3 ]; - V = [ 1 .5 .5 1 ]; - [U R Q X] = qncsmvald(N,Sld,V); - assert( Q, [0.624 0.473 0.686 1.217], 1e-3 ); - assert( R, [0.512 0.776 1.127 1], 1e-3 ); - assert( all( U<=1) ); -***** test - # Example 8.4 p. 333 Bolch et al. - N = 3; - S = [ .5 .6 .8 1 ]; - m = [2 1 1 N]; - Sld = zeros(3,N); - Sld(1,:) = .5 ./ [1 2 2]; - Sld(2,:) = [.6 .6 .6]; - Sld(3,:) = [.8 .8 .8]; - Sld(4,:) = 1 ./ [1 2 3]; - V = [ 1 .5 .5 1 ]; - [U1 R1 Q1 X1] = qncsmvald(N,Sld,V); - [U2 R2 Q2 X2] = qncsmva(N,S,V,m); - ## Note that qncsmvald computes the utilization in a different - ## way as qncsmva; in fact, qncsmva knows that service - ## center i has m(i)>1 servers, but qncsmvald does not. Thus, - ## utilizations for multiple-server nodes cannot be compared - assert( U1([2,3]), U2([2,3]), 1e-3 ); - assert( R1, R2, 1e-3 ); - assert( Q1, Q2, 1e-3 ); - assert( X1, X2, 1e-3 ); -4 tests, 4 passed, 0 known failure, 0 skipped -[inst/dtmcbd.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmcbd.m -***** test - birth = [.5 .5 .3]; - death = [.6 .2 .3]; - fail("dtmcbd(birth,death)","must be"); -***** demo - birth = [ .2 .3 .4 ]; - death = [ .1 .2 .3 ]; - P = dtmcbd( birth, death ); - disp(P) -1 test, 1 passed, 0 known failure, 0 skipped -[inst/ctmc_exps.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmc_exps.m -***** test - Q = [-1 1; 1 -1]; - L = ctmc_exps(Q,10,[1 0]); - L = ctmc_exps(Q,linspace(0,10,100),[1 0]); -warning: ctmc_exps is deprecated. Please use ctmcexps instead -***** test - Q = ctmc_bd( [1 2 3], [3 2 1] ); - p0 = [1 0 0 0]; - t = linspace(0,10,10); - L1 = L2 = zeros(length(t),4); - # compute L using the differential equation formulation - ff = @(x,t) (x(:)'*Q+p0); - fj = @(x,t) (Q); - L1 = lsode( {ff, fj}, zeros(size(p0)), t ); - # compute L using ctmc_exps (integral formulation) - for i=1:length(t) - L2(i,:) = ctmc_exps(Q,t(i),p0); - endfor - assert( L1, L2, 1e-5); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/erlangc.m] ->>>>> /build/octave-queueing-1.2.6/inst/erlangc.m -***** test - fail("erlangc('foo',1)", "positive"); - fail("erlangc(1,'bar')", "positive"); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qncsaba.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncsaba.m -***** test - fail("qncsaba(-1,0)", "N must be"); - fail("qncsaba(1,[])", "nonempty"); - fail("qncsaba(1,[-1 2])", "nonnegative"); - fail("qncsaba(1,[1 2],[1 2 3])", "incompatible size"); - fail("qncsaba(1,[1 2 3],[1 2 -1])", "nonnegative"); - fail("qncsaba(1,[1 2 3],[1 2 3],[1 2])", "incompatible size"); - fail("qncsaba(1,[1 2 3],[1 2 3],[1 2 1])", "not supported"); - fail("qncsaba(1,[1 2 3],[1 2 3],[1 1 1],-1)", "nonnegative"); - fail("qncsaba(1,[1 2 3],[1 2 3],1,[0 0])", "scalar"); -***** test - N = 20; - S = [ 4.6*2 8 ]; - Z = 120; - [X_l X_u R_l R_u] = qncsaba(N, S, ones(size(S)), ones(size(S)), Z); - assert( [X_u R_l], [0.109 64], 1e-3 ); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qnosbsb.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnosbsb.m -***** test - fail( "qnosbsb( 0.1, [] )", "vector" ); - fail( "qnosbsb( 0.1, [0 -1])", "nonnegative" ); - fail( "qnosbsb( 0, [1 2] )", "lambda" ); - fail( "qnosbsb( -1, [1 2])", "lambda" ); -***** test - [Xl Xu Rl Ru] = qnosbsb(0.1,[1 2 3]); - assert( Xl, 0 ); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/ctmc_mtta.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmc_mtta.m -***** test - Q = [0 1 0; 1 0 1; 0 1 0 ]; Q -= diag( sum(Q,2) ); - fail( "ctmc_mtta(Q,[1 0 0])", "no absorbing"); -warning: ctmc_mtta is deprecated. Please use ctmcmtta instead -***** test - Q = [0 1 0; 1 0 1; 0 0 0; 0 0 0 ]; - fail( "ctmc_mtta(Q,[1 0 0])", "square matrix"); -***** test - Q = [0 1 0; 1 0 1; 0 0 0 ]; - fail( "ctmc_mtta(Q,[1 0 0])", "infinitesimal"); -***** test - Q = [ 0 0.1 0 0; ... - 0.9 0 0.1 0; ... - 0 0.9 0 0.1; ... - 0 0 0 0 ]; - Q -= diag( sum(Q,2) ); - assert( ctmc_mtta( Q,[0 0 0 1] ), 0 ); # state 4 is absorbing -***** test - Q = [-1 1; 0 0]; - assert( ctmc_mtta( Q, [0 1] ), 0 ); # state 2 is absorbing - assert( ctmc_mtta( Q, [1 0] ), 1 ); # the result has been computed by hand -5 tests, 5 passed, 0 known failure, 0 skipped -[inst/dtmc_exps.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmc_exps.m -***** test - P = dtmc_bd([1 1 1 1], [0 0 0 0]); - L = dtmc_exps(P,[1 0 0 0 0]); - t = dtmc_mtta(P,[1 0 0 0 0]); - assert( L, [1 1 1 1 0] ); - assert( sum(L), t ); -warning: dtmc_exps is deprecated. Please use dtmcexps instead -warning: dtmc_mtta is deprecated. Please use dtmcmtta instead -***** test - P = dtmc_bd(linspace(0.1,0.4,5),linspace(0.4,0.1,5)); - p0 = [1 0 0 0 0 0]; - L = dtmc_exps(P,0,p0); - assert( L, p0 ); -2 tests, 2 passed, 0 known failure, 0 skipped [inst/qncsconv.m] >>>>> /build/octave-queueing-1.2.6/inst/qncsconv.m ***** test @@ -3234,11 +2955,184 @@ printf("Prob( n(%d) = %d )=%f\n", k, n(k), p(k) ); endfor 3 tests, 3 passed, 0 known failure, 0 skipped -[inst/qsmminf.m] ->>>>> /build/octave-queueing-1.2.6/inst/qsmminf.m +[inst/qnmarkov.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnmarkov.m ***** test - fail( "qsmminf( [1 2], [1 2 3] )", "incompatible size"); - fail( "qsmminf( [-1 -1], [1 1] )", ">0" ); + S = [5 2.5]; + P = [0 1; 1 0]; + C = [3 3]; + m = [1 1]; + [U R Q X] = qnmarkov( 3, S, C, P, m ); + assert( U, [0.9333 0.4667], 1e-4 ); + assert( X, [0.1867 0.1867], 1e-4 ); + assert( R, [12.1429 3.9286], 1e-4 ); +***** test + S = [1/0.8 1/0.6 1/0.4]; + P = [0.6 0.3 0.1; 0.2 0.3 0.5; 0.4 0.1 0.5]; + C = [3 3 3]; + [U R Q X] = qnmarkov( 3, S, C, P ); + assert( U, [0.543 0.386 0.797], 1e-3 ); + assert( Q, [0.873 0.541 1.585], 1e-3 ); +***** xtest + S = [2 0.9]; + C = [7 5]; + P = [0 1; 1 0]; + [U R Q X] = qnmarkov( 10, S, C, P ); + assert( Q, [6.73 3.27], 1e-3 ); +!!!!! known failure +ASSERT errors for: assert (Q,[6.73, 3.27],1e-3) + + Location | Observed | Expected | Reason + (1) 6.4826 6.73 Abs err 0.2474 exceeds tol 0.001 by 0.2 + (2) 3.5174 3.27 Abs err 0.2474 exceeds tol 0.001 by 0.2 +***** test + S = [1/0.8 1/0.6 1/0.4]; + P = [(1-0.667-0.2) 0.667 0.2; 1 0 0; 1 0 0]; + m = [2 3 1]; + C = [3 3 3]; + [U R Q X] = qnmarkov( 3, S, C, P, m ); + assert( U, [0.590 0.350 0.473], 1e-3 ); + assert( Q(1:2), [1.290 1.050], 1e-3 ); +***** test + p = 0.5; # transition prob. from S2 to S1 + mu = [1 2]; # Service rates + C = [2 1]; # Capacities + lambda = [0.5 0]; # arrival rate at service center 1 + + PP = [ 0 1; p 0 ]; + [U R Q X] = qnmarkov( lambda, 1./mu, C, PP ); + ## Now we generate explicitly the infinitesimal generator matrix + ## of the underlying MC. + ## 00 01 10 11 20 21 + QQ = [ 0 0 lambda(1) 0 0 0; ... ## 00 + mu(2)*(1-p) 0 mu(2)*p lambda(1) 0 0; ... ## 01 + 0 mu(1) 0 0 lambda(1) 0; ... ## 10 + 0 0 mu(2)*(1-p) 0 mu(2)*p lambda(1); ... ## 11 + 0 0 0 mu(1) 0 0; ... ## 20 + 0 0 0 0 mu(2)*(1-p) 0 ]; ## 21 + ## Complete matrix + sum_el = sum(QQ,2); + QQ -= diag(sum_el); + q = ctmc(QQ); + ## Compare results + assert( U(1), 1-sum(q([1, 2])), 1e-5 ); + assert( U(2), 1-sum(q([1,3,5])), 1e-5 ); +***** test + P = [0 0.5 0.5; 1 0 0; 1 0 0]; + C = [6 6 6]; + S = [1 0.8 1.8]; + N = 6; + [U1 R1 Q1 X1] = qnclosed( N, S, qncsvisits(P) ); + [U2 R2 Q2 X2] = qnmarkov( N, S, C, P ); + assert( U1, U2, 1e-6 ); + assert( R1, R2, 1e-6 ); + assert( Q1, Q2, 1e-6 ); + assert( X1, X2, 1e-6 ); +6 tests, 5 passed, 1 known failure, 0 skipped +[inst/qncspb.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncspb.m +***** test + fail( "qncspb( 1, [] )", "vector" ); + fail( "qncspb( 1, [0 -1])", "nonnegative" ); + fail( "qncspb( 0, [1 2] )", "positive" ); + fail( "qncspb( -1, [1 2])", "nonnegative" ); + fail( "qncspb( 1, [1 2], [1,1], [2, 2])", "single server" ); + fail( "qncspb( 1, [1 2], [1,1], [1, 1], -1)", "nonnegative" ); +***** # shared test function +***** function test_pb( D, expected, Z=0 ) + for i=1:rows(expected) + N = expected(i,1); + [X_lower X_upper] = qncspb(N,D,ones(size(D)),ones(size(D)),Z); + X_exp_lower = expected(i,2); + X_exp_upper = expected(i,3); + assert( [N X_lower X_upper], [N X_exp_lower X_exp_upper], 1e-4 ) + endfor +***** test + # table IV + D = [ 0.1 0.1 0.09 0.08 ]; + # N X_lower X_upper + expected = [ 2 4.3174 4.3174; ... + 5 6.6600 6.7297; ... + 10 8.0219 8.2700; ... + 20 8.8672 9.3387; ... + 80 9.6736 10.000 ]; + test_pb(D, expected); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/dtmcfpt.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmcfpt.m +***** test + P = [1 1 1; 1 1 1]; + fail( "dtmcfpt(P)" ); +***** test + P = dtmcbd([1 1 1], [0 0 0] ); + fail( "dtmcfpt(P)", "absorbing" ); +***** test + P = [ 0.0 0.9 0.1; ... + 0.1 0.0 0.9; ... + 0.9 0.1 0.0 ]; + p = dtmc(P); + M = dtmcfpt(P); + assert( diag(M)', 1./p, 1e-8 ); +***** test + P = [ 0 1 0 0 0; ... + .25 .0 .75 0 0; ... + 0 .5 0 .5 0; ... + 0 0 .75 0 .25; ... + 0 0 0 1 0 ]; + M = dtmcfpt(P); + assert( M, [16 1 2.6667 6.3333 21.3333; ... + 15 4 1.6667 5.3333 20.3333; ... + 18.6667 3.6667 2.6667 3.6667 18.6667; ... + 20.3333 5.3333 1.6667 4 15; ... + 21.3333 6.3333 2.6667 1 16 ], 1e-4 ); +***** test + sz = 10; + P = reshape( 1:sz^2, sz, sz ); + normP = repmat(sum(P,2),1,columns(P)); + P = P./normP; + M = dtmcfpt(P); + for i=1:rows(P) + for j=1:columns(P) + assert( M(i,j), 1 + dot(P(i,:), M(:,j)) - P(i,j)*M(j,j), 1e-8); + endfor + endfor +***** test + P = zeros(9,9); + P(1,[2 4]) = .5; + P(2,[1 5 3]) = 1/3; + P(3,[2 6]) = .5; + P(4,[1 5 7]) = 1/3; + P(5,[2 4 6 8]) = 1/4; + P(6,[3 5 9]) = 1/3; + P(7,[4 8]) = .5; + P(8,[7 5 9]) = 1/3; + P(9,[6 8]) = .5; + M = dtmcfpt(P); + assert( M(1:9 != 5,5)', [6 5 6 5 5 6 5 6], 100*eps ); +6 tests, 6 passed, 0 known failure, 0 skipped +[inst/dtmctaexps.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmctaexps.m +***** test + P = dtmcbd([1 1 1 1], [0 0 0 0]); + p0 = [1 0 0 0 0]; + L = dtmctaexps(P,p0); + assert( L, [.25 .25 .25 .25 0], 10*eps ); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/ctmcfpt.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmcfpt.m +***** demo + Q = [ -1.0 0.9 0.1; ... + 0.1 -1.0 0.9; ... + 0.9 0.1 -1.0 ]; + M = ctmcfpt(Q) + m = ctmcfpt(Q,1,3) +***** test + N = 10; + Q = reshape(1:N^2,N,N); + Q(1:N+1:end) = 0; + Q -= diag(sum(Q,2)); + M = ctmcfpt(Q); + assert( all(diag(M) < 10*eps) ); 1 test, 1 passed, 0 known failure, 0 skipped [inst/ctmcexps.m] >>>>> /build/octave-queueing-1.2.6/inst/ctmcexps.m @@ -3289,58 +3183,6 @@ L = ctmcexps(Q,p0); disp(L); 2 tests, 2 passed, 0 known failure, 0 skipped -[inst/dtmcchkP.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmcchkP.m -***** test - [r err] = dtmcchkP( [1 1 1; 1 1 1] ); - assert( r, 0 ); - assert( index(err, "square") > 0 ); -***** test - [r err] = dtmcchkP( [1 0 0; 0 0.5 0; 0 0 0] ); - assert( r, 0 ); - assert( index(err, "stochastic") > 0 ); -***** test - P = [0 1; 1 0]; - assert( dtmcchkP(P), 2 ); -***** test - P = dtmcbd( linspace(0.1,0.4,10), linspace(0.4,0.1,10) ); - assert( dtmcchkP(P), rows(P) ); -***** test - N = 1000; - P = reshape( 1:N^2, N, N ); - P(1:N+1:end) = 0; - P = P ./ repmat(sum(P,2),1,N); - assert( dtmcchkP(P), N ); -5 tests, 5 passed, 0 known failure, 0 skipped -[inst/qncspb.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncspb.m -***** test - fail( "qncspb( 1, [] )", "vector" ); - fail( "qncspb( 1, [0 -1])", "nonnegative" ); - fail( "qncspb( 0, [1 2] )", "positive" ); - fail( "qncspb( -1, [1 2])", "nonnegative" ); - fail( "qncspb( 1, [1 2], [1,1], [2, 2])", "single server" ); - fail( "qncspb( 1, [1 2], [1,1], [1, 1], -1)", "nonnegative" ); -***** # shared test function -***** function test_pb( D, expected, Z=0 ) - for i=1:rows(expected) - N = expected(i,1); - [X_lower X_upper] = qncspb(N,D,ones(size(D)),ones(size(D)),Z); - X_exp_lower = expected(i,2); - X_exp_upper = expected(i,3); - assert( [N X_lower X_upper], [N X_exp_lower X_exp_upper], 1e-4 ) - endfor -***** test - # table IV - D = [ 0.1 0.1 0.09 0.08 ]; - # N X_lower X_upper - expected = [ 2 4.3174 4.3174; ... - 5 6.6600 6.7297; ... - 10 8.0219 8.2700; ... - 20 8.8672 9.3387; ... - 80 9.6736 10.000 ]; - test_pb(D, expected); -2 tests, 2 passed, 0 known failure, 0 skipped [inst/qnos.m] >>>>> /build/octave-queueing-1.2.6/inst/qnos.m ***** test @@ -3421,757 +3263,24 @@ assert( R, [0.2 0.043 0.15 0.0625], 1e-3 ); assert( Q, [4, 0.429 1.5 0.25], 1e-3 ); 6 tests, 6 passed, 0 known failure, 0 skipped -[inst/qncscmva.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncscmva.m +[inst/dtmcisir.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmcisir.m ***** test - N=5; - S = [1 0.3 0.8 0.9]; - V = [1 1 1 1]; - [U1 R1 Q1 X1] = qncscmva( N, S(1:3), repmat(S(4),1,N), V ); - [U2 R2 Q2 X2] = qncsmva(N, S, V); - assert( X1, X2, 1e-5 ); - assert( U1, U2, 1e-5 ); - assert( R1, R2, 1e-5 ); - assert( Q1, Q2, 1e-5 ); + P = [0 .5 0; 0 0 0]; + fail( "dtmcisir(P)" ); ***** test - N=5; - S = [1 1 1 1 1; ... - 1 1 1 1 1; ... - 1 1 1 1 1; ... - 1 1/2 1/3 1/4 1/5]; - V = [1 1 1 1]; - [U1 R1 Q1 X1] = qncscmva( N, S(1:3,1), S(4,:), V ); - [U2 R2 Q2 X2] = qncsmvald(N, S, V); - assert( U1, U2, 1e-5 ); - assert( R1, R2, 1e-5 ); - assert( Q1, Q2, 1e-5 ); - assert( X1, X2, 1e-5 ); + P = [0 1 0; 0 .5 .5; 0 1 0]; + [r s] = dtmcisir(P); + assert( r == 0 ); + assert( max(s), 2 ); + assert( min(s), 1 ); ***** test - N=5; - S = [1 1 1 1 1; ... - 1 1 1 1 1; ... - 1 1 1 1 1; ... - 1 1/2 1/3 1/4 1/5]; - V = [1 2 1 1]; - Z = 3; - [U1 R1 Q1 X1] = qncscmva( N, S(1:3,1), S(4,:), V, Z ); - [U2 R2 Q2 X2] = qncsmvald(N, S, V, Z); - assert( U1, U2, 1e-5 ); - assert( R1, R2, 1e-5 ); - assert( Q1, Q2, 1e-5 ); - assert( X1, X2, 1e-5 ); -***** demo - maxN = 90; # Max population size - Rmva = Rconv = Rcmva = zeros(1,maxN); # Results - S = 4; Z = 10; m = 8; - old = warning("query","qn:numerical-instability"); - warning("off","qn:numerical-instability"); - for N=1:maxN - [U R] = qncsmva(N,S,1,m,Z); # Use MVA - Rmva(N) = R(1); - [U R] = qncsconv(N,[S Z],[1 1],[m -1]); # Use Convolution - Rconv(N) = R(1); - if ( N > m ) - Scmva = S ./ min(1:N,m); - else - Scmva = S ./ (1:N); - endif - [U R] = qncscmva(N,[],Scmva,1,Z); # Use CMVA - Rcmva(N) = R(1); - endfor - warning(old.state,"qn:numerical-instability"); - plot(1:maxN, Rmva, ";MVA;", ... - 1:maxN, Rconv, ";Convolution;", ... - 1:maxN, Rcmva, ";CNVA;", "linewidth",2); - xlabel("Population size (N)"); - ylabel("Response Time"); - ax=axis(); ax(3) = 0; ax(4) = 40; axis(ax); - legend("location","northwest"); legend("boxoff"); + P = [.5 .5 0; .2 .3 .5; 0 .2 .8]; + [r s] = dtmcisir(P); + assert( r == 1 ); + assert( max(s), 1 ); + assert( min(s), 1 ); 3 tests, 3 passed, 0 known failure, 0 skipped -[inst/qnosaba.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnosaba.m -***** test - fail( "qnosaba( 0.1, [] )", "vector" ); - fail( "qnosaba( 0.1, [0 -1])", "nonnegative" ); - fail( "qnosaba( 0, [1 2] )", "lambda" ); - fail( "qnosaba( -1, [1 2])", "lambda" ); - fail( "qnosaba( 1, [1 2 3], [1 2] )", "incompatible size"); - fail( "qnosaba( 1, [1 2 3], [-1 2 3] )", "nonnegative"); -***** test - [Xl Xu Rl Ru] = qnosaba( 1, [1 1] ); - assert( Xl, 0 ); - assert( Ru, +inf ); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qnmvablo.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnmvablo.m -***** test - fail( "qnmvablo( 10, [1 1], [4 5], [0 1; 1 0] )", "capacity"); - fail( "qnmvablo( 6, [1 1], [4 5], [0 1; 1 1] )", "stochastic"); - fail( "qnmvablo( 5, [1 1 1], [1 1], [0 1; 1 1] )", "3 elements"); -warning: qnmvablo is deprecated. Please use qncsmvablo instead -***** test - # This is the example on section v) p. 422 of the reference paper - M = [12 10 14]; - P = [0 1 0; 0 0 1; 1 0 0]; - S = [1/1 1/2 1/3]; - K = 27; - [U R Q X]=qnmvablo( K, S, M, P ); - assert( R, [11.80 1.66 14.4], 1e-2 ); -***** test - # This is example 2, i) and ii) p. 424 of the reference paper - M = [4 5 5]; - S = [1.5 2 1]; - P = [0 1 0; 0 0 1; 1 0 0]; - K = 10; - [U R Q X]=qnmvablo( K, S, M, P ); - assert( R, [6.925 8.061 4.185], 1e-3 ); - K = 12; - [U R Q X]=qnmvablo( K, S, M, P ); - assert( R, [7.967 9.019 8.011], 1e-3 ); -***** test - # This is example 3, i) and ii) p. 424 of the reference paper - M = [8 7 6]; - S = [0.2 1.2 1.4]; - P = [ 0 0.5 0.5; 1 0 0; 1 0 0 ]; - K = 10; - [U R Q X] = qnmvablo( K, S, M, P ); - assert( R, [1.674 5.007 7.639], 1e-3 ); - K = 12; - [U R Q X] = qnmvablo( K, S, M, P ); - assert( R, [2.166 5.372 6.567], 1e-3 ); -***** test - # Network which never blocks, central server model - M = [50 50 50]; - S = [1 1/0.8 1/0.4]; - P = [0 0.7 0.3; 1 0 0; 1 0 0]; - K = 40; - [U1 R1 Q1] = qnmvablo( K, S, M, P ); - V = qncsvisits(P); - [U2 R2 Q2] = qnclosedsinglemva( K, S, V ); - assert( U1, U2, 1e-5 ); - assert( R1, R2, 1e-5 ); - assert( Q1, Q2, 1e-5 ); -warning: qnclosedsinglemva is deprecated. Please use qncsmva instead -5 tests, 5 passed, 0 known failure, 0 skipped -[inst/ctmcmtta.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmcmtta.m -***** test - Q = [0 1 0; 1 0 1; 0 1 0 ]; Q -= diag( sum(Q,2) ); - fail( "ctmcmtta(Q,[1 0 0])", "no absorbing"); -***** test - Q = [0 1 0; 1 0 1; 0 0 0; 0 0 0 ]; - fail( "ctmcmtta(Q,[1 0 0])", "square matrix"); -***** test - Q = [0 1 0; 1 0 1; 0 0 0 ]; - fail( "ctmcmtta(Q,[1 0 0])", "infinitesimal"); -***** test - Q = [ 0 0.1 0 0; ... - 0.9 0 0.1 0; ... - 0 0.9 0 0.1; ... - 0 0 0 0 ]; - Q -= diag( sum(Q,2) ); - assert( ctmcmtta( Q,[0 0 0 1] ), 0 ); # state 4 is absorbing -***** test - Q = [-1 1; 0 0]; - assert( ctmcmtta( Q, [0 1] ), 0 ); # state 2 is absorbing - assert( ctmcmtta( Q, [1 0] ), 1 ); # the result has been computed by hand -***** demo - mu = 0.01; - death = [ 3 4 5 ] * mu; - birth = 0*death; - Q = ctmcbd(birth,death); - t = ctmcmtta(Q,[0 0 0 1]) -***** demo - N = 100; - birth = death = ones(1,N-1); birth(1) = death(N-1) = 0; - Q = diag(birth,1)+diag(death,-1); - Q -= diag(sum(Q,2)); - t = zeros(1,N/2); - initial_state = 1:(N/2); - for i=initial_state - p = zeros(1,N); p(i) = 1; - t(i) = ctmcmtta(Q,p); - endfor - plot(initial_state,t,"+"); - xlabel("Initial state"); - ylabel("MTTA"); -5 tests, 5 passed, 0 known failure, 0 skipped -[inst/qncsmvablo.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncsmvablo.m -***** test - fail( "qncsmvablo( 10, [1 1], [4 5], [0 1; 1 0] )", "capacity"); - fail( "qncsmvablo( 6, [1 1], [4 5], [0 1; 1 1] )", "stochastic"); - fail( "qncsmvablo( 5, [1 1 1], [1 1], [0 1; 1 1] )", "3 elements"); -***** test - # This is the example on section v) p. 422 of the reference paper - M = [12 10 14]; - P = [0 1 0; 0 0 1; 1 0 0]; - S = [1/1 1/2 1/3]; - K = 27; - [U R Q X]=qncsmvablo( K, S, M, P ); - assert( R, [11.80 1.66 14.4], 1e-2 ); -***** test - # This is example 2, i) and ii) p. 424 of the reference paper - M = [4 5 5]; - S = [1.5 2 1]; - P = [0 1 0; 0 0 1; 1 0 0]; - K = 10; - [U R Q X]=qncsmvablo( K, S, M, P ); - assert( R, [6.925 8.061 4.185], 1e-3 ); - K = 12; - [U R Q X]=qncsmvablo( K, S, M, P ); - assert( R, [7.967 9.019 8.011], 1e-3 ); -***** test - # This is example 3, i) and ii) p. 424 of the reference paper - M = [8 7 6]; - S = [0.2 1.2 1.4]; - P = [ 0 0.5 0.5; 1 0 0; 1 0 0 ]; - K = 10; - [U R Q X] = qncsmvablo( K, S, M, P ); - assert( R, [1.674 5.007 7.639], 1e-3 ); - K = 12; - [U R Q X] = qncsmvablo( K, S, M, P ); - assert( R, [2.166 5.372 6.567], 1e-3 ); -***** test - # Network which never blocks, central server model - M = [50 50 50]; - S = [1 1/0.8 1/0.4]; - P = [0 0.7 0.3; 1 0 0; 1 0 0]; - K = 40; - [U1 R1 Q1] = qncsmvablo( K, S, M, P ); - V = qncsvisits(P); - [U2 R2 Q2] = qncsmva( K, S, V ); - assert( U1, U2, 1e-5 ); - assert( R1, R2, 1e-5 ); - assert( Q1, Q2, 1e-5 ); -5 tests, 5 passed, 0 known failure, 0 skipped -[inst/dtmctaexps.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmctaexps.m -***** test - P = dtmcbd([1 1 1 1], [0 0 0 0]); - p0 = [1 0 0 0 0]; - L = dtmctaexps(P,p0); - assert( L, [.25 .25 .25 .25 0], 10*eps ); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qncmaba.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncmaba.m -***** test - fail("qncmaba([],[])", "nonempty"); - fail("qncmaba([1 0], [1 2 3])", "2 rows"); - fail("qncmaba([1 0], [1 2 3; 4 5 -1])", "nonnegative"); - fail("qncmaba([1 2], [1 2 3; 4 5 6], [1 2 3])", "2 x 3"); - fail("qncmaba([1 2], [1 2 3; 4 5 6], [1 2 3; 4 5 -1])", "nonnegative"); - fail("qncmaba([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1])", "3 elements"); - fail("qncmaba([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 2])", "not supported"); - fail("qncmaba([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 2 3])", "2 elements"); - fail("qncmaba([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 -2])", "nonnegative"); -***** test - [Xl Xu Rl Ru] = qncmaba([0 0], [1 2 3; 1 2 3]); - assert( all(Xl(:) == 0) ); - assert( all(Xu(:) == 0) ); - assert( all(Rl(:) == 0) ); - assert( all(Ru(:) == 0) ); -***** demo - S = [10 7 5 4; ... - 5 2 4 6]; - NN=20; - Xl = Xu = Rl = Ru = Xmva = Rmva = zeros(NN,2); - for n=1:NN - N=[n,10]; - [a b c d] = qncmaba(N,S); - Xl(n,:) = a; Xu(n,:) = b; Rl(n,:) = c; Ru(n,:) = d; - [U R Q X] = qncmmva(N,S,ones(size(S))); - Xmva(n,:) = X(:,1)'; Rmva(n,:) = sum(R,2)'; - endfor - subplot(2,2,1); - plot(1:NN,Xl(:,1), 1:NN,Xu(:,1), 1:NN,Xmva(:,1), ";MVA;", "linewidth", 2); - title("Class 1 throughput"); legend("boxoff"); - subplot(2,2,2); - plot(1:NN,Xl(:,2), 1:NN,Xu(:,2), 1:NN,Xmva(:,2), ";MVA;", "linewidth", 2); - title("Class 2 throughput"); legend("boxoff"); - subplot(2,2,3); - plot(1:NN,Rl(:,1), 1:NN,Ru(:,1), 1:NN,Rmva(:,1), ";MVA;", "linewidth", 2); - title("Class 1 response time"); legend("location", "northwest"); legend("boxoff"); - subplot(2,2,4); - plot(1:NN,Rl(:,2), 1:NN,Ru(:,2), 1:NN,Rmva(:,2), ";MVA;", "linewidth", 2); - title("Class 2 response time"); legend("location", "northwest"); legend("boxoff"); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qnopenbsb.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnopenbsb.m -***** test - fail( "qnopenbsb( 0.1, [] )", "vector" ); - fail( "qnopenbsb( 0.1, [0 -1])", "nonnegative" ); - fail( "qnopenbsb( 0, [1 2] )", "lambda" ); - fail( "qnopenbsb( -1, [1 2])", "lambda" ); -warning: qnopenbsb is deprecated. Please use qnosbsb instead -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qncsconvld.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncsconvld.m -***** test - K=3; - S = [ 1 1 1; 1 1 1 ]; - V = [ 1 .667 .2 ]; - fail( "qncsconvld(K,S,V)", "size mismatch" ); -***** test - # Example 8.1 p. 318 Bolch et al. - K=3; - S = [ 1/0.8 ./ [1 2 2]; - 1/0.6 ./ [1 2 3]; - 1/0.4 ./ [1 1 1] ]; - V = [ 1 .667 .2 ]; - [U R Q X G] = qncsconvld( K, S, V ); - assert( G, [1 2.861 4.218 4.465], 5e-3 ); - assert( X, [0.945 0.630 0.189], 1e-3 ); - assert( Q, [1.290 1.050 0.660], 1e-3 ); - assert( R, [1.366 1.667 3.496], 1e-3 ); -***** test - # Example 8.3 p. 331 Bolch et al. - # compare results of convolution with those of mva - K = 6; - S = [ 0.02 0.2 0.4 0.6 ]; - V = [ 1 0.4 0.2 0.1 ]; - [U_mva R_mva Q_mva X_mva] = qncsmva(K, S, V); - [U_con R_con Q_con X_con G] = qncsconvld(K, repmat(S',1,K), V ); - assert( U_mva, U_con, 1e-5 ); - assert( R_mva, R_con, 1e-5 ); - assert( Q_mva, Q_con, 1e-5 ); - assert( X_mva, X_con, 1e-5 ); -***** test - # Compare the results of convolution to those of mva - S = [ 0.02 0.2 0.4 0.6 ]; - K = 6; - V = [ 1 0.4 0.2 0.1 ]; - m = [ 1 5 2 1 ]; - [U_mva R_mva Q_mva X_mva] = qncsmva(K, S, V); - [U_con R_con Q_con X_con G] = qncsconvld(K, repmat(S',1,K), V); - assert( U_mva, U_con, 1e-5 ); - assert( R_mva, R_con, 1e-5 ); - assert( Q_mva, Q_con, 1e-5 ); - assert( X_mva, X_con, 1e-5 ); -***** function r = S_function(k,n) - M = [ 1/0.8 ./ [1 2 2]; - 1/0.6 ./ [1 2 3]; - 1/0.4 ./ [1 1 1] ]; - r = M(k,n); -***** test - # Example 8.1 p. 318 Bolch et al. - K=3; - V = [ 1 .667 .2 ]; - [U R Q X G] = qncsconvld( K, @S_function, V ); - assert( G, [1 2.861 4.218 4.465], 5e-3 ); - assert( X, [0.945 0.630 0.189], 1e-3 ); - assert( Q, [1.290 1.050 0.660], 1e-3 ); - assert( R, [1.366 1.667 3.496], 1e-3 ); -5 tests, 5 passed, 0 known failure, 0 skipped -[inst/qnmmmk.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnmmmk.m -***** test - lambda = mu = m = 1; - k = 10; - [U R Q X p0] = qnmmmk(lambda,mu,m,k); - assert( Q, k/2, 1e-7 ); - assert( U, 1-p0, 1e-7 ); -warning: qnmmmk is deprecated. Please use qsmmmk instead -***** test - lambda = [1 0.8 2 9.2 0.01]; - mu = lambda + 0.17; - k = 12; - [U1 R1 Q1 X1] = qnmm1k(lambda,mu,k); - [U2 R2 Q2 X2] = qnmmmk(lambda,mu,1,k); - assert( U1, U2, 1e-5 ); - assert( R1, R2, 1e-5 ); - assert( Q1, Q2, 1e-5 ); - assert( X1, X2, 1e-5 ); - #assert( [U1 R1 Q1 X1], [U2 R2 Q2 X2], 1e-5 ); -warning: qnmm1k is deprecated. Please use qsmm1k instead -***** test - lambda = 0.9; - mu = 0.75; - k = 10; - [U1 R1 Q1 X1 p01] = qnmmmk(lambda,mu,1,k); - [U2 R2 Q2 X2 p02] = qnmm1k(lambda,mu,k); - assert( [U1 R1 Q1 X1 p01], [U2 R2 Q2 X2 p02], 1e-5 ); -***** test - lambda = 0.8; - mu = 0.85; - m = 3; - k = 5; - [U1 R1 Q1 X1 p0] = qnmmmk( lambda, mu, m, k ); - birth = lambda*ones(1,k); - death = [ mu*linspace(1,m,m) mu*m*ones(1,k-m) ]; - q = ctmc(ctmc_bd( birth, death )); - U2 = dot( q, min( 0:k, m )/m ); - assert( U1, U2, 1e-4 ); - Q2 = dot( [0:k], q ); - assert( Q1, Q2, 1e-4 ); - assert( p0, q(1), 1e-4 ); -***** test - # This test comes from an example I found on the web - lambda = 40; - mu = 30; - m = 3; - k = 7; - [U R Q X p0] = qnmmmk( lambda, mu, m, k ); - assert( p0, 0.255037, 1e-6 ); - assert( R, 0.036517, 1e-6 ); -***** test - # This test comes from an example I found on the web - lambda = 50; - mu = 10; - m = 4; - k = 6; - [U R Q X p0 pk] = qnmmmk( lambda, mu, m, k ); - assert( pk, 0.293543, 1e-6 ); -***** test - # This test comes from an example I found on the web - lambda = 3; - mu = 2; - m = 2; - k = 5; - [U R Q X p0 pk] = qnmmmk( lambda, mu, m, k ); - assert( p0, 0.179334, 1e-6 ); - assert( pk, 0.085113, 1e-6 ); - assert( Q, 2.00595, 1e-5 ); - assert( R-1/mu, 0.230857, 1e-6 ); # waiting time in the queue -7 tests, 7 passed, 0 known failure, 0 skipped -[inst/qncmpopmix.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncmpopmix.m -***** test - N = [2 3 4]; - f = qncmpopmix( 1, N ); - assert( f, [1 0 0; 0 1 0; 0 0 1] ); - f = qncmpopmix( 2, N ); - assert( f, [2 0 0; 1 1 0; 0 2 0; 1 0 1; 0 1 1; 0 0 2] ); - f = qncmpopmix( 3, N ); - assert( f, [2 1 0; 1 2 0; 0 3 0; 2 0 1; 1 1 1; 0 2 1; 1 0 2; 0 1 2; 0 0 3] ); -***** test - N = [2 1]; - f = qncmpopmix( 1, N ); - assert( f, [1 0; 0 1] ); - f = qncmpopmix( 2, N ); - assert( f, [2 0; 1 1] ); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/ctmcbd.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmcbd.m -***** test - birth = [ 1 1 1 ]; - death = [ 2 2 2 ]; - Q = ctmcbd( birth, death ); - assert( ctmc(Q), [ 8/15 4/15 2/15 1/15 ], 1e-5 ); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/ctmcfpt.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmcfpt.m -***** demo - Q = [ -1.0 0.9 0.1; ... - 0.1 -1.0 0.9; ... - 0.9 0.1 -1.0 ]; - M = ctmcfpt(Q) - m = ctmcfpt(Q,1,3) -***** test - N = 10; - Q = reshape(1:N^2,N,N); - Q(1:N+1:end) = 0; - Q -= diag(sum(Q,2)); - M = ctmcfpt(Q); - assert( all(diag(M) < 10*eps) ); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/dtmc_bd.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmc_bd.m -***** test - birth = [.5 .5 .3]; - death = [.6 .2 .3]; - fail("dtmc_bd(birth,death)","must be"); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/dtmc.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmc.m -***** test - P = [0.75 0.25; 0.5 0.5]; - p = dtmc(P); - assert( p*P, p, 1e-5 ); - assert( p, [0.6666 0.3333], 1e-4 ); -***** test - #Example 2.11 p. 44 Bolch et al. - P = [0.5 0.5; 0.5 0.5]; - p = dtmc(P); - assert( p, [0.5 0.5], 1e-3 ); -***** test - fail("dtmc( [1 1 1; 1 1 1] )", "square"); -***** test - a = 0.2; - b = 0.8; - P = [1-a a; b 1-b]; - plim = dtmc(P); - p = dtmc(P, 100, [1 0]); - assert( plim, p, 1e-5 ); -***** test - P = [0 1 0 0 0; ... - .25 0 .75 0 0; ... - 0 .5 0 .5 0; ... - 0 0 .75 0 .25; ... - 0 0 0 1 0 ]; - p = dtmc(P); - assert( p, [.0625 .25 .375 .25 .0625], 10*eps ); -***** test - P = zeros(9,9); - P(1,[2 4]) = 1/2; - P(2,[1 5 3]) = 1/3; - P(3,[2 6]) = 1/2; - P(4,[1 5 7]) = 1/3; - P(5,[2 4 6 8]) = 1/4; - P(6,[3 5 9]) = 1/3; - P(7,[4 8]) = 1/2; - P(8,[7 5 9]) = 1/3; - P(9,[6 8]) = 1/2; - p = dtmc(P); - assert( p, [1/12 1/8 1/12 1/8 1/6 1/8 1/12 1/8 1/12], 10*eps ); -***** demo - P = zeros(9,9); - P(1,[2 4] ) = 1/2; - P(2,[1 5 3] ) = 1/3; - P(3,[2 6] ) = 1/2; - P(4,[1 5 7] ) = 1/3; - P(5,[2 4 6 8]) = 1/4; - P(6,[3 5 9] ) = 1/3; - P(7,[4 8] ) = 1/2; - P(8,[7 5 9] ) = 1/3; - P(9,[6 8] ) = 1/2; - p = dtmc(P); - disp(p) -***** demo - a = 0.2; - b = 0.15; - P = [ 1-a a; b 1-b]; - T = 0:14; - pp = zeros(2,length(T)); - for i=1:length(T) - pp(:,i) = dtmc(P,T(i),[1 0]); - endfor - ss = dtmc(P); # compute steady state probabilities - plot( T, pp(1,:), "b+;p_0(t);", "linewidth", 2, ... - T, ss(1)*ones(size(T)), "b;Steady State;", ... - T, pp(2,:), "r+;p_1(t);", "linewidth", 2, ... - T, ss(2)*ones(size(T)), "r;Steady State;" ); - xlabel("Time Step"); - legend("boxoff"); -6 tests, 6 passed, 0 known failure, 0 skipped -[inst/ctmc.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmc.m -***** test - Q = [-1 1 0 0; 2 -3 1 0; 0 2 -3 1; 0 0 2 -2]; - q = ctmc(Q); - assert( q*Q, 0*q, 1e-5 ); - assert( q, [8/15 4/15 2/15 1/15], 1e-5 ); -***** test - fail( "ctmc([1 1; 1 1])", "infinitesimal" ); - fail( "ctmc([1 1 1; 1 1 1])", "square" ); -***** test - Q = [0 0 0; ... - 0 -1 1; ... - 0 1 -1]; - q = ctmc(Q); - assert( q*Q, 0*q, 1e-5 ); - assert( q, [ 0 0.5 0.5 ], 1e-5 ); -***** test - lambda = 1; - mu = 2; - Q = [ -lambda lambda 0 0 ; ... - mu -(lambda+mu) lambda 0 ; ... - 0 mu -(lambda+mu) lambda ; ... - 0 0 mu -mu ]; - q = ctmc(Q); - assert( q, [8/15 4/15 2/15 1/15], 1e-5 ); -***** test - Q = [ -1 0.4 0.6 0 0 0; ... - 2 -3 0 0.4 0.6 0; ... - 3 0 -4 0 0.4 0.6; ... - 0 2 0 -2 0 0; ... - 0 3 2 0 -5 0; ... - 0 0 3 0 0 -3 ]; - q = ctmc(Q); - assert( q, [0.6578 0.1315 0.1315 0.0263 0.0263 0.0263], 1e-4 ); -***** test - Q = [-1 1 0 0 0 0 0; ... - 0 -3 1 0 2 0 0; ... - 0 0 -3 1 0 2 0; ... - 0 0 0 -2 0 0 2; ... - 2 0 0 0 -3 1 0; ... - 0 2 0 0 0 -3 1; ... - 0 0 2 0 0 0 -2 ]; - q = ctmc(Q); - assert( q, [0.2192 0.1644 0.1507 0.0753 0.1096 0.1370 0.1438], 1e-4 ); -***** test - a = 0.2; - b = 0.8; - Q = [-a a; b -b]; - qlim = ctmc(Q); - q = ctmc(Q, 100, [1 0]); - assert( qlim, q, 1e-5 ); -***** test - ll = 0.1; - mu = 100; - eta = 5; - Q = zeros(9,9); - ## 6--1, 7=sleep2 8=sleep1 9=crash - Q(6,5) = 6*ll; - Q(5,4) = 5*ll; - Q(4,3) = 4*ll; - Q(3,2) = 3*ll; - Q(2,1) = 2*ll; - Q(2,7) = mu; - Q(1,9) = ll; - Q(1,8) = mu; - Q(8,9) = ll; - Q(7,8) = 2*ll; - Q(7,6) = eta; - Q(8,6) = eta; - Q -= diag(sum(Q,2)); - q0 = zeros(1,9); q0(6) = 1; - q = ctmc(Q,10,q0); - assert( q(9), 0.000504, 1e-6 ); - q = ctmc(Q,2,q0); - assert( q, [3.83e-7 1.938e-4 0.0654032 0.2216998 0.4016008 0.3079701 0.0030271 0.0000998 5e-6], 1e-5 ); - # Compute probability that no shuttle needs to leave during 10 years - Q(7,:) = Q(8,:) = 0; # make states 7 and 8 absorbing - q = ctmc(Q,10,q0); - assert( 1-sum(q(7:9)), 0.3901, 1e-4 ); -***** demo - Q = [ -1 1; ... - 1 -1 ]; - q = ctmc(Q) -***** demo - a = 0.2; - b = 0.15; - Q = [ -a a; b -b]; - T = linspace(0,14,50); - pp = zeros(2,length(T)); - for i=1:length(T) - pp(:,i) = ctmc(Q,T(i),[1 0]); - endfor - ss = ctmc(Q); # compute steady state probabilities - plot( T, pp(1,:), "b;p_0(t);", "linewidth", 2, ... - T, ss(1)*ones(size(T)), "b;Steady State;", ... - T, pp(2,:), "r;p_1(t);", "linewidth", 2, ... - T, ss(2)*ones(size(T)), "r;Steady State;" ); - xlabel("Time"); - legend("boxoff"); -***** test - sec = 1; - min = 60*sec; - hour = 60*min; - ## the state space enumeration is {2, RC, RB, 1, 0} - a = 1/(10*min); # 1/a = duration of reboot (10 min) - b = 1/(30*sec); # 1/b = reconfiguration time (30 sec) - g = 1/(5000*hour); # 1/g = processor MTTF (5000 hours) - d = 1/(4*hour); # 1/d = processor MTTR (4 hours) - c = 0.9; # coverage - Q = [ -2*g 2*c*g 2*(1-c)*g 0 0 ; ... - 0 -b 0 b 0 ; ... - 0 0 -a a 0 ; ... - d 0 0 -(g+d) g ; ... - 0 0 0 d -d]; - p = ctmc(Q); - assert( p, [0.9983916, 0.000002995, 0.0000066559, 0.00159742, 0.0000012779], 1e-6 ); - Q(3,:) = Q(5,:) = 0; # make states 3 and 5 absorbing - p0 = [1 0 0 0 0]; - MTBF = ctmcmtta(Q, p0) / hour; - assert( fix(MTBF), 24857); -***** demo - sec = 1; - min = 60*sec; - hour = 60*min; - day = 24*hour; - year = 365*day; - # state space enumeration {2, RC, RB, 1, 0} - a = 1/(10*min); # 1/a = duration of reboot (10 min) - b = 1/(30*sec); # 1/b = reconfiguration time (30 sec) - g = 1/(5000*hour); # 1/g = processor MTTF (5000 hours) - d = 1/(4*hour); # 1/d = processor MTTR (4 hours) - c = 0.9; # coverage - Q = [ -2*g 2*c*g 2*(1-c)*g 0 0; ... - 0 -b 0 b 0; ... - 0 0 -a a 0; ... - d 0 0 -(g+d) g; ... - 0 0 0 d -d]; - p = ctmc(Q); - A = p(1) + p(4); - printf("System availability %9.2f min/year\n",A*year/min); - printf("Mean time in RB state %9.2f min/year\n",p(3)*year/min); - printf("Mean time in RC state %9.2f min/year\n",p(2)*year/min); - printf("Mean time in 0 state %9.2f min/year\n",p(5)*year/min); - Q(3,:) = Q(5,:) = 0; # make states 3 and 5 absorbing - p0 = [1 0 0 0 0]; - MTBF = ctmcmtta(Q, p0) / hour; - printf("System MTBF %.2f hours\n",MTBF); -9 tests, 9 passed, 0 known failure, 0 skipped -[inst/qnclosedsinglemvaapprox.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnclosedsinglemvaapprox.m -***** test - fail( "qnclosedsinglemvaapprox()", "Invalid" ); - fail( "qnclosedsinglemvaapprox( 10, [1 2], [1 2 3] )", "S, V and m" ); - fail( "qnclosedsinglemvaapprox( 10, [-1 1], [1 1] )", ">= 0" ); - fail( "qnclosedsinglemvaapprox( 10, [1 2], [1 2], [1 2] )", "supports"); - fail( "qnclosedsinglemvaapprox( 10, [1 2], [1 2], [1 1], 0, -1)", "tol"); -warning: qnclosedsinglemvaapprox is deprecated. Please use qncsmvaap instead -***** test - # Example p. 117 Lazowska et al. - S = [0.605 2.1 1.35]; - V = [1 1 1]; - N = 3; - Z = 15; - m = 1; - [U R Q X] = qnclosedsinglemvaapprox(N, S, V, m, Z); - Rs = dot(V,R); - Xs = N/(Z+Rs); - assert( Q, [0.0973 0.4021 0.2359], 1e-3 ); - assert( Xs, 0.1510, 1e-3 ); - assert( Rs, 4.87, 1e-3 ); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qncsmvaap.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncsmvaap.m -***** test - fail( "qncsmvaap()", "Invalid" ); - fail( "qncsmvaap( 10, [1 2], [1 2 3] )", "S, V and m" ); - fail( "qncsmvaap( 10, [-1 1], [1 1] )", ">= 0" ); - fail( "qncsmvaap( 10, [1 2], [1 2], [1 2] )", "supports"); - fail( "qncsmvaap( 10, [1 2], [1 2], [1 1], 0, -1)", "tol"); -***** test - # Example p. 117 Lazowska et al. - S = [0.605 2.1 1.35]; - V = [1 1 1]; - N = 3; - Z = 15; - m = 1; - [U R Q X] = qncsmvaap(N, S, V, m, Z); - Rs = dot(V,R); - Xs = N/(Z+Rs); - assert( Q, [0.0973 0.4021 0.2359], 1e-3 ); - assert( Xs, 0.1510, 1e-3 ); - assert( Rs, 4.87, 1e-3 ); -***** demo - S = [ 0.125 0.3 0.2 ]; - V = [ 16 10 5 ]; - N = 30; - m = ones(1,3); - Z = 4; - Xmva = Xapp = Rmva = Rapp = zeros(1,N); - for n=1:N - [U R Q X] = qncsmva(n,S,V,m,Z); - Xmva(n) = X(1)/V(1); - Rmva(n) = dot(R,V); - [U R Q X] = qncsmvaap(n,S,V,m,Z); - Xapp(n) = X(1)/V(1); - Rapp(n) = dot(R,V); - endfor - subplot(2,1,1); - plot(1:N, Xmva, ";Exact;", "linewidth", 2, 1:N, Xapp, "x;Approximate;", "markersize", 7); - legend("location","southeast"); legend("boxoff"); - ylabel("Throughput X(n)"); - subplot(2,1,2); - plot(1:N, Rmva, ";Exact;", "linewidth", 2, 1:N, Rapp, "x;Approximate;", "markersize", 7); - legend("location","southeast"); legend("boxoff"); - ylabel("Response Time R(n)"); - xlabel("Number of Requests n"); -2 tests, 2 passed, 0 known failure, 0 skipped [inst/qnom.m] >>>>> /build/octave-queueing-1.2.6/inst/qnom.m ***** test @@ -4273,68 +3382,127 @@ xlabel("Class 1 interarrival time"); ylabel("Throughput"); 5 tests, 5 passed, 0 known failure, 0 skipped -[inst/dtmc_check_P.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmc_check_P.m +[inst/qsmm1.m] +>>>>> /build/octave-queueing-1.2.6/inst/qsmm1.m ***** test - [r err] = dtmc_check_P( [1 1 1; 1 1 1] ); - assert( r, 0 ); - assert( index(err, "square") > 0 ); -warning: dtmc_check_P is deprecated. Please use dtmcchkP instead + fail( "qsmm1(10,5)", "not ergodic" ); + fail( "qsmm1([2 2], [1 1 1])", "incompatible size"); ***** test - [r err] = dtmc_check_P( [1 0 0; 0 0.5 0; 0 0 0] ); - assert( r, 0 ); - assert( index(err, "stochastic") > 0 ); + [U R Q X P0] = qsmm1(0, 1); + assert( U, 0 ); + assert( R, 1 ); + assert( Q, 0 ); + assert( X, 0 ); + assert( P0, 1 ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/ctmc_fpt.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmc_fpt.m ***** test - P = [0 1; 1 0]; - assert( dtmc_check_P(P), 2 ); + N = 10; + Q = reshape(1:N^2,N,N); + Q(1:N+1:end) = 0; + Q -= diag(sum(Q,2)); + M = ctmc_fpt(Q); + assert( all(diag(M) < 10*eps) ); +warning: ctmc_fpt is deprecated. Please use ctmcfpt instead +1 test, 1 passed, 0 known failure, 0 skipped +[inst/ctmc_check_Q.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmc_check_Q.m ***** test - P = dtmc_bd( linspace(0.1,0.4,10), linspace(0.4,0.1,10) ); - assert( dtmc_check_P(P), rows(P) ); + Q = [0]; + [result err] = ctmc_check_Q(Q); + assert( result, 1 ); + assert( err, "" ); +warning: ctmc_check_Q is deprecated. Please use ctmcchkQ instead ***** test - N = 1000; - P = reshape( 1:N^2, N, N ); - P(1:N+1:end) = 0; - P = P ./ repmat(sum(P,2),1,N); - assert( dtmc_check_P(P), N ); + N = 10; + Q = ctmc_bd(rand(1,N-1),rand(1,N-1)); + [result err] = ctmc_check_Q(Q); + assert( result, N ); + assert( err, "" ); +***** test + Q = [1 2 3; 4 5 6]; + [result err] = ctmc_check_Q(Q); + assert( result, 0 ); + assert( index(err, "square") > 0 ); +***** test + N = 10; + Q = ctmc_bd(rand(1,N-1),rand(1,N-1)); + Q(2,1) = -1; + [result err] = ctmc_check_Q(Q); + assert( result, 0 ); + assert( index(err, "infinitesimal") > 0 ); +***** test + N = 10; + Q = ctmc_bd(rand(1,N-1),rand(1,N-1)); + Q(1,1) += 7; + [result err] = ctmc_check_Q(Q); + assert( result, 0 ); + assert( index(err, "infinitesimal") > 0 ); 5 tests, 5 passed, 0 known failure, 0 skipped -[inst/qncsvisits.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncsvisits.m +[inst/dtmc_is_irreducible.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmc_is_irreducible.m ***** test - P = [-1 0; 0 0]; - fail( "qncsvisits(P)", "invalid" ); - P = [1 0; 0.5 0]; - fail( "qncsvisits(P)", "invalid" ); - P = [1 2 3; 1 2 3]; - fail( "qncsvisits(P)", "square" ); - P = [0 1; 1 0]; - fail( "qncsvisits(P,0)", "range" ); - fail( "qncsvisits(P,3)", "range" ); + P = [0 .5 0; 0 0 0]; + fail( "dtmc_is_irresudible(P)" ); ***** test - - ## Closed, single class network - - P = [0 0.3 0.7; 1 0 0; 1 0 0]; - V = qncsvisits(P); - assert( V*P,V,1e-5 ); - assert( V, [1 0.3 0.7], 1e-5 ); + P = [0 1 0; 0 .5 .5; 0 1 0]; + [r s] = dtmc_is_irreducible(P); + assert( r == 0 ); + assert( max(s), 2 ); + assert( min(s), 1 ); +warning: dtmc_is_irreducible is deprecated. Please use dtmcisir instead ***** test - - ## Test tolerance of the qncsvisits() function. - ## This test builds transition probability matrices and tries - ## to compute the visit counts on them. - - for k=[5, 10, 20, 50] - P = reshape(1:k^2, k, k); - P = P ./ repmat(sum(P,2),1,k); - V = qncsvisits(P); - assert( V*P, V, 1e-5 ); - endfor -***** demo - P = [0 0.3 0.7; ... - 1 0 0 ; ... - 1 0 0 ]; - V = qncsvisits(P) + P = [.5 .5 0; .2 .3 .5; 0 .2 .8]; + [r s] = dtmc_is_irreducible(P); + assert( r == 1 ); + assert( max(s), 1 ); + assert( min(s), 1 ); 3 tests, 3 passed, 0 known failure, 0 skipped +[inst/qnmknode.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnmknode.m +***** test + fail( "qnmknode( 'pippo', 1 )", "must be one" ); + fail( "qnmknode( '-/g/1-ps', 1, 1, 1)", "Invalid call" ); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/qsammm.m] +>>>>> /build/octave-queueing-1.2.6/inst/qsammm.m +***** test + [U R Q X] = qsammm( 73,[10,15,20,20,25] ); + assert( U, 0.81, 1e-2 ); + assert( Q, 6.5278, 1e-4 ); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/ctmc_exps.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmc_exps.m +***** test + Q = [-1 1; 1 -1]; + L = ctmc_exps(Q,10,[1 0]); + L = ctmc_exps(Q,linspace(0,10,100),[1 0]); +warning: ctmc_exps is deprecated. Please use ctmcexps instead +***** test + Q = ctmc_bd( [1 2 3], [3 2 1] ); + p0 = [1 0 0 0]; + t = linspace(0,10,10); + L1 = L2 = zeros(length(t),4); + # compute L using the differential equation formulation + ff = @(x,t) (x(:)'*Q+p0); + fj = @(x,t) (Q); + L1 = lsode( {ff, fj}, zeros(size(p0)), t ); + # compute L using ctmc_exps (integral formulation) + for i=1:length(t) + L2(i,:) = ctmc_exps(Q,t(i),p0); + endfor + assert( L1, L2, 1e-5); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qnopenbsb.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnopenbsb.m +***** test + fail( "qnopenbsb( 0.1, [] )", "vector" ); + fail( "qnopenbsb( 0.1, [0 -1])", "nonnegative" ); + fail( "qnopenbsb( 0, [1 2] )", "lambda" ); + fail( "qnopenbsb( -1, [1 2])", "lambda" ); +warning: qnopenbsb is deprecated. Please use qnosbsb instead +1 test, 1 passed, 0 known failure, 0 skipped [inst/ctmc_taexps.m] >>>>> /build/octave-queueing-1.2.6/inst/ctmc_taexps.m ***** test @@ -4347,21 +3515,6 @@ assert( sum(M), 1, 10*eps ); warning: ctmc_taexps is deprecated. Please use ctmctaexps instead 1 test, 1 passed, 0 known failure, 0 skipped -[inst/qnclosedab.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnclosedab.m -***** test - fail("qnclosedab(-1,0)", "N must be"); - fail("qnclosedab(1,[])", "nonempty"); - fail("qnclosedab(1,[-1 2])", "nonnegative"); - fail("qnclosedab(1,[1 2 3],-1)", "nonnegative"); -warning: qnclosedab is deprecated. Please use qncsaba instead -***** test - N = 20; - D = [ 4.6*2 8 ]; - Z = 120; - [X_l X_u R_l R_u] = qnclosedab(N, D, Z); - assert( [X_u R_l], [0.109 64], 1e-3 ); -2 tests, 2 passed, 0 known failure, 0 skipped [inst/qncsmva.m] >>>>> /build/octave-queueing-1.2.6/inst/qncsmva.m ***** test @@ -4484,431 +3637,594 @@ endfor printf("\nSystem\t %8.4f %8.4f %8.4f\n\n", N-X_s*Z, R_s, X_s ); 9 tests, 9 passed, 0 known failure, 0 skipped -[inst/qnmknode.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnmknode.m +[inst/qsmmmk.m] +>>>>> /build/octave-queueing-1.2.6/inst/qsmmmk.m ***** test - fail( "qnmknode( 'pippo', 1 )", "must be one" ); - fail( "qnmknode( '-/g/1-ps', 1, 1, 1)", "Invalid call" ); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qnclosedbsb.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnclosedbsb.m + lambda = mu = m = 1; + k = 10; + [U R Q X p0] = qsmmmk(lambda,mu,m,k); + assert( Q, k/2, 1e-7 ); + assert( U, 1-p0, 1e-7 ); ***** test - fail("qnclosedbsb(-1,0)", "N must be"); - fail("qnclosedbsb(1,[])", "nonempty"); - fail("qnclosedbsb(1,[-1 2])", "nonnegative"); - fail("qnclosedbsb(1,[1 2 3],-1)", "nonnegative"); -warning: qnclosedbsb is deprecated. Please use qncsbsb instead -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qsammm.m] ->>>>> /build/octave-queueing-1.2.6/inst/qsammm.m + lambda = [1 0.8 2 9.2 0.01]; + mu = lambda + 0.17; + k = 12; + [U1 R1 Q1 X1] = qsmm1k(lambda,mu,k); + [U2 R2 Q2 X2] = qsmmmk(lambda,mu,1,k); + assert( U1, U2, 1e-5 ); + assert( R1, R2, 1e-5 ); + assert( Q1, Q2, 1e-5 ); + assert( X1, X2, 1e-5 ); + #assert( [U1 R1 Q1 X1], [U2 R2 Q2 X2], 1e-5 ); ***** test - [U R Q X] = qsammm( 73,[10,15,20,20,25] ); - assert( U, 0.81, 1e-2 ); - assert( Q, 6.5278, 1e-4 ); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qnmarkov.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnmarkov.m + lambda = 0.9; + mu = 0.75; + k = 10; + [U1 R1 Q1 X1 p01] = qsmmmk(lambda,mu,1,k); + [U2 R2 Q2 X2 p02] = qsmm1k(lambda,mu,k); + assert( [U1 R1 Q1 X1 p01], [U2 R2 Q2 X2 p02], 1e-5 ); ***** test - S = [5 2.5]; - P = [0 1; 1 0]; - C = [3 3]; - m = [1 1]; - [U R Q X] = qnmarkov( 3, S, C, P, m ); - assert( U, [0.9333 0.4667], 1e-4 ); - assert( X, [0.1867 0.1867], 1e-4 ); - assert( R, [12.1429 3.9286], 1e-4 ); + lambda = 0.8; + mu = 0.85; + m = 3; + k = 5; + [U1 R1 Q1 X1 p0] = qsmmmk( lambda, mu, m, k ); + birth = lambda*ones(1,k); + death = [ mu*linspace(1,m,m) mu*m*ones(1,k-m) ]; + q = ctmc(ctmcbd( birth, death )); + U2 = dot( q, min( 0:k, m )/m ); + assert( U1, U2, 1e-4 ); + Q2 = dot( [0:k], q ); + assert( Q1, Q2, 1e-4 ); + assert( p0, q(1), 1e-4 ); ***** test - S = [1/0.8 1/0.6 1/0.4]; - P = [0.6 0.3 0.1; 0.2 0.3 0.5; 0.4 0.1 0.5]; - C = [3 3 3]; - [U R Q X] = qnmarkov( 3, S, C, P ); - assert( U, [0.543 0.386 0.797], 1e-3 ); - assert( Q, [0.873 0.541 1.585], 1e-3 ); -***** xtest - S = [2 0.9]; - C = [7 5]; - P = [0 1; 1 0]; - [U R Q X] = qnmarkov( 10, S, C, P ); - assert( Q, [6.73 3.27], 1e-3 ); -!!!!! known failure -ASSERT errors for: assert (Q,[6.73, 3.27],1e-3) - - Location | Observed | Expected | Reason - (1) 6.4826 6.73 Abs err 0.2474 exceeds tol 0.001 by 0.2 - (2) 3.5174 3.27 Abs err 0.2474 exceeds tol 0.001 by 0.2 + # This test comes from an example I found on the web + lambda = 40; + mu = 30; + m = 3; + k = 7; + [U R Q X p0] = qsmmmk( lambda, mu, m, k ); + assert( p0, 0.255037, 1e-6 ); + assert( R, 0.036517, 1e-6 ); ***** test - S = [1/0.8 1/0.6 1/0.4]; - P = [(1-0.667-0.2) 0.667 0.2; 1 0 0; 1 0 0]; - m = [2 3 1]; - C = [3 3 3]; - [U R Q X] = qnmarkov( 3, S, C, P, m ); - assert( U, [0.590 0.350 0.473], 1e-3 ); - assert( Q(1:2), [1.290 1.050], 1e-3 ); + # This test comes from an example I found on the web + lambda = 50; + mu = 10; + m = 4; + k = 6; + [U R Q X p0 pk] = qsmmmk( lambda, mu, m, k ); + assert( pk, 0.293543, 1e-6 ); ***** test - p = 0.5; # transition prob. from S2 to S1 - mu = [1 2]; # Service rates - C = [2 1]; # Capacities - lambda = [0.5 0]; # arrival rate at service center 1 - - PP = [ 0 1; p 0 ]; - [U R Q X] = qnmarkov( lambda, 1./mu, C, PP ); - ## Now we generate explicitly the infinitesimal generator matrix - ## of the underlying MC. - ## 00 01 10 11 20 21 - QQ = [ 0 0 lambda(1) 0 0 0; ... ## 00 - mu(2)*(1-p) 0 mu(2)*p lambda(1) 0 0; ... ## 01 - 0 mu(1) 0 0 lambda(1) 0; ... ## 10 - 0 0 mu(2)*(1-p) 0 mu(2)*p lambda(1); ... ## 11 - 0 0 0 mu(1) 0 0; ... ## 20 - 0 0 0 0 mu(2)*(1-p) 0 ]; ## 21 - ## Complete matrix - sum_el = sum(QQ,2); - QQ -= diag(sum_el); - q = ctmc(QQ); - ## Compare results - assert( U(1), 1-sum(q([1, 2])), 1e-5 ); - assert( U(2), 1-sum(q([1,3,5])), 1e-5 ); + # This test comes from an example I found on the web + lambda = 3; + mu = 2; + m = 2; + k = 5; + [U R Q X p0 pk] = qsmmmk( lambda, mu, m, k ); + assert( p0, 0.179334, 1e-6 ); + assert( pk, 0.085113, 1e-6 ); + assert( Q, 2.00595, 1e-5 ); + assert( R-1/mu, 0.230857, 1e-6 ); # waiting time in the queue +7 tests, 7 passed, 0 known failure, 0 skipped +[inst/qnosaba.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnosaba.m ***** test - P = [0 0.5 0.5; 1 0 0; 1 0 0]; - C = [6 6 6]; - S = [1 0.8 1.8]; - N = 6; - [U1 R1 Q1 X1] = qnclosed( N, S, qncsvisits(P) ); - [U2 R2 Q2 X2] = qnmarkov( N, S, C, P ); - assert( U1, U2, 1e-6 ); - assert( R1, R2, 1e-6 ); - assert( Q1, Q2, 1e-6 ); - assert( X1, X2, 1e-6 ); -6 tests, 5 passed, 1 known failure, 0 skipped -[inst/dtmcfpt.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmcfpt.m + fail( "qnosaba( 0.1, [] )", "vector" ); + fail( "qnosaba( 0.1, [0 -1])", "nonnegative" ); + fail( "qnosaba( 0, [1 2] )", "lambda" ); + fail( "qnosaba( -1, [1 2])", "lambda" ); + fail( "qnosaba( 1, [1 2 3], [1 2] )", "incompatible size"); + fail( "qnosaba( 1, [1 2 3], [-1 2 3] )", "nonnegative"); ***** test - P = [1 1 1; 1 1 1]; - fail( "dtmcfpt(P)" ); + [Xl Xu Rl Ru] = qnosaba( 1, [1 1] ); + assert( Xl, 0 ); + assert( Ru, +inf ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/dtmc_taexps.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmc_taexps.m ***** test - P = dtmcbd([1 1 1], [0 0 0] ); - fail( "dtmcfpt(P)", "absorbing" ); + P = dtmc_bd([1 1 1 1], [0 0 0 0]); + p0 = [1 0 0 0 0]; + L = dtmc_taexps(P,p0); + assert( L, [.25 .25 .25 .25 0], 10*eps ); +warning: dtmc_taexps is deprecated. Please use dtmctaexps instead +1 test, 1 passed, 0 known failure, 0 skipped +[inst/dtmc_check_P.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmc_check_P.m ***** test - P = [ 0.0 0.9 0.1; ... - 0.1 0.0 0.9; ... - 0.9 0.1 0.0 ]; - p = dtmc(P); - M = dtmcfpt(P); - assert( diag(M)', 1./p, 1e-8 ); + [r err] = dtmc_check_P( [1 1 1; 1 1 1] ); + assert( r, 0 ); + assert( index(err, "square") > 0 ); +warning: dtmc_check_P is deprecated. Please use dtmcchkP instead ***** test - P = [ 0 1 0 0 0; ... - .25 .0 .75 0 0; ... - 0 .5 0 .5 0; ... - 0 0 .75 0 .25; ... - 0 0 0 1 0 ]; - M = dtmcfpt(P); - assert( M, [16 1 2.6667 6.3333 21.3333; ... - 15 4 1.6667 5.3333 20.3333; ... - 18.6667 3.6667 2.6667 3.6667 18.6667; ... - 20.3333 5.3333 1.6667 4 15; ... - 21.3333 6.3333 2.6667 1 16 ], 1e-4 ); + [r err] = dtmc_check_P( [1 0 0; 0 0.5 0; 0 0 0] ); + assert( r, 0 ); + assert( index(err, "stochastic") > 0 ); ***** test - sz = 10; - P = reshape( 1:sz^2, sz, sz ); - normP = repmat(sum(P,2),1,columns(P)); - P = P./normP; - M = dtmcfpt(P); - for i=1:rows(P) - for j=1:columns(P) - assert( M(i,j), 1 + dot(P(i,:), M(:,j)) - P(i,j)*M(j,j), 1e-8); + P = [0 1; 1 0]; + assert( dtmc_check_P(P), 2 ); +***** test + P = dtmc_bd( linspace(0.1,0.4,10), linspace(0.4,0.1,10) ); + assert( dtmc_check_P(P), rows(P) ); +***** test + N = 1000; + P = reshape( 1:N^2, N, N ); + P(1:N+1:end) = 0; + P = P ./ repmat(sum(P,2),1,N); + assert( dtmc_check_P(P), N ); +5 tests, 5 passed, 0 known failure, 0 skipped +[inst/qnomvisits.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnomvisits.m +***** test + fail( "qnomvisits( zeros(3,3,3), [1 1 1] )", "matrix"); +***** test + C = 2; K = 4; + P = zeros(C,K,C,K); + # class 1 routing + P(1,1,1,1) = .05; + P(1,1,1,2) = .45; + P(1,1,1,3) = .5; + P(1,2,1,1) = 0.1; + P(1,3,1,1) = 0.2; + # class 2 routing + P(2,1,2,1) = .01; + P(2,1,2,3) = .5; + P(2,1,2,4) = .49; + P(2,3,2,1) = 0.2; + P(2,4,2,1) = 0.16; + lambda = [0.1 0 0 0.1 ; 0 0 0.2 0.1]; + lambda_sum = sum(lambda(:)); + V = qnomvisits(P, lambda); + assert( all(V(:)>=0) ); + for i=1:K + for c=1:C + assert(V(c,i), lambda(c,i) / lambda_sum + sum(sum(V .* P(:,:,c,i))), 1e-5); endfor endfor ***** test - P = zeros(9,9); - P(1,[2 4]) = .5; - P(2,[1 5 3]) = 1/3; - P(3,[2 6]) = .5; - P(4,[1 5 7]) = 1/3; - P(5,[2 4 6 8]) = 1/4; - P(6,[3 5 9]) = 1/3; - P(7,[4 8]) = .5; - P(8,[7 5 9]) = 1/3; - P(9,[6 8]) = .5; - M = dtmcfpt(P); - assert( M(1:9 != 5,5)', [6 5 6 5 5 6 5 6], 100*eps ); -6 tests, 6 passed, 0 known failure, 0 skipped -[inst/qnammm.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnammm.m + # example 7.7 p. 304 Bolch et al. + # Note that the book uses a slightly different notation than + # what we use here. Specifically, the book defines the routing + # probabilities as P(i,r,j,s) (i,j are service centers, r,s are job + # classes) while the queueing package uses P(r,i,s,j). + # A more serious problem arises in the definition of external arrivals. + # The computation of V(r,i) as given in the book (called e_ir + # in Eq 7.14) is performed in terms of P_{0, js}, defined as + # "the probability in an open network that a job from outside the network + # enters the jth node as a job of the sth class" (p. 267). This is + # compliant with eq. 7.12 where the external class r arrival rate at center + # i is computed as \lambda * P_{0,ir}. However, example 7.7 wrongly + # defines P_{0,11} = P_{0,12} = 1, instead of P_{0,11} = P_{0,12} = 0.5 + # Therefore the resulting visit ratios they obtain must be divided by two. + P = zeros(2,3,2,3); + lambda = S = zeros(2,3); + P(1,1,1,2) = 0.4; + P(1,1,1,3) = 0.3; + P(1,2,1,1) = 0.6; + P(1,2,1,3) = 0.4; + P(1,3,1,1) = 0.5; + P(1,3,1,2) = 0.5; + P(2,1,2,2) = 0.3; + P(2,1,2,3) = 0.6; + P(2,2,2,1) = 0.7; + P(2,2,2,3) = 0.3; + P(2,3,2,1) = 0.4; + P(2,3,2,2) = 0.6; + lambda(1,1) = lambda(2,1) = 1; + V = qnomvisits(P,lambda); + assert( V, [ 3.333 2.292 1.917; 10 8.049 8.415] ./ 2, 1e-3); +3 tests, 3 passed, 0 known failure, 0 skipped +[inst/ctmc_mtta.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmc_mtta.m ***** test - [U R Q X] = qnammm( 73,[10,15,20,20,25] ); - assert( U, 0.81, 1e-2 ); - assert( Q, 6.5278, 1e-4 ); -warning: qnammm is deprecated. Please use qsammm instead -1 test, 1 passed, 0 known failure, 0 skipped -[inst/ctmc_fpt.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmc_fpt.m + Q = [0 1 0; 1 0 1; 0 1 0 ]; Q -= diag( sum(Q,2) ); + fail( "ctmc_mtta(Q,[1 0 0])", "no absorbing"); +warning: ctmc_mtta is deprecated. Please use ctmcmtta instead ***** test - N = 10; - Q = reshape(1:N^2,N,N); - Q(1:N+1:end) = 0; - Q -= diag(sum(Q,2)); - M = ctmc_fpt(Q); - assert( all(diag(M) < 10*eps) ); -warning: ctmc_fpt is deprecated. Please use ctmcfpt instead -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qncmnpop.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncmnpop.m + Q = [0 1 0; 1 0 1; 0 0 0; 0 0 0 ]; + fail( "ctmc_mtta(Q,[1 0 0])", "square matrix"); ***** test - H = qncmnpop( [1 2 2] ); - assert( H, [1 1 0 0 0 0; 1 2 2 1 0 0; 1 3 5 5 3 1] ); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/ctmcisir.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmcisir.m + Q = [0 1 0; 1 0 1; 0 0 0 ]; + fail( "ctmc_mtta(Q,[1 0 0])", "infinitesimal"); ***** test - Q = [-.5 .5 0; 1 0 0]; - fail( "ctmcisir(Q)" ); + Q = [ 0 0.1 0 0; ... + 0.9 0 0.1 0; ... + 0 0.9 0 0.1; ... + 0 0 0 0 ]; + Q -= diag( sum(Q,2) ); + assert( ctmc_mtta( Q,[0 0 0 1] ), 0 ); # state 4 is absorbing ***** test - Q = [-1 1 0; .5 -.5 0; 0 0 0]; - [r s] = ctmcisir(Q); - assert( r == 0 ); - assert( max(s), 2 ); - assert( min(s), 1 ); + Q = [-1 1; 0 0]; + assert( ctmc_mtta( Q, [0 1] ), 0 ); # state 2 is absorbing + assert( ctmc_mtta( Q, [1 0] ), 1 ); # the result has been computed by hand +5 tests, 5 passed, 0 known failure, 0 skipped +[inst/qncmmvaap.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncmmvaap.m ***** test - Q = [-.5 .5 0; .2 -.7 .5; .2 0 -.2]; - [r s] = ctmcisir(Q); - assert( r == 1 ); - assert( max(s), 1 ); - assert( min(s), 1 ); -3 tests, 3 passed, 0 known failure, 0 skipped -[inst/qnmm1k.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnmm1k.m + S = [ 1 3 3; 2 4 3]; + V = [ 1 1 3; 1 1 3]; + N = [ 1 1 ]; + m = [1 ; 1 ]; + Z = [2 2 2]; + fail( "qncmmvaap(N,S,V,m,Z)", "m must be" ); + m = [1 ; 1 ; 1]; + fail( "qncmmvaap(N,S,V,m,Z)", "Z must be" ); ***** test - lambda = mu = 1; - K = 10; - [U R Q X p0] = qnmm1k(lambda,mu,K); - assert( Q, K/2, 1e-7 ); - assert( U, 1-p0, 1e-7 ); + S = [ 1 3; 2 4]; + V = [ 1 1; 1 1]; + N = [ 1 1 ]; + m = ones(1,2); + [U R Q X] = qncmmvaap(N,S,V,m); + assert( Q, [ .192 .808; .248 .752 ], 1e-3 ); + Xc = ( X(:,1)./V(:,1) )'; + assert( Xc, [ .154 .104 ], 1e-3 ); + # Compute the (overall) class-c system response time + R_c = N ./ Xc; + assert( R_c, [ 6.508 9.614 ], 5e-3 ); +***** demo + S = [ 1, 1, 1, 1; 2, 1, 3, 1; 4, 2, 3, 3 ]; + V = ones(3,4); + N = [10 5 1]; + m = [1 0 1 1]; + [U R Q X] = qncmmvaap(N,S,V,m); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qnclosedmultimvaapprox.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnclosedmultimvaapprox.m ***** test - # Compare result with one obtained by solvind the CTMC - lambda = 0.8; - mu = 0.8; - K = 10; - [U1 R1 Q1 X1] = qnmm1k( lambda, mu, K ); - birth = lambda*ones(1,K); - death = mu*ones(1,K); - q = ctmc(ctmc_bd( birth, death )); - U2 = 1-q(1); - Q2 = dot( [0:K], q ); - assert( U1, U2, 1e-4 ); - assert( Q1, Q2, 1e-4 ); + S = [ 1 3 3; 2 4 3]; + V = [ 1 1 3; 1 1 3]; + N = [ 1 1 ]; + m = [1 ; 1 ]; + Z = [2 2 2]; + fail( "qnclosedmultimvaapprox(N,S,V,m,Z)", "m must be" ); + m = [1 ; 1 ; 1]; + fail( "qnclosedmultimvaapprox(N,S,V,m,Z)", "Z must be" ); +warning: qqnclosedmultimvaapprox is deprecated. Please use qncmmvaap instead +***** test + S = [ 1 3; 2 4]; + V = [ 1 1; 1 1]; + N = [ 1 1 ]; + m = ones(1,2); + [U R Q X] = qnclosedmultimvaapprox(N,S,V,m); + assert( Q, [ .192 .808; .248 .752 ], 1e-3 ); + Xc = ( X(:,1)./V(:,1) )'; + assert( Xc, [ .154 .104 ], 1e-3 ); + # Compute the (overall) class-c system response time + R_c = N ./ Xc; + assert( R_c, [ 6.508 9.614 ], 5e-3 ); 2 tests, 2 passed, 0 known failure, 0 skipped -[inst/qnsolve.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnsolve.m +[inst/qnvisits.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnvisits.m ***** test - # Example 8.7 p. 349 Bolch et al. - N = 3; - Q1 = qnmknode( "m/m/m-fcfs", .5, 2 ); - Q2 = qnmknode( "m/m/m-fcfs", 1/1.667 ); - Q3 = qnmknode( "m/m/m-fcfs", 1/1.25 ); - Q4 = qnmknode( "m/m/m-fcfs", 1./[1 2 3] ); - V = [ 1 .5 .5 1 ]; - [U R Q X] = qnsolve("closed",N, { Q1, Q2, Q3, Q4 }, V); - assert( Q, [0.624 0.473 0.686 1.217], 1e-3 ); - assert( R, [0.512 0.776 1.127 1], 1e-3 ); + P = [-1 0; 0 0]; + fail( "qnvisits(P)", "not a transition probability" ); + P = [1 0; 0.5 0]; + fail( "qnvisits(P)", "not a transition probability" ); + P = [1 0; 0 1]; lambda=[0 -1]; + fail( "qnvisits(P,lambda)", "contains negative" ); +warning: qnvisits is deprecated. Please use one of qncsvisits, qnosvisits, qncmvisits, qnomvisits instead ***** test - # Example 8.7 p. 349 Bolch et al. - N = 3; - Q1 = qnmknode( "m/m/m-fcfs", 1/2, 2 ); - Q2 = qnmknode( "m/m/m-fcfs", 1/1.667 ); - Q3 = qnmknode( "m/m/m-fcfs", 1/1.25 ); - Q4 = qnmknode( "-/g/inf", 1 ); - V = [ 1 .5 .5 1 ]; - [U R Q X] = qnsolve("closed",N, { Q1, Q2, Q3, Q4 }, V); - assert( Q, [0.624 0.473 0.686 1.217], 1e-3 ); - assert( R, [0.512 0.776 1.127 1], 1e-3 ); + + ## Closed, single class network + + P = [0 0.3 0.7; 1 0 0; 1 0 0]; + V = qnvisits(P); + assert( V*P,V,1e-5 ); + assert( V, [1 0.3 0.7], 1e-5 ); ***** test - # Example 8.4 p. 333 Bolch et al. - N = 3; - Q1 = qnmknode( "m/m/m-fcfs", .5, 2 ); - Q2 = qnmknode( "m/m/m-fcfs", .6 ); - Q3 = qnmknode( "m/m/m-fcfs", .8 ); - Q4 = qnmknode( "-/g/inf", 1 ); - V = [ 1 .5 .5 1 ]; - [U R Q X] = qnsolve("closed",N, { Q1, Q2, Q3, Q4 }, V); - assert( U(1:3), [.304 .365 .487], 1e-3 ); - assert( X, [1.218 0.609 0.609 1.218], 1e-3 ); + + ## Open, single class network + + P = [0 0.2 0.5; 1 0 0; 1 0 0]; + lambda = [ 0.1 0.3 0.2 ]; + V = qnvisits(P,lambda); + assert( V*P+lambda/sum(lambda),V,1e-5 ); ***** test - # Same as above, with center 1 replaced with a load-dependent service center - N = 3; - Q1 = qnmknode( "m/m/m-fcfs", [.5 .25 .25] ); - Q2 = qnmknode( "m/m/m-fcfs", .6 ); - Q3 = qnmknode( "m/m/m-fcfs", .8 ); - Q4 = qnmknode( "m/m/m-fcfs", [1 1/2 1/3] ); - V = [ 1 .5 .5 1 ]; - [U R Q X] = qnsolve("closed",N, { Q1, Q2, Q3, Q4 }, V); - assert( U(2:3), [.365 .487], 1e-3 ); ## NOTE: Utilization U(1) is computed differently from M/M/m nodes and load-dependent M/M/1 nodes - assert( X, [1.218 0.609 0.609 1.218], 1e-3 ); + + ## Test tolerance of the qnvisits() function. + ## This test builds transition probability matrices and tries + ## to compute the visit counts on them. + + for k=[5, 10, 20, 50] + P = reshape(1:k^2, k, k); + P = P ./ repmat(sum(P,2),1,k); + V = qnvisits(P); + assert( V*P, V, 1e-5 ); + endfor ***** test - # Example 7.4 p. 287 Bolch et al. - QQ = { qnmknode( "m/m/m-fcfs", 0.04 ), ... - qnmknode( "m/m/m-fcfs", 0.03 ), ... - qnmknode( "m/m/m-fcfs", 0.06 ), ... - qnmknode( "m/m/m-fcfs", 0.05 ) }; - P = [ 0 0.5 0.5 0; 1 0 0 0; 0.6 0 0 0; 1 0 0 0 ]; - lambda = [0 0 0 4]; - [U R Q X] = qnsolve("open", sum(lambda), QQ, qnosvisits(P,lambda) ); - assert( X, [20 10 10 4], 1e-4 ); - assert( U, [0.8 0.3 0.6 0.2], 1e-2 ); - assert( R, [0.2 0.043 0.15 0.0625], 1e-3 ); - assert( Q, [4, 0.429 1.5 0.25], 1e-3 ); + + ## Closed, multiclass network + + C = 2; K = 3; + P = zeros(C,K,C,K); + P(1,1,1,2) = 1; + P(1,2,1,1) = 1; + P(2,1,2,3) = 1; + P(2,3,2,1) = 1; + V = qnvisits(P); + for c=1:C + for k=1:K + assert(V(c,k), sum(sum(V .* P(:,:,c,k))), 1e-5); + endfor + endfor ***** test - V = [1 1; 1 1]; - Q1 = qnmknode( "m/m/m-fcfs", [1;2] ); - Q2 = qnmknode( "m/m/m-fcfs", [3;4] ); - lambda = [3/19 2/19]; - [U R Q] = qnsolve("open", lambda, { Q1, Q2 }, diag( lambda / sum(lambda) ) * V); - assert( U(1,1), 3/19, 1e-6 ); - assert( U(2,1), 4/19, 1e-6 ); - assert( R(1,1), 19/12, 1e-6 ); - assert( R(1,2), 57/2, 1e-6 ); - assert( Q(1,1), .25, 1e-6 ); + + ## Test multiclass network. Example from Schwetman (figure 7, page 9 of + ## hhttp://docs.lib.purdue.edu/cstech/259/ + ## "Testing network-of-queues software, technical report CSD-TR 330, + ## Purdue University). + + C = 2; K = 4; + P = zeros(C,K,C,K); + # class 1 routing + P(1,1,1,1) = .05; + P(1,1,1,2) = .45; + P(1,1,1,3) = .5; + P(1,2,1,1) = 1; + P(1,3,1,1) = 1; + # class 2 routing + P(2,1,2,1) = .01; + P(2,1,2,3) = .5; + P(2,1,2,4) = .49; + P(2,3,2,1) = 1; + P(2,4,2,1) = 1; + V = qnvisits(P); + for c=1:C + for i=1:K + assert(V(c,i), sum(sum(V .* P(:,:,c,i))), 1e-5); + endfor + endfor ***** test - QQ = { qnmknode( "m/m/m-fcfs", [0.2; 0.2], 2 ), ... - qnmknode( "-/g/1-ps", [0.4; 0.6] ), ... - qnmknode( "-/g/inf", [1; 2] ) }; - V = [ 1 0.6 0.4; 1 0.3 0.7 ]; - N = [ 2 1 ]; - [U R Q X] = qnsolve( "closed", N, QQ, V ); - assert( Q, [ 0.428 0.726 0.845; 0.108 0.158 0.734 ], 1e-3 ); - assert( X(1,1), 2.113, 1e-3 ); # CHECK - assert( X(2,1), 0.524, 1e-3 ); # CHECK - assert( all( all(U(:,[1,2])<=1) ) ); + C = 2; K = 4; + P = zeros(C,K,C,K); + # class 1 routing + P(1,1,1,1) = .05; + P(1,1,1,2) = .45; + P(1,1,1,3) = .5; + P(1,2,1,1) = 0.1; + P(1,3,1,1) = 0.2; + # class 2 routing + P(2,1,2,1) = .01; + P(2,1,2,3) = .5; + P(2,1,2,4) = .49; + P(2,3,2,1) = 0.2; + P(2,4,2,1) = 0.16; + lambda = [0.1 0 0 0.1 ; 0 0 0.2 0.1]; + lambda_sum = sum(lambda(:)); + V = qnvisits(P, lambda); + assert( all(V(:)>=0) ); + for i=1:K + for c=1:C + assert(V(c,i), lambda(c,i) / lambda_sum + sum(sum(V .* P(:,:,c,i))), 1e-5); + endfor + endfor ***** test - QQ = { qnmknode( "m/m/m-fcfs", [0.2 0.1 0.1; 0.2 0.1 0.1] ), ... - qnmknode( "-/g/1-ps", [0.4; 0.6] ), ... - qnmknode( "-/g/inf", [1; 2] ) }; - V = [ 1 0.6 0.4; 1 0.3 0.7 ]; - N = [ 2 1 ]; - [U R Q X] = qnsolve( "closed", N, QQ, V ); - assert( Q, [ 0.428 0.726 0.845; 0.108 0.158 0.734 ], 1e-3 ); - assert( X(1,1), 2.113, 1e-3 ); # CHECK - assert( X(2,1), 0.524, 1e-3 ); # CHECK - assert( all( all(U(:,[1,2])<=1) ) ); + + ## Network with class switching. + ## This is example in figure 9 of + ## Schwetman, "Implementing the Mean Value Analysis + ## Algorithm fort the solution of Queueing Network Models", Technical + ## Report CSD-TR-355, Department of Computer Science, Purdue Univrsity, + ## Feb 15, 1982 + ## http://docs.lib.purdue.edu/cstech/286/ + + C = 2; K = 3; + S = [.01 .07 .10; ... + .05 0.7 .10 ]; + P = zeros(C,K,C,K); + P(1,1,1,2) = .7; + P(1,1,1,3) = .2; + P(1,1,2,1) = .1; + P(2,1,2,2) = .3; + P(2,1,2,3) = .5; + P(2,1,1,1) = .2; + P(1,2,1,1) = P(1,3,1,1) = 1; + P(2,2,2,1) = P(2,3,2,1) = 1; + N = [3 0]; + V = qnvisits(P); + VV = [10 7 2; 5 1.5 2.5]; # result given in Schwetman; our function computes something different, but that's ok since visit counts are actually ratios + assert( V ./ repmat(V(:,1),1,K), VV ./ repmat(VV(:,1),1,K), 1e-5 ); ***** test - # example p. 26 Schwetman - QQ = { qnmknode( "m/m/m-fcfs", [.25; .25] ), - qnmknode( "-/g/1-ps", [0; .1] ) }; - V = [1 0; 1 1]; - lambda = [1 0]; - N = [0 3]; - [U R Q X] = qnsolve( "mixed", lambda, N, QQ, V ); - assert( U(1,1), .25, 1e-3 ); - assert( X(1,1), 1.0, 1e-3 ); - assert( [R(1,1) R(2,1) R(2,2)], [1.201 0.885 0.135], 1e-3 ); -***** demo - QQ = { qnmknode( "m/m/m-fcfs", [0.2 0.1 0.1; 0.2 0.1 0.1] ), ... - qnmknode( "-/g/1-ps", [0.4; 0.6] ), ... - qnmknode( "-/g/inf", [1; 2] ) }; - V = [ 1 0.6 0.4; ... - 1 0.3 0.7 ]; - N = [ 2 1 ]; - [U R Q X] = qnsolve( "closed", N, QQ, V ); -9 tests, 9 passed, 0 known failure, 0 skipped -[inst/engset.m] ->>>>> /build/octave-queueing-1.2.6/inst/engset.m + + ## two disjoint classes: must produce two disjoing chains + + C = 2; K = 3; + P = zeros(C,K,C,K); + P(1,1,1,2) = 1; + P(1,2,1,1) = 1; + P(2,1,2,3) = 1; + P(2,3,2,1) = 1; + [nc r] = qnvisits(P); + assert( r(1) != r(2) ); ***** test - fail("erlangb(1, -1)", "positive"); - fail("erlangb(-1, 1)", "positive"); - fail("erlangb(1, 0)", "positive"); - fail("erlangb(0, 1)", "positive"); - fail("erlangb('foo',1)", "positive"); - fail("erlangb(1,'bar')", "positive"); - fail("erlangb([1 1],[1 1 1])","common size"); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/dtmcexps.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmcexps.m + + ## two classes, one chain + + C = 2; K = 3; + P = zeros(C,K,C,K); + P(1,1,1,2) = .5; + P(1,2,2,1) = 1; + P(2,1,2,3) = .5; + P(2,3,1,1) = 1; + [nc r] = qnvisits(P); + assert( r(1) == r(2) ); ***** test - P = dtmcbd([1 1 1 1], [0 0 0 0]); - L = dtmcexps(P,[1 0 0 0 0]); - t = dtmcmtta(P,[1 0 0 0 0]); - assert( L, [1 1 1 1 0] ); - assert( sum(L), t ); + + ## a "Moebius strip". Note that this configuration is invalid, and + ## therefore our algorithm must raise an error. This is because this + ## network has two chains, but both chains contain both classes + + C = 2; K = 2; + P = zeros(C,K,C,K); + P(1,1,2,2) = 1; + P(2,2,1,1) = 1; + P(2,1,1,2) = 1; + P(1,2,2,1) = 1; + fail( "qnvisits(P)", "different"); ***** test - P = dtmcbd(linspace(0.1,0.4,5),linspace(0.4,0.1,5)); - p0 = [1 0 0 0 0 0]; - L = dtmcexps(P,0,p0); - assert( L, p0 ); -2 tests, 2 passed, 0 known failure, 0 skipped -[inst/dtmc_mtta.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmc_mtta.m + + ## Network with two classes representing independent chains. + ## This is example in figure 8 of + ## Schwetman, "Implementing the Mean Value Analysis + ## Algorithm fort the solution of Queueing Network Models", Technical + ## Report CSD-TR-355, Department of Computer Science, Purdue Univrsity, + ## Feb 15, 1982, http://docs.lib.purdue.edu/cstech/286/ + + C = 2; K = 2; + P = zeros(C,K,C,K); + P(1,1,1,3) = P(1,3,1,1) = 1; + P(2,2,2,3) = P(2,3,2,2) = 1; + V = qnvisits(P); + assert( V, [1 0 1; 0 1 1], 1e-5 ); ***** test - fail( "dtmc_mtta(1,2,3)" ); - fail( "dtmc_mtta()" ); + C = 2; + K = 3; + P = zeros(C,K,C,K); + P(1,1,1,2) = 1; + P(1,2,1,3) = 1; + P(1,3,2,2) = 1; + P(2,2,1,1) = 1; + [V ch] = qnvisits(P); + assert( ch, [1 1] ); ***** test - P = dtmcbd([0 .5 .5 .5], [.5 .5 .5 0]); - [t N B] = dtmc_mtta(P); - assert( t, [0 3 4 3 0], 10*eps ); - assert( B([2 3 4],[1 5]), [3/4 1/4; 1/2 1/2; 1/4 3/4], 10*eps ); - assert( B(1,1), 1 ); - assert( B(5,5), 1 ); + C = 2; + K = 3; + P = zeros(C,K,C,K); + P(1,1,1,2) = 1; + P(1,2,1,3) = 1; + P(1,3,2,2) = 1; + P(2,2,2,1) = 1; + P(2,1,1,2) = 1; + [V ch] = qnvisits(P); + assert( ch, [1 1] ); +14 tests, 14 passed, 0 known failure, 0 skipped +[inst/ctmc.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmc.m ***** test - P = dtmcbd([0 .5 .5 .5], [.5 .5 .5 0]); - [t N B] = dtmc_mtta(P); - assert( t(3), 4, 10*eps ); - assert( B(3,1), 0.5, 10*eps ); - assert( B(3,5), 0.5, 10*eps ); + Q = [-1 1 0 0; 2 -3 1 0; 0 2 -3 1; 0 0 2 -2]; + q = ctmc(Q); + assert( q*Q, 0*q, 1e-5 ); + assert( q, [8/15 4/15 2/15 1/15], 1e-5 ); ***** test - P = dtmcbd([0 .5 .5 .5 .5], [.5 .5 .5 .5 0]); - [t N B] = dtmc_mtta(P); - assert( t(2:5), [4 6 6 4], 100*eps ); - assert( B(2:5,1), [.8 .6 .4 .2]', 100*eps ); - assert( B(2:5,6), [.2 .4 .6 .8]', 100*eps ); + fail( "ctmc([1 1; 1 1])", "infinitesimal" ); + fail( "ctmc([1 1 1; 1 1 1])", "square" ); ***** test - P = zeros(9,9); - P(1,[2 4]) = .5; - P(2,[1 5 3]) = 1/3; - P(3,[2 6]) = .5; - P(4,[1 5 7]) = 1/3; - P(5,:) = 0; P(5,5) = 1; - P(6,[3 5 9]) = 1/3; - P(7,[4 8]) = .5; - P(8,[7 5 9]) = 1/3; - P(9,[6 8]) = .5; - t = dtmc_mtta(P); - assert( t, [6 5 6 5 0 5 6 5 6], 10*eps ); -5 tests, 5 passed, 0 known failure, 0 skipped -[inst/ctmctaexps.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmctaexps.m + Q = [0 0 0; ... + 0 -1 1; ... + 0 1 -1]; + q = ctmc(Q); + assert( q*Q, 0*q, 1e-5 ); + assert( q, [ 0 0.5 0.5 ], 1e-5 ); ***** test - Q = [ 0 0.1 0 0; ... - 0.9 0 0.1 0; ... - 0 0.9 0 0.1; ... - 0 0 0 0 ]; - Q -= diag( sum(Q,2) ); - M = ctmctaexps(Q, [1 0 0 0]); - assert( sum(M), 1, 10*eps ); -***** demo - lambda = 0.5; - N = 4; - birth = lambda*linspace(1,N-1,N-1); - death = zeros(1,N-1); - Q = diag(birth,1)+diag(death,-1); + lambda = 1; + mu = 2; + Q = [ -lambda lambda 0 0 ; ... + mu -(lambda+mu) lambda 0 ; ... + 0 mu -(lambda+mu) lambda ; ... + 0 0 mu -mu ]; + q = ctmc(Q); + assert( q, [8/15 4/15 2/15 1/15], 1e-5 ); +***** test + Q = [ -1 0.4 0.6 0 0 0; ... + 2 -3 0 0.4 0.6 0; ... + 3 0 -4 0 0.4 0.6; ... + 0 2 0 -2 0 0; ... + 0 3 2 0 -5 0; ... + 0 0 3 0 0 -3 ]; + q = ctmc(Q); + assert( q, [0.6578 0.1315 0.1315 0.0263 0.0263 0.0263], 1e-4 ); +***** test + Q = [-1 1 0 0 0 0 0; ... + 0 -3 1 0 2 0 0; ... + 0 0 -3 1 0 2 0; ... + 0 0 0 -2 0 0 2; ... + 2 0 0 0 -3 1 0; ... + 0 2 0 0 0 -3 1; ... + 0 0 2 0 0 0 -2 ]; + q = ctmc(Q); + assert( q, [0.2192 0.1644 0.1507 0.0753 0.1096 0.1370 0.1438], 1e-4 ); +***** test + a = 0.2; + b = 0.8; + Q = [-a a; b -b]; + qlim = ctmc(Q); + q = ctmc(Q, 100, [1 0]); + assert( qlim, q, 1e-5 ); +***** test + ll = 0.1; + mu = 100; + eta = 5; + Q = zeros(9,9); + ## 6--1, 7=sleep2 8=sleep1 9=crash + Q(6,5) = 6*ll; + Q(5,4) = 5*ll; + Q(4,3) = 4*ll; + Q(3,2) = 3*ll; + Q(2,1) = 2*ll; + Q(2,7) = mu; + Q(1,9) = ll; + Q(1,8) = mu; + Q(8,9) = ll; + Q(7,8) = 2*ll; + Q(7,6) = eta; + Q(8,6) = eta; Q -= diag(sum(Q,2)); - t = linspace(1e-5,30,100); - p = zeros(1,N); p(1)=1; - M = zeros(length(t),N); - for i=1:length(t) - M(i,:) = ctmctaexps(Q,t(i),p); + q0 = zeros(1,9); q0(6) = 1; + q = ctmc(Q,10,q0); + assert( q(9), 0.000504, 1e-6 ); + q = ctmc(Q,2,q0); + assert( q, [3.83e-7 1.938e-4 0.0654032 0.2216998 0.4016008 0.3079701 0.0030271 0.0000998 5e-6], 1e-5 ); + # Compute probability that no shuttle needs to leave during 10 years + Q(7,:) = Q(8,:) = 0; # make states 7 and 8 absorbing + q = ctmc(Q,10,q0); + assert( 1-sum(q(7:9)), 0.3901, 1e-4 ); +***** demo + Q = [ -1 1; ... + 1 -1 ]; + q = ctmc(Q) +***** demo + a = 0.2; + b = 0.15; + Q = [ -a a; b -b]; + T = linspace(0,14,50); + pp = zeros(2,length(T)); + for i=1:length(T) + pp(:,i) = ctmc(Q,T(i),[1 0]); endfor - clf; - plot(t, M(:,1), ";State 1;", "linewidth", 2, ... - t, M(:,2), ";State 2;", "linewidth", 2, ... - t, M(:,3), ";State 3;", "linewidth", 2, ... - t, M(:,4), ";State 4 (absorbing);", "linewidth", 2 ); - legend("location","east"); legend("boxoff"); + ss = ctmc(Q); # compute steady state probabilities + plot( T, pp(1,:), "b;p_0(t);", "linewidth", 2, ... + T, ss(1)*ones(size(T)), "b;Steady State;", ... + T, pp(2,:), "r;p_1(t);", "linewidth", 2, ... + T, ss(2)*ones(size(T)), "r;Steady State;" ); xlabel("Time"); - ylabel("Time-averaged Expected sojourn time"); -***** demo + legend("boxoff"); +***** test sec = 1; - min = sec*60; + min = 60*sec; hour = 60*min; - day = 24*hour; - + ## the state space enumeration is {2, RC, RB, 1, 0} + a = 1/(10*min); # 1/a = duration of reboot (10 min) + b = 1/(30*sec); # 1/b = reconfiguration time (30 sec) + g = 1/(5000*hour); # 1/g = processor MTTF (5000 hours) + d = 1/(4*hour); # 1/d = processor MTTR (4 hours) + c = 0.9; # coverage + Q = [ -2*g 2*c*g 2*(1-c)*g 0 0 ; ... + 0 -b 0 b 0 ; ... + 0 0 -a a 0 ; ... + d 0 0 -(g+d) g ; ... + 0 0 0 d -d]; + p = ctmc(Q); + assert( p, [0.9983916, 0.000002995, 0.0000066559, 0.00159742, 0.0000012779], 1e-6 ); + Q(3,:) = Q(5,:) = 0; # make states 3 and 5 absorbing + p0 = [1 0 0 0 0]; + MTBF = ctmcmtta(Q, p0) / hour; + assert( fix(MTBF), 24857); +***** demo + sec = 1; + min = 60*sec; + hour = 60*min; + day = 24*hour; + year = 365*day; # state space enumeration {2, RC, RB, 1, 0} a = 1/(10*min); # 1/a = duration of reboot (10 min) b = 1/(30*sec); # 1/b = reconfiguration time (30 sec) @@ -4921,141 +4237,146 @@ d 0 0 -(g+d) g; ... 0 0 0 d -d]; p = ctmc(Q); - printf("System availability: %f\n",p(1)+p(4)); - TT = linspace(0,1*day,101); - PP = ctmctaexps(Q,TT,[1 0 0 0 0]); - A = At = Abart = zeros(size(TT)); - A(:) = p(1) + p(4); # steady-state availability - for n=1:length(TT) - t = TT(n); - p = ctmc(Q,t,[1 0 0 0 0]); - At(n) = p(1) + p(4); # instantaneous availability - Abart(n) = PP(n,1) + PP(n,4); # interval base availability - endfor - clf; - semilogy(TT,A,";Steady-state;", ... - TT,At,";Instantaneous;", ... - TT,Abart,";Interval base;"); - ax = axis(); - ax(3) = 1-1e-5; - axis(ax); - legend("boxoff"); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/qncsbsb.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncsbsb.m -***** test - fail("qncsbsb(-1,0)", "N must be"); - fail("qncsbsb(1,[])", "nonempty"); - fail("qncsbsb(1,[-1 2])", "nonnegative"); - fail("qncsbsb(1,[1 2],[1 2 3])", "incompatible size"); - fail("qncsbsb(1,[1 2 3],[1 2 3],[1 2])", "incompatible size"); - fail("qncsbsb(1,[1 2 3],[1 2 3],[1 2 1])", "M/M/1 servers"); - fail("qncsbsb(1,[1 2 3],[1 2 3],[1 1 1],-1)", "nonnegative"); - fail("qncsbsb(1,[1 2 3],[1 2 3],[1 1 1],[0 0])", "scalar"); -1 test, 1 passed, 0 known failure, 0 skipped -[inst/dtmc_fpt.m] ->>>>> /build/octave-queueing-1.2.6/inst/dtmc_fpt.m -***** test - P = [1 1 1; 1 1 1]; - fail( "dtmc_fpt(P)" ); -warning: dtmc_fpt is deprecated. Please use dtmcfpt instead -***** test - P = dtmc_bd([1 1 1], [0 0 0] ); - fail( "dtmc_fpt(P)", "absorbing" ); -***** test - P = [ 0.0 0.9 0.1; ... - 0.1 0.0 0.9; ... - 0.9 0.1 0.0 ]; - p = dtmc(P); - M = dtmc_fpt(P); - assert( diag(M)', 1./p, 1e-8 ); + A = p(1) + p(4); + printf("System availability %9.2f min/year\n",A*year/min); + printf("Mean time in RB state %9.2f min/year\n",p(3)*year/min); + printf("Mean time in RC state %9.2f min/year\n",p(2)*year/min); + printf("Mean time in 0 state %9.2f min/year\n",p(5)*year/min); + Q(3,:) = Q(5,:) = 0; # make states 3 and 5 absorbing + p0 = [1 0 0 0 0]; + MTBF = ctmcmtta(Q, p0) / hour; + printf("System MTBF %.2f hours\n",MTBF); +9 tests, 9 passed, 0 known failure, 0 skipped +[inst/qncmaba.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncmaba.m ***** test - P = [ 0 1 0 0 0; ... - .25 .0 .75 0 0; ... - 0 .5 0 .5 0; ... - 0 0 .75 0 .25; ... - 0 0 0 1 0 ]; - M = dtmc_fpt(P); - assert( M, [16 1 2.6667 6.3333 21.3333; ... - 15 4 1.6667 5.3333 20.3333; ... - 18.6667 3.6667 2.6667 3.6667 18.6667; ... - 20.3333 5.3333 1.6667 4 15; ... - 21.3333 6.3333 2.6667 1 16 ], 1e-4 ); + fail("qncmaba([],[])", "nonempty"); + fail("qncmaba([1 0], [1 2 3])", "2 rows"); + fail("qncmaba([1 0], [1 2 3; 4 5 -1])", "nonnegative"); + fail("qncmaba([1 2], [1 2 3; 4 5 6], [1 2 3])", "2 x 3"); + fail("qncmaba([1 2], [1 2 3; 4 5 6], [1 2 3; 4 5 -1])", "nonnegative"); + fail("qncmaba([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1])", "3 elements"); + fail("qncmaba([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 2])", "not supported"); + fail("qncmaba([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 2 3])", "2 elements"); + fail("qncmaba([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 -2])", "nonnegative"); ***** test - sz = 10; - P = reshape( 1:sz^2, sz, sz ); - normP = repmat(sum(P,2),1,columns(P)); - P = P./normP; - M = dtmc_fpt(P); - for i=1:rows(P) - for j=1:columns(P) - assert( M(i,j), 1 + dot(P(i,:), M(:,j)) - P(i,j)*M(j,j), 1e-8); - endfor + [Xl Xu Rl Ru] = qncmaba([0 0], [1 2 3; 1 2 3]); + assert( all(Xl(:) == 0) ); + assert( all(Xu(:) == 0) ); + assert( all(Rl(:) == 0) ); + assert( all(Ru(:) == 0) ); +***** demo + S = [10 7 5 4; ... + 5 2 4 6]; + NN=20; + Xl = Xu = Rl = Ru = Xmva = Rmva = zeros(NN,2); + for n=1:NN + N=[n,10]; + [a b c d] = qncmaba(N,S); + Xl(n,:) = a; Xu(n,:) = b; Rl(n,:) = c; Ru(n,:) = d; + [U R Q X] = qncmmva(N,S,ones(size(S))); + Xmva(n,:) = X(:,1)'; Rmva(n,:) = sum(R,2)'; endfor + subplot(2,2,1); + plot(1:NN,Xl(:,1), 1:NN,Xu(:,1), 1:NN,Xmva(:,1), ";MVA;", "linewidth", 2); + title("Class 1 throughput"); legend("boxoff"); + subplot(2,2,2); + plot(1:NN,Xl(:,2), 1:NN,Xu(:,2), 1:NN,Xmva(:,2), ";MVA;", "linewidth", 2); + title("Class 2 throughput"); legend("boxoff"); + subplot(2,2,3); + plot(1:NN,Rl(:,1), 1:NN,Ru(:,1), 1:NN,Rmva(:,1), ";MVA;", "linewidth", 2); + title("Class 1 response time"); legend("location", "northwest"); legend("boxoff"); + subplot(2,2,4); + plot(1:NN,Rl(:,2), 1:NN,Ru(:,2), 1:NN,Rmva(:,2), ";MVA;", "linewidth", 2); + title("Class 2 response time"); legend("location", "northwest"); legend("boxoff"); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qnosbsb.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnosbsb.m ***** test - P = zeros(9,9); - P(1,[2 4]) = .5; - P(2,[1 5 3]) = 1/3; - P(3,[2 6]) = .5; - P(4,[1 5 7]) = 1/3; - P(5,[2 4 6 8]) = 1/4; - P(6,[3 5 9]) = 1/3; - P(7,[4 8]) = .5; - P(8,[7 5 9]) = 1/3; - P(9,[6 8]) = .5; - M = dtmc_fpt(P); - assert( M(1:9 != 5,5)', [6 5 6 5 5 6 5 6], 100*eps ); -6 tests, 6 passed, 0 known failure, 0 skipped -[inst/erlangb.m] ->>>>> /build/octave-queueing-1.2.6/inst/erlangb.m + fail( "qnosbsb( 0.1, [] )", "vector" ); + fail( "qnosbsb( 0.1, [0 -1])", "nonnegative" ); + fail( "qnosbsb( 0, [1 2] )", "lambda" ); + fail( "qnosbsb( -1, [1 2])", "lambda" ); ***** test - fail("erlangb(1, -1)", "positive"); - fail("erlangb(-1, 1)", "positive"); - fail("erlangb(1, 0)", "positive"); - fail("erlangb(0, 1)", "positive"); - fail("erlangb('foo',1)", "positive"); - fail("erlangb(1,'bar')", "positive"); - fail("erlangb([1 1],[1 1 1])","common size"); + [Xl Xu Rl Ru] = qnosbsb(0.1,[1 2 3]); + assert( Xl, 0 ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qnomaba.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnomaba.m +***** test + fail( "qnomaba( [1 1], [1 1 1; 1 1 1; 1 1 1] )", "2 rows" ); 1 test, 1 passed, 0 known failure, 0 skipped -[inst/ctmc_check_Q.m] ->>>>> /build/octave-queueing-1.2.6/inst/ctmc_check_Q.m +[inst/qnmmmk.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnmmmk.m ***** test - Q = [0]; - [result err] = ctmc_check_Q(Q); - assert( result, 1 ); - assert( err, "" ); -warning: ctmc_check_Q is deprecated. Please use ctmcchkQ instead + lambda = mu = m = 1; + k = 10; + [U R Q X p0] = qnmmmk(lambda,mu,m,k); + assert( Q, k/2, 1e-7 ); + assert( U, 1-p0, 1e-7 ); +warning: qnmmmk is deprecated. Please use qsmmmk instead ***** test - N = 10; - Q = ctmc_bd(rand(1,N-1),rand(1,N-1)); - [result err] = ctmc_check_Q(Q); - assert( result, N ); - assert( err, "" ); + lambda = [1 0.8 2 9.2 0.01]; + mu = lambda + 0.17; + k = 12; + [U1 R1 Q1 X1] = qnmm1k(lambda,mu,k); + [U2 R2 Q2 X2] = qnmmmk(lambda,mu,1,k); + assert( U1, U2, 1e-5 ); + assert( R1, R2, 1e-5 ); + assert( Q1, Q2, 1e-5 ); + assert( X1, X2, 1e-5 ); + #assert( [U1 R1 Q1 X1], [U2 R2 Q2 X2], 1e-5 ); +warning: qnmm1k is deprecated. Please use qsmm1k instead ***** test - Q = [1 2 3; 4 5 6]; - [result err] = ctmc_check_Q(Q); - assert( result, 0 ); - assert( index(err, "square") > 0 ); + lambda = 0.9; + mu = 0.75; + k = 10; + [U1 R1 Q1 X1 p01] = qnmmmk(lambda,mu,1,k); + [U2 R2 Q2 X2 p02] = qnmm1k(lambda,mu,k); + assert( [U1 R1 Q1 X1 p01], [U2 R2 Q2 X2 p02], 1e-5 ); ***** test - N = 10; - Q = ctmc_bd(rand(1,N-1),rand(1,N-1)); - Q(2,1) = -1; - [result err] = ctmc_check_Q(Q); - assert( result, 0 ); - assert( index(err, "infinitesimal") > 0 ); + lambda = 0.8; + mu = 0.85; + m = 3; + k = 5; + [U1 R1 Q1 X1 p0] = qnmmmk( lambda, mu, m, k ); + birth = lambda*ones(1,k); + death = [ mu*linspace(1,m,m) mu*m*ones(1,k-m) ]; + q = ctmc(ctmc_bd( birth, death )); + U2 = dot( q, min( 0:k, m )/m ); + assert( U1, U2, 1e-4 ); + Q2 = dot( [0:k], q ); + assert( Q1, Q2, 1e-4 ); + assert( p0, q(1), 1e-4 ); ***** test - N = 10; - Q = ctmc_bd(rand(1,N-1),rand(1,N-1)); - Q(1,1) += 7; - [result err] = ctmc_check_Q(Q); - assert( result, 0 ); - assert( index(err, "infinitesimal") > 0 ); -5 tests, 5 passed, 0 known failure, 0 skipped -[inst/qnomaba.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnomaba.m + # This test comes from an example I found on the web + lambda = 40; + mu = 30; + m = 3; + k = 7; + [U R Q X p0] = qnmmmk( lambda, mu, m, k ); + assert( p0, 0.255037, 1e-6 ); + assert( R, 0.036517, 1e-6 ); ***** test - fail( "qnomaba( [1 1], [1 1 1; 1 1 1; 1 1 1] )", "2 rows" ); -1 test, 1 passed, 0 known failure, 0 skipped + # This test comes from an example I found on the web + lambda = 50; + mu = 10; + m = 4; + k = 6; + [U R Q X p0 pk] = qnmmmk( lambda, mu, m, k ); + assert( pk, 0.293543, 1e-6 ); +***** test + # This test comes from an example I found on the web + lambda = 3; + mu = 2; + m = 2; + k = 5; + [U R Q X p0 pk] = qnmmmk( lambda, mu, m, k ); + assert( p0, 0.179334, 1e-6 ); + assert( pk, 0.085113, 1e-6 ); + assert( Q, 2.00595, 1e-5 ); + assert( R-1/mu, 0.230857, 1e-6 ); # waiting time in the queue +7 tests, 7 passed, 0 known failure, 0 skipped [inst/qncmmva.m] >>>>> /build/octave-queueing-1.2.6/inst/qncmmva.m ***** test @@ -5372,183 +4693,195 @@ N = [3 0]; [U R Q X] = qncmmva(N, S, P) 17 tests, 17 passed, 0 known failure, 0 skipped -[inst/qnmix.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnmix.m +[inst/qnopen.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnopen.m ***** test - lambda = [1 0 0]; - N = [1 1 1]; - S = V = [1 1 1; 1 1 1; 1 1 1]; - fail( "qnmix( lambda, N, S, V)", "same time"); - N = [0 0 1]; - fail( "qnmix( lambda, N, S, V)", "open nor closed" ); - N = [0 1 2]; - m = [ 1 1 2 ]; - fail( "qnmix( lambda, N, S, V, m)", "single-server and delay" ); - S = V = [1 1 1; 1 1 1]; - fail( "qnmix( lambda, N, S, V)", "rows" ); + # Example 34.1 p. 572 + lambda = 3; + V = [16 7 8]; + S = [0.01 0.02 0.03]; + [U R Q X] = qnopen( lambda, S, V ); + assert( R, [0.0192 0.0345 0.107], 1e-2 ); + assert( U, [0.48 0.42 0.72], 1e-2 ); ***** test - # Example p. 148 Zahorjan et al. - lambda = [1 1/2 0 0]; - N = [0 0 1 1]; - V = [1 1; 1 1; 1 1; 1 1]; - S = [1/4 1/6; 1/2 1; 1/2 1; 1 4/3]; - [U R Q X] = qnmix(lambda, N, S, V ); - assert( Q(3,1), 4/19, 1e-4 ); - assert( Q(3,2), 15/19, 1e-4 ); - assert( Q(4,1), 5/19, 1e-4 ); - assert( Q(4,2), 14/19, 1e-4 ); - assert( Q, R.*X, 1e-5 ); # Little's Law + V = [1 1; 1 1]; + S = [1 3; 2 4]; + lambda = [3/19 2/19]; + [U R Q] = qnopen(lambda, S, diag( lambda / sum(lambda) ) * V); + assert( U(1,1), 3/19, 1e-6 ); + assert( U(2,1), 4/19, 1e-6 ); + assert( R(1,1), 19/12, 1e-6 ); + assert( R(1,2), 57/2, 1e-6 ); + assert( Q(1,1), .25, 1e-6 ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qnmm1k.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnmm1k.m ***** test - # Example 8.6 p. 345 Bolch et al. - lambda = [0.5 0.25 0 0]; - N = [0 0 1 1]; - V = [2 1; 2.5 1.5; 1 0.5; 1 0.4]; - S = [0.4 0.6; 0.8 1.6; 0.3 0.5; 0.5 0.8]; - [U R Q X] = qnmix( lambda, N, S, V ); - assert( U([1 2],:), [0.4 0.3; 0.5 0.6], 1e-3 ); - assert( R([3 4],:), [4.829 6.951; 7.727 11.636], 1e-3 ); - assert( Q([3 4],:), [0.582 0.418; 0.624 0.376], 1e-3 ); - assert( Q([1 2],:), [8.822 5.383; 11.028 10.766], 1e-3 ); #FIXME - assert( R([1 2],:), [8.822 10.766; 17.645 28.710], 1e-3 ); - assert( X(3,1)/V(3,1), 0.120, 1e-3 ); - assert( X(4,1)/V(4,1), 0.081, 1e-3 ); - assert( Q, R.*X, 1e-5 ); # Little's Law + lambda = mu = 1; + K = 10; + [U R Q X p0] = qnmm1k(lambda,mu,K); + assert( Q, K/2, 1e-7 ); + assert( U, 1-p0, 1e-7 ); ***** test - ## example figure 10 p. 26 Schwetman, "Implementing the Mean Value - ## Analysis for the Solution of Queueing Network Models", Technical - ## Report CSD-TR-355, feb 15, 1982, Purdue University. - S = [.25 0; .25 .10]; - V = [1 0; 1 1]; - lambda = [1 0]; - N = [0 3]; - [U R Q X] = qnmix( lambda, N, S, V ); - assert( U(1,1), .25, 1e-3 ); - assert( X(1,1), 1.0, 1e-3 ); - assert( [R(1,1) R(2,1) R(2,2)], [1.201 0.885 0.135], 1e-3 ); - assert( Q, R.*X, 1e-5 ); # Little's Law -4 tests, 4 passed, 0 known failure, 0 skipped -[inst/qncsgb.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncsgb.m + # Compare result with one obtained by solvind the CTMC + lambda = 0.8; + mu = 0.8; + K = 10; + [U1 R1 Q1 X1] = qnmm1k( lambda, mu, K ); + birth = lambda*ones(1,K); + death = mu*ones(1,K); + q = ctmc(ctmc_bd( birth, death )); + U2 = 1-q(1); + Q2 = dot( [0:K], q ); + assert( U1, U2, 1e-4 ); + assert( Q1, Q2, 1e-4 ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qncsmvaap.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncsmvaap.m ***** test - fail( "qncsgb( 1, [] )", "vector" ); - fail( "qncsgb( 1, [0 -1])", "nonnegative" ); - fail( "qncsgb( 0, [1 2] )", "> 0" ); - fail( "qncsgb( -1, [1 2])", "nonnegative" ); - fail( "qncsgb( 1, [1 2],1,[1 -1])", "single server" ); -***** # shared test function -***** function test_gb( D, expected, Z=0 ) - for i=1:rows(expected) - N = expected(i,1); - [X_lower X_upper Q_lower Q_upper] = qncsgb(N,D,1,1,Z); - X_exp_lower = expected(i,2); - X_exp_upper = expected(i,3); - assert( [N X_lower X_upper], [N X_exp_lower X_exp_upper], 1e-4 ) - endfor -***** xtest - # table IV - D = [ 0.1 0.1 0.09 0.08 ]; - # N X_lower X_upper - expected = [ 2 4.3040 4.3174; ... - 5 6.6859 6.7524; ... - 10 8.1521 8.2690; ... - 20 9.0947 9.2431; ... - 80 9.8233 9.8765 ]; - test_gb(D, expected); -!!!!! known failure -ASSERT errors for: assert ([N, X_lower, X_upper],[N, X_exp_lower, X_exp_upper],1e-4) - - Location | Observed | Expected | Reason - (3) 4.3813 4.3174 Abs err 0.063891 exceeds tol 0.0001 by 0.06 -***** xtest - # table V - D = [ 0.1 0.1 0.09 0.08 ]; - Z = 1; - # N X_lower X_upper - expected = [ 2 1.4319 1.5195; ... - 5 3.3432 3.5582; ... - 10 5.7569 6.1410; ... - 20 8.0856 8.6467; ... - 80 9.7147 9.8594]; - test_gb(D, expected, Z); -!!!!! known failure -ASSERT errors for: assert ([N, X_lower, X_upper],[N, X_exp_lower, X_exp_upper],1e-4) - - Location | Observed | Expected | Reason - (3) 1.5219 1.5195 Abs err 0.0023822 exceeds tol 0.0001 by 0.002 + fail( "qncsmvaap()", "Invalid" ); + fail( "qncsmvaap( 10, [1 2], [1 2 3] )", "S, V and m" ); + fail( "qncsmvaap( 10, [-1 1], [1 1] )", ">= 0" ); + fail( "qncsmvaap( 10, [1 2], [1 2], [1 2] )", "supports"); + fail( "qncsmvaap( 10, [1 2], [1 2], [1 1], 0, -1)", "tol"); ***** test - P = [0 0.3 0.7; 1 0 0; 1 0 0]; - S = [1 0.6 0.2]; + # Example p. 117 Lazowska et al. + S = [0.605 2.1 1.35]; + V = [1 1 1]; + N = 3; + Z = 15; + m = 1; + [U R Q X] = qncsmvaap(N, S, V, m, Z); + Rs = dot(V,R); + Xs = N/(Z+Rs); + assert( Q, [0.0973 0.4021 0.2359], 1e-3 ); + assert( Xs, 0.1510, 1e-3 ); + assert( Rs, 4.87, 1e-3 ); +***** demo + S = [ 0.125 0.3 0.2 ]; + V = [ 16 10 5 ]; + N = 30; m = ones(1,3); - V = qncsvisits(P); - Z = 2; - Nmax = 20; - tol = 1e-5; # compensate for numerical errors - ## Test case with Z>0 - for n=1:Nmax - [X_gb_lower X_gb_upper NC NC Q_gb_lower Q_gb_upper] = qncsgb(n, S.*V, 1, 1, Z); - [U R Q X] = qnclosed( n, S, V, m, Z ); - X_mva = X(1)/V(1); - assert( X_gb_lower <= X_mva+tol ); - assert( X_gb_upper >= X_mva-tol ); - assert( Q_gb_lower <= Q+tol ); # compensate for numerical errors - assert( Q_gb_upper >= Q-tol ); # compensate for numerical errors + Z = 4; + Xmva = Xapp = Rmva = Rapp = zeros(1,N); + for n=1:N + [U R Q X] = qncsmva(n,S,V,m,Z); + Xmva(n) = X(1)/V(1); + Rmva(n) = dot(R,V); + [U R Q X] = qncsmvaap(n,S,V,m,Z); + Xapp(n) = X(1)/V(1); + Rapp(n) = dot(R,V); endfor + subplot(2,1,1); + plot(1:N, Xmva, ";Exact;", "linewidth", 2, 1:N, Xapp, "x;Approximate;", "markersize", 7); + legend("location","southeast"); legend("boxoff"); + ylabel("Throughput X(n)"); + subplot(2,1,2); + plot(1:N, Rmva, ";Exact;", "linewidth", 2, 1:N, Rapp, "x;Approximate;", "markersize", 7); + legend("location","southeast"); legend("boxoff"); + ylabel("Response Time R(n)"); + xlabel("Number of Requests n"); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/ctmctaexps.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmctaexps.m ***** test - P = [0 0.3 0.7; 1 0 0; 1 0 0]; - S = [1 0.6 0.2]; - V = qncsvisits(P); - Nmax = 20; - tol = 1e-5; # compensate for numerical errors + Q = [ 0 0.1 0 0; ... + 0.9 0 0.1 0; ... + 0 0.9 0 0.1; ... + 0 0 0 0 ]; + Q -= diag( sum(Q,2) ); + M = ctmctaexps(Q, [1 0 0 0]); + assert( sum(M), 1, 10*eps ); +***** demo + lambda = 0.5; + N = 4; + birth = lambda*linspace(1,N-1,N-1); + death = zeros(1,N-1); + Q = diag(birth,1)+diag(death,-1); + Q -= diag(sum(Q,2)); + t = linspace(1e-5,30,100); + p = zeros(1,N); p(1)=1; + M = zeros(length(t),N); + for i=1:length(t) + M(i,:) = ctmctaexps(Q,t(i),p); + endfor + clf; + plot(t, M(:,1), ";State 1;", "linewidth", 2, ... + t, M(:,2), ";State 2;", "linewidth", 2, ... + t, M(:,3), ";State 3;", "linewidth", 2, ... + t, M(:,4), ";State 4 (absorbing);", "linewidth", 2 ); + legend("location","east"); legend("boxoff"); + xlabel("Time"); + ylabel("Time-averaged Expected sojourn time"); +***** demo + sec = 1; + min = sec*60; + hour = 60*min; + day = 24*hour; - ## Test case with Z=0 - for n=1:Nmax - [X_gb_lower X_gb_upper NC NC Q_gb_lower Q_gb_upper] = qncsgb(n, S.*V); - [U R Q X] = qnclosed( n, S, V ); - X_mva = X(1)/V(1); - assert( X_gb_lower <= X_mva+tol ); - assert( X_gb_upper >= X_mva-tol ); - assert( Q_gb_lower <= Q+tol ); - assert( Q_gb_upper >= Q-tol ); + # state space enumeration {2, RC, RB, 1, 0} + a = 1/(10*min); # 1/a = duration of reboot (10 min) + b = 1/(30*sec); # 1/b = reconfiguration time (30 sec) + g = 1/(5000*hour); # 1/g = processor MTTF (5000 hours) + d = 1/(4*hour); # 1/d = processor MTTR (4 hours) + c = 0.9; # coverage + Q = [ -2*g 2*c*g 2*(1-c)*g 0 0; ... + 0 -b 0 b 0; ... + 0 0 -a a 0; ... + d 0 0 -(g+d) g; ... + 0 0 0 d -d]; + p = ctmc(Q); + printf("System availability: %f\n",p(1)+p(4)); + TT = linspace(0,1*day,101); + PP = ctmctaexps(Q,TT,[1 0 0 0 0]); + A = At = Abart = zeros(size(TT)); + A(:) = p(1) + p(4); # steady-state availability + for n=1:length(TT) + t = TT(n); + p = ctmc(Q,t,[1 0 0 0 0]); + At(n) = p(1) + p(4); # instantaneous availability + Abart(n) = PP(n,1) + PP(n,4); # interval base availability endfor -5 tests, 3 passed, 2 known failures, 0 skipped -[inst/qnvisits.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnvisits.m + clf; + semilogy(TT,A,";Steady-state;", ... + TT,At,";Instantaneous;", ... + TT,Abart,";Interval base;"); + ax = axis(); + ax(3) = 1-1e-5; + axis(ax); + legend("boxoff"); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/dtmcexps.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmcexps.m ***** test - P = [-1 0; 0 0]; - fail( "qnvisits(P)", "not a transition probability" ); - P = [1 0; 0.5 0]; - fail( "qnvisits(P)", "not a transition probability" ); - P = [1 0; 0 1]; lambda=[0 -1]; - fail( "qnvisits(P,lambda)", "contains negative" ); -warning: qnvisits is deprecated. Please use one of qncsvisits, qnosvisits, qncmvisits, qnomvisits instead + P = dtmcbd([1 1 1 1], [0 0 0 0]); + L = dtmcexps(P,[1 0 0 0 0]); + t = dtmcmtta(P,[1 0 0 0 0]); + assert( L, [1 1 1 1 0] ); + assert( sum(L), t ); ***** test - - ## Closed, single class network - - P = [0 0.3 0.7; 1 0 0; 1 0 0]; - V = qnvisits(P); - assert( V*P,V,1e-5 ); - assert( V, [1 0.3 0.7], 1e-5 ); + P = dtmcbd(linspace(0.1,0.4,5),linspace(0.4,0.1,5)); + p0 = [1 0 0 0 0 0]; + L = dtmcexps(P,0,p0); + assert( L, p0 ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qnclosedab.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnclosedab.m ***** test - - ## Open, single class network - - P = [0 0.2 0.5; 1 0 0; 1 0 0]; - lambda = [ 0.1 0.3 0.2 ]; - V = qnvisits(P,lambda); - assert( V*P+lambda/sum(lambda),V,1e-5 ); + fail("qnclosedab(-1,0)", "N must be"); + fail("qnclosedab(1,[])", "nonempty"); + fail("qnclosedab(1,[-1 2])", "nonnegative"); + fail("qnclosedab(1,[1 2 3],-1)", "nonnegative"); +warning: qnclosedab is deprecated. Please use qncsaba instead ***** test - - ## Test tolerance of the qnvisits() function. - ## This test builds transition probability matrices and tries - ## to compute the visit counts on them. - - for k=[5, 10, 20, 50] - P = reshape(1:k^2, k, k); - P = P ./ repmat(sum(P,2),1,k); - V = qnvisits(P); - assert( V*P, V, 1e-5 ); - endfor + N = 20; + D = [ 4.6*2 8 ]; + Z = 120; + [X_l X_u R_l R_u] = qnclosedab(N, D, Z); + assert( [X_u R_l], [0.109 64], 1e-3 ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qncmvisits.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncmvisits.m ***** test ## Closed, multiclass network @@ -5559,7 +4892,7 @@ P(1,2,1,1) = 1; P(2,1,2,3) = 1; P(2,3,2,1) = 1; - V = qnvisits(P); + V = qncmvisits(P); for c=1:C for k=1:K assert(V(c,k), sum(sum(V .* P(:,:,c,k))), 1e-5); @@ -5568,7 +4901,7 @@ ***** test ## Test multiclass network. Example from Schwetman (figure 7, page 9 of - ## hhttp://docs.lib.purdue.edu/cstech/259/ + ## http://docs.lib.purdue.edu/cstech/259/ ## "Testing network-of-queues software, technical report CSD-TR 330, ## Purdue University). @@ -5586,45 +4919,20 @@ P(2,1,2,4) = .49; P(2,3,2,1) = 1; P(2,4,2,1) = 1; - V = qnvisits(P); + V = qncmvisits(P); for c=1:C for i=1:K assert(V(c,i), sum(sum(V .* P(:,:,c,i))), 1e-5); endfor endfor ***** test - C = 2; K = 4; - P = zeros(C,K,C,K); - # class 1 routing - P(1,1,1,1) = .05; - P(1,1,1,2) = .45; - P(1,1,1,3) = .5; - P(1,2,1,1) = 0.1; - P(1,3,1,1) = 0.2; - # class 2 routing - P(2,1,2,1) = .01; - P(2,1,2,3) = .5; - P(2,1,2,4) = .49; - P(2,3,2,1) = 0.2; - P(2,4,2,1) = 0.16; - lambda = [0.1 0 0 0.1 ; 0 0 0.2 0.1]; - lambda_sum = sum(lambda(:)); - V = qnvisits(P, lambda); - assert( all(V(:)>=0) ); - for i=1:K - for c=1:C - assert(V(c,i), lambda(c,i) / lambda_sum + sum(sum(V .* P(:,:,c,i))), 1e-5); - endfor - endfor -***** test ## Network with class switching. ## This is example in figure 9 of ## Schwetman, "Implementing the Mean Value Analysis ## Algorithm fort the solution of Queueing Network Models", Technical ## Report CSD-TR-355, Department of Computer Science, Purdue Univrsity, - ## Feb 15, 1982 - ## http://docs.lib.purdue.edu/cstech/286/ + ## Feb 15, 1982, http://docs.lib.purdue.edu/cstech/286/ C = 2; K = 3; S = [.01 .07 .10; ... @@ -5639,7 +4947,7 @@ P(1,2,1,1) = P(1,3,1,1) = 1; P(2,2,2,1) = P(2,3,2,1) = 1; N = [3 0]; - V = qnvisits(P); + V = qncmvisits(P); VV = [10 7 2; 5 1.5 2.5]; # result given in Schwetman; our function computes something different, but that's ok since visit counts are actually ratios assert( V ./ repmat(V(:,1),1,K), VV ./ repmat(VV(:,1),1,K), 1e-5 ); ***** test @@ -5652,7 +4960,7 @@ P(1,2,1,1) = 1; P(2,1,2,3) = 1; P(2,3,2,1) = 1; - [nc r] = qnvisits(P); + [nc r] = qncmvisits(P); assert( r(1) != r(2) ); ***** test @@ -5664,7 +4972,7 @@ P(1,2,2,1) = 1; P(2,1,2,3) = .5; P(2,3,1,1) = 1; - [nc r] = qnvisits(P); + [nc r] = qncmvisits(P); assert( r(1) == r(2) ); ***** test @@ -5678,7 +4986,7 @@ P(2,2,1,1) = 1; P(2,1,1,2) = 1; P(1,2,2,1) = 1; - fail( "qnvisits(P)", "different"); + fail( "qncmvisits(P)", "different"); ***** test ## Network with two classes representing independent chains. @@ -5692,7 +5000,7 @@ P = zeros(C,K,C,K); P(1,1,1,3) = P(1,3,1,1) = 1; P(2,2,2,3) = P(2,3,2,2) = 1; - V = qnvisits(P); + V = qncmvisits(P,[1,2]); assert( V, [1 0 1; 0 1 1], 1e-5 ); ***** test C = 2; @@ -5702,7 +5010,7 @@ P(1,2,1,3) = 1; P(1,3,2,2) = 1; P(2,2,1,1) = 1; - [V ch] = qnvisits(P); + [V ch] = qncmvisits(P); assert( ch, [1 1] ); ***** test C = 2; @@ -5713,114 +5021,668 @@ P(1,3,2,2) = 1; P(2,2,2,1) = 1; P(2,1,1,2) = 1; - [V ch] = qnvisits(P); + [V ch] = qncmvisits(P); assert( ch, [1 1] ); -14 tests, 14 passed, 0 known failure, 0 skipped -[inst/qnomvisits.m] ->>>>> /build/octave-queueing-1.2.6/inst/qnomvisits.m +9 tests, 9 passed, 0 known failure, 0 skipped +[inst/qncmpopmix.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncmpopmix.m ***** test - fail( "qnomvisits( zeros(3,3,3), [1 1 1] )", "matrix"); + N = [2 3 4]; + f = qncmpopmix( 1, N ); + assert( f, [1 0 0; 0 1 0; 0 0 1] ); + f = qncmpopmix( 2, N ); + assert( f, [2 0 0; 1 1 0; 0 2 0; 1 0 1; 0 1 1; 0 0 2] ); + f = qncmpopmix( 3, N ); + assert( f, [2 1 0; 1 2 0; 0 3 0; 2 0 1; 1 1 1; 0 2 1; 1 0 2; 0 1 2; 0 0 3] ); ***** test - C = 2; K = 4; - P = zeros(C,K,C,K); - # class 1 routing - P(1,1,1,1) = .05; - P(1,1,1,2) = .45; - P(1,1,1,3) = .5; - P(1,2,1,1) = 0.1; - P(1,3,1,1) = 0.2; - # class 2 routing - P(2,1,2,1) = .01; - P(2,1,2,3) = .5; - P(2,1,2,4) = .49; - P(2,3,2,1) = 0.2; - P(2,4,2,1) = 0.16; - lambda = [0.1 0 0 0.1 ; 0 0 0.2 0.1]; - lambda_sum = sum(lambda(:)); - V = qnomvisits(P, lambda); - assert( all(V(:)>=0) ); - for i=1:K - for c=1:C - assert(V(c,i), lambda(c,i) / lambda_sum + sum(sum(V .* P(:,:,c,i))), 1e-5); - endfor + N = [2 1]; + f = qncmpopmix( 1, N ); + assert( f, [1 0; 0 1] ); + f = qncmpopmix( 2, N ); + assert( f, [2 0; 1 1] ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/dtmcbd.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmcbd.m +***** test + birth = [.5 .5 .3]; + death = [.6 .2 .3]; + fail("dtmcbd(birth,death)","must be"); +***** demo + birth = [ .2 .3 .4 ]; + death = [ .1 .2 .3 ]; + P = dtmcbd( birth, death ); + disp(P) +1 test, 1 passed, 0 known failure, 0 skipped +[inst/qnosvisits.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnosvisits.m +***** test + fail( "qnosvisits([0 .5; .5 0],[0 -1])", "contains negative" ); + fail( "qnosvisits([1 1 1; 1 1 1], [1 1])", "square" ); +***** test + + ## Open, single class network + + P = [0 0.2 0.5; 1 0 0; 1 0 0]; + lambda = [ 0.1 0.3 0.2 ]; + V = qnosvisits(P,lambda); + assert( V*P+lambda/sum(lambda),V,1e-5 ); +***** demo + p = 0.3; + lambda = 1.2 + P = [0 0.3 0.5; ... + 1 0 0 ; ... + 1 0 0 ]; + V = qnosvisits(P,[1.2 0 0]) +***** demo + P = [ 0 0.4 0.6 0; ... + 0.2 0 0.2 0.6; ... + 0 0 0 1; ... + 0 0 0 0 ]; + lambda = [0.1 0 0 0.3]; + V = qnosvisits(P,lambda); + S = [2 1 2 1.8]; + m = [3 1 1 2]; + [U R Q X] = qnos( sum(lambda), S, V, m ) +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/qncsaba.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncsaba.m +***** test + fail("qncsaba(-1,0)", "N must be"); + fail("qncsaba(1,[])", "nonempty"); + fail("qncsaba(1,[-1 2])", "nonnegative"); + fail("qncsaba(1,[1 2],[1 2 3])", "incompatible size"); + fail("qncsaba(1,[1 2 3],[1 2 -1])", "nonnegative"); + fail("qncsaba(1,[1 2 3],[1 2 3],[1 2])", "incompatible size"); + fail("qncsaba(1,[1 2 3],[1 2 3],[1 2 1])", "not supported"); + fail("qncsaba(1,[1 2 3],[1 2 3],[1 1 1],-1)", "nonnegative"); + fail("qncsaba(1,[1 2 3],[1 2 3],1,[0 0])", "scalar"); +***** test + N = 20; + S = [ 4.6*2 8 ]; + Z = 120; + [X_l X_u R_l R_u] = qncsaba(N, S, ones(size(S)), ones(size(S)), Z); + assert( [X_u R_l], [0.109 64], 1e-3 ); +2 tests, 2 passed, 0 known failure, 0 skipped +[inst/erlangc.m] +>>>>> /build/octave-queueing-1.2.6/inst/erlangc.m +***** test + fail("erlangc('foo',1)", "positive"); + fail("erlangc(1,'bar')", "positive"); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/qncsmvald.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncsmvald.m +***** test + N = 0; + S = [1 2; 3 4; 5 6; 7 8]; + V = [1 1 1 4]; + [U R Q X] = qncsmvald(N, S, V); + assert( U, 0*V ); + assert( R, 0*V ); + assert( Q, 0*V ); + assert( X, 0*V ); +***** test + # Exsample 3.42 p. 577 Jain + V = [ 16 10 5 ]; + N = 20; + S = [ 0.125 0.3 0.2 ]; + Sld = repmat( S', 1, N ); + Z = 4; + [U1 R1 Q1 X1] = qncsmvald(N,Sld,V,Z); + [U2 R2 Q2 X2] = qncsmva(N,S,V,ones(1,3),Z); + assert( U1, U2, 1e-3 ); + assert( R1, R2, 1e-3 ); + assert( Q1, Q2, 1e-3 ); + assert( X1, X2, 1e-3 ); +***** test + # Example 8.7 p. 349 Bolch et al. + N = 3; + Sld = 1 ./ [ 2 4 4; ... + 1.667 1.667 1.667; ... + 1.25 1.25 1.25; ... + 1 2 3 ]; + V = [ 1 .5 .5 1 ]; + [U R Q X] = qncsmvald(N,Sld,V); + assert( Q, [0.624 0.473 0.686 1.217], 1e-3 ); + assert( R, [0.512 0.776 1.127 1], 1e-3 ); + assert( all( U<=1) ); +***** test + # Example 8.4 p. 333 Bolch et al. + N = 3; + S = [ .5 .6 .8 1 ]; + m = [2 1 1 N]; + Sld = zeros(3,N); + Sld(1,:) = .5 ./ [1 2 2]; + Sld(2,:) = [.6 .6 .6]; + Sld(3,:) = [.8 .8 .8]; + Sld(4,:) = 1 ./ [1 2 3]; + V = [ 1 .5 .5 1 ]; + [U1 R1 Q1 X1] = qncsmvald(N,Sld,V); + [U2 R2 Q2 X2] = qncsmva(N,S,V,m); + ## Note that qncsmvald computes the utilization in a different + ## way as qncsmva; in fact, qncsmva knows that service + ## center i has m(i)>1 servers, but qncsmvald does not. Thus, + ## utilizations for multiple-server nodes cannot be compared + assert( U1([2,3]), U2([2,3]), 1e-3 ); + assert( R1, R2, 1e-3 ); + assert( Q1, Q2, 1e-3 ); + assert( X1, X2, 1e-3 ); +4 tests, 4 passed, 0 known failure, 0 skipped +[inst/qncsmvablo.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncsmvablo.m +***** test + fail( "qncsmvablo( 10, [1 1], [4 5], [0 1; 1 0] )", "capacity"); + fail( "qncsmvablo( 6, [1 1], [4 5], [0 1; 1 1] )", "stochastic"); + fail( "qncsmvablo( 5, [1 1 1], [1 1], [0 1; 1 1] )", "3 elements"); +***** test + # This is the example on section v) p. 422 of the reference paper + M = [12 10 14]; + P = [0 1 0; 0 0 1; 1 0 0]; + S = [1/1 1/2 1/3]; + K = 27; + [U R Q X]=qncsmvablo( K, S, M, P ); + assert( R, [11.80 1.66 14.4], 1e-2 ); +***** test + # This is example 2, i) and ii) p. 424 of the reference paper + M = [4 5 5]; + S = [1.5 2 1]; + P = [0 1 0; 0 0 1; 1 0 0]; + K = 10; + [U R Q X]=qncsmvablo( K, S, M, P ); + assert( R, [6.925 8.061 4.185], 1e-3 ); + K = 12; + [U R Q X]=qncsmvablo( K, S, M, P ); + assert( R, [7.967 9.019 8.011], 1e-3 ); +***** test + # This is example 3, i) and ii) p. 424 of the reference paper + M = [8 7 6]; + S = [0.2 1.2 1.4]; + P = [ 0 0.5 0.5; 1 0 0; 1 0 0 ]; + K = 10; + [U R Q X] = qncsmvablo( K, S, M, P ); + assert( R, [1.674 5.007 7.639], 1e-3 ); + K = 12; + [U R Q X] = qncsmvablo( K, S, M, P ); + assert( R, [2.166 5.372 6.567], 1e-3 ); +***** test + # Network which never blocks, central server model + M = [50 50 50]; + S = [1 1/0.8 1/0.4]; + P = [0 0.7 0.3; 1 0 0; 1 0 0]; + K = 40; + [U1 R1 Q1] = qncsmvablo( K, S, M, P ); + V = qncsvisits(P); + [U2 R2 Q2] = qncsmva( K, S, V ); + assert( U1, U2, 1e-5 ); + assert( R1, R2, 1e-5 ); + assert( Q1, Q2, 1e-5 ); +5 tests, 5 passed, 0 known failure, 0 skipped +[inst/qncsgb.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncsgb.m +***** test + fail( "qncsgb( 1, [] )", "vector" ); + fail( "qncsgb( 1, [0 -1])", "nonnegative" ); + fail( "qncsgb( 0, [1 2] )", "> 0" ); + fail( "qncsgb( -1, [1 2])", "nonnegative" ); + fail( "qncsgb( 1, [1 2],1,[1 -1])", "single server" ); +***** # shared test function +***** function test_gb( D, expected, Z=0 ) + for i=1:rows(expected) + N = expected(i,1); + [X_lower X_upper Q_lower Q_upper] = qncsgb(N,D,1,1,Z); + X_exp_lower = expected(i,2); + X_exp_upper = expected(i,3); + assert( [N X_lower X_upper], [N X_exp_lower X_exp_upper], 1e-4 ) endfor +***** xtest + # table IV + D = [ 0.1 0.1 0.09 0.08 ]; + # N X_lower X_upper + expected = [ 2 4.3040 4.3174; ... + 5 6.6859 6.7524; ... + 10 8.1521 8.2690; ... + 20 9.0947 9.2431; ... + 80 9.8233 9.8765 ]; + test_gb(D, expected); +!!!!! known failure +ASSERT errors for: assert ([N, X_lower, X_upper],[N, X_exp_lower, X_exp_upper],1e-4) + + Location | Observed | Expected | Reason + (3) 4.3813 4.3174 Abs err 0.063891 exceeds tol 0.0001 by 0.06 +***** xtest + # table V + D = [ 0.1 0.1 0.09 0.08 ]; + Z = 1; + # N X_lower X_upper + expected = [ 2 1.4319 1.5195; ... + 5 3.3432 3.5582; ... + 10 5.7569 6.1410; ... + 20 8.0856 8.6467; ... + 80 9.7147 9.8594]; + test_gb(D, expected, Z); +!!!!! known failure +ASSERT errors for: assert ([N, X_lower, X_upper],[N, X_exp_lower, X_exp_upper],1e-4) + + Location | Observed | Expected | Reason + (3) 1.5219 1.5195 Abs err 0.0023822 exceeds tol 0.0001 by 0.002 ***** test - # example 7.7 p. 304 Bolch et al. - # Note that the book uses a slightly different notation than - # what we use here. Specifically, the book defines the routing - # probabilities as P(i,r,j,s) (i,j are service centers, r,s are job - # classes) while the queueing package uses P(r,i,s,j). - # A more serious problem arises in the definition of external arrivals. - # The computation of V(r,i) as given in the book (called e_ir - # in Eq 7.14) is performed in terms of P_{0, js}, defined as - # "the probability in an open network that a job from outside the network - # enters the jth node as a job of the sth class" (p. 267). This is - # compliant with eq. 7.12 where the external class r arrival rate at center - # i is computed as \lambda * P_{0,ir}. However, example 7.7 wrongly - # defines P_{0,11} = P_{0,12} = 1, instead of P_{0,11} = P_{0,12} = 0.5 - # Therefore the resulting visit ratios they obtain must be divided by two. - P = zeros(2,3,2,3); - lambda = S = zeros(2,3); - P(1,1,1,2) = 0.4; - P(1,1,1,3) = 0.3; - P(1,2,1,1) = 0.6; - P(1,2,1,3) = 0.4; - P(1,3,1,1) = 0.5; - P(1,3,1,2) = 0.5; - P(2,1,2,2) = 0.3; - P(2,1,2,3) = 0.6; - P(2,2,2,1) = 0.7; - P(2,2,2,3) = 0.3; - P(2,3,2,1) = 0.4; - P(2,3,2,2) = 0.6; - lambda(1,1) = lambda(2,1) = 1; - V = qnomvisits(P,lambda); - assert( V, [ 3.333 2.292 1.917; 10 8.049 8.415] ./ 2, 1e-3); -3 tests, 3 passed, 0 known failure, 0 skipped -[inst/qncmbsb.m] ->>>>> /build/octave-queueing-1.2.6/inst/qncmbsb.m + P = [0 0.3 0.7; 1 0 0; 1 0 0]; + S = [1 0.6 0.2]; + m = ones(1,3); + V = qncsvisits(P); + Z = 2; + Nmax = 20; + tol = 1e-5; # compensate for numerical errors + ## Test case with Z>0 + for n=1:Nmax + [X_gb_lower X_gb_upper NC NC Q_gb_lower Q_gb_upper] = qncsgb(n, S.*V, 1, 1, Z); + [U R Q X] = qnclosed( n, S, V, m, Z ); + X_mva = X(1)/V(1); + assert( X_gb_lower <= X_mva+tol ); + assert( X_gb_upper >= X_mva-tol ); + assert( Q_gb_lower <= Q+tol ); # compensate for numerical errors + assert( Q_gb_upper >= Q-tol ); # compensate for numerical errors + endfor ***** test - fail("qncmbsb([],[])", "nonempty"); - fail("qncmbsb([1 0], [1 2 3])", "2 rows"); - fail("qncmbsb([1 0], [1 2 3; 4 5 -1])", "nonnegative"); - fail("qncmbsb([1 2], [1 2 3; 4 5 6], [1 2 3])", "2 x 3"); - fail("qncmbsb([1 2], [1 2 3; 4 5 6], [1 2 3; 4 5 -1])", "nonnegative"); - fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1])", "3 elements"); - fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 2])", "not supported"); - fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 2 3])", "2 elements"); - fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 -2])", "nonnegative"); - fail("qncmbsb([1 2], [1 2 3; 1 2 3], [1 2 3; 1 2 3], [1 1 -1],[1 0])", "only supports"); + P = [0 0.3 0.7; 1 0 0; 1 0 0]; + S = [1 0.6 0.2]; + V = qncsvisits(P); + Nmax = 20; + tol = 1e-5; # compensate for numerical errors + + ## Test case with Z=0 + for n=1:Nmax + [X_gb_lower X_gb_upper NC NC Q_gb_lower Q_gb_upper] = qncsgb(n, S.*V); + [U R Q X] = qnclosed( n, S, V ); + X_mva = X(1)/V(1); + assert( X_gb_lower <= X_mva+tol ); + assert( X_gb_upper >= X_mva-tol ); + assert( Q_gb_lower <= Q+tol ); + assert( Q_gb_upper >= Q-tol ); + endfor +5 tests, 3 passed, 2 known failures, 0 skipped +[inst/dtmc.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmc.m ***** test - [Xl Xu Rl Ru] = qncmbsb([0 0], [1 2 3; 1 2 3]); - assert( all(Xl(:) == 0) ); - assert( all(Xu(:) == 0) ); - assert( all(Rl(:) == 0) ); - assert( all(Ru(:) == 0) ); + P = [0.75 0.25; 0.5 0.5]; + p = dtmc(P); + assert( p*P, p, 1e-5 ); + assert( p, [0.6666 0.3333], 1e-4 ); +***** test + #Example 2.11 p. 44 Bolch et al. + P = [0.5 0.5; 0.5 0.5]; + p = dtmc(P); + assert( p, [0.5 0.5], 1e-3 ); +***** test + fail("dtmc( [1 1 1; 1 1 1] )", "square"); +***** test + a = 0.2; + b = 0.8; + P = [1-a a; b 1-b]; + plim = dtmc(P); + p = dtmc(P, 100, [1 0]); + assert( plim, p, 1e-5 ); +***** test + P = [0 1 0 0 0; ... + .25 0 .75 0 0; ... + 0 .5 0 .5 0; ... + 0 0 .75 0 .25; ... + 0 0 0 1 0 ]; + p = dtmc(P); + assert( p, [.0625 .25 .375 .25 .0625], 10*eps ); +***** test + P = zeros(9,9); + P(1,[2 4]) = 1/2; + P(2,[1 5 3]) = 1/3; + P(3,[2 6]) = 1/2; + P(4,[1 5 7]) = 1/3; + P(5,[2 4 6 8]) = 1/4; + P(6,[3 5 9]) = 1/3; + P(7,[4 8]) = 1/2; + P(8,[7 5 9]) = 1/3; + P(9,[6 8]) = 1/2; + p = dtmc(P); + assert( p, [1/12 1/8 1/12 1/8 1/6 1/8 1/12 1/8 1/12], 10*eps ); ***** demo - S = [10 7 5 4; ... - 5 2 4 6]; - NN=20; - Xl = Xu = Rl = Ru = Xmva = Rmva = zeros(NN,2); - for n=1:NN - N=[n,10]; - [a b c d] = qncmbsb(N,S); - Xl(n,:) = a; Xu(n,:) = b; Rl(n,:) = c; Ru(n,:) = d; - [U R Q X] = qncmmva(N,S,ones(size(S))); - Xmva(n,:) = X(:,1)'; Rmva(n,:) = sum(R,2)'; + P = zeros(9,9); + P(1,[2 4] ) = 1/2; + P(2,[1 5 3] ) = 1/3; + P(3,[2 6] ) = 1/2; + P(4,[1 5 7] ) = 1/3; + P(5,[2 4 6 8]) = 1/4; + P(6,[3 5 9] ) = 1/3; + P(7,[4 8] ) = 1/2; + P(8,[7 5 9] ) = 1/3; + P(9,[6 8] ) = 1/2; + p = dtmc(P); + disp(p) +***** demo + a = 0.2; + b = 0.15; + P = [ 1-a a; b 1-b]; + T = 0:14; + pp = zeros(2,length(T)); + for i=1:length(T) + pp(:,i) = dtmc(P,T(i),[1 0]); endfor - subplot(2,2,1); - plot(1:NN,Xl(:,1), 1:NN,Xu(:,1), 1:NN,Xmva(:,1),";MVA;", "linewidth", 2); - title("Class 1 throughput"); legend("boxoff"); - subplot(2,2,2); - plot(1:NN,Xl(:,2), 1:NN,Xu(:,2), 1:NN,Xmva(:,2),";MVA;", "linewidth", 2); - title("Class 2 throughput"); legend("boxoff"); - subplot(2,2,3); - plot(1:NN,Rl(:,1), 1:NN,Ru(:,1), 1:NN,Rmva(:,1),";MVA;", "linewidth", 2); - title("Class 1 response time"); legend("location", "northwest"); legend("boxoff"); - subplot(2,2,4); - plot(1:NN,Rl(:,2), 1:NN,Ru(:,2), 1:NN,Rmva(:,2),";MVA;", "linewidth", 2); - title("Class 2 response time"); legend("location", "northwest"); legend("boxoff"); -2 tests, 2 passed, 0 known failure, 0 skipped + ss = dtmc(P); # compute steady state probabilities + plot( T, pp(1,:), "b+;p_0(t);", "linewidth", 2, ... + T, ss(1)*ones(size(T)), "b;Steady State;", ... + T, pp(2,:), "r+;p_1(t);", "linewidth", 2, ... + T, ss(2)*ones(size(T)), "r;Steady State;" ); + xlabel("Time Step"); + legend("boxoff"); +6 tests, 6 passed, 0 known failure, 0 skipped +[inst/qnmix.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnmix.m +***** test + lambda = [1 0 0]; + N = [1 1 1]; + S = V = [1 1 1; 1 1 1; 1 1 1]; + fail( "qnmix( lambda, N, S, V)", "same time"); + N = [0 0 1]; + fail( "qnmix( lambda, N, S, V)", "open nor closed" ); + N = [0 1 2]; + m = [ 1 1 2 ]; + fail( "qnmix( lambda, N, S, V, m)", "single-server and delay" ); + S = V = [1 1 1; 1 1 1]; + fail( "qnmix( lambda, N, S, V)", "rows" ); +***** test + # Example p. 148 Zahorjan et al. + lambda = [1 1/2 0 0]; + N = [0 0 1 1]; + V = [1 1; 1 1; 1 1; 1 1]; + S = [1/4 1/6; 1/2 1; 1/2 1; 1 4/3]; + [U R Q X] = qnmix(lambda, N, S, V ); + assert( Q(3,1), 4/19, 1e-4 ); + assert( Q(3,2), 15/19, 1e-4 ); + assert( Q(4,1), 5/19, 1e-4 ); + assert( Q(4,2), 14/19, 1e-4 ); + assert( Q, R.*X, 1e-5 ); # Little's Law +***** test + # Example 8.6 p. 345 Bolch et al. + lambda = [0.5 0.25 0 0]; + N = [0 0 1 1]; + V = [2 1; 2.5 1.5; 1 0.5; 1 0.4]; + S = [0.4 0.6; 0.8 1.6; 0.3 0.5; 0.5 0.8]; + [U R Q X] = qnmix( lambda, N, S, V ); + assert( U([1 2],:), [0.4 0.3; 0.5 0.6], 1e-3 ); + assert( R([3 4],:), [4.829 6.951; 7.727 11.636], 1e-3 ); + assert( Q([3 4],:), [0.582 0.418; 0.624 0.376], 1e-3 ); + assert( Q([1 2],:), [8.822 5.383; 11.028 10.766], 1e-3 ); #FIXME + assert( R([1 2],:), [8.822 10.766; 17.645 28.710], 1e-3 ); + assert( X(3,1)/V(3,1), 0.120, 1e-3 ); + assert( X(4,1)/V(4,1), 0.081, 1e-3 ); + assert( Q, R.*X, 1e-5 ); # Little's Law +***** test + ## example figure 10 p. 26 Schwetman, "Implementing the Mean Value + ## Analysis for the Solution of Queueing Network Models", Technical + ## Report CSD-TR-355, feb 15, 1982, Purdue University. + S = [.25 0; .25 .10]; + V = [1 0; 1 1]; + lambda = [1 0]; + N = [0 3]; + [U R Q X] = qnmix( lambda, N, S, V ); + assert( U(1,1), .25, 1e-3 ); + assert( X(1,1), 1.0, 1e-3 ); + assert( [R(1,1) R(2,1) R(2,2)], [1.201 0.885 0.135], 1e-3 ); + assert( Q, R.*X, 1e-5 ); # Little's Law +4 tests, 4 passed, 0 known failure, 0 skipped +[inst/ctmcisir.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmcisir.m +***** test + Q = [-.5 .5 0; 1 0 0]; + fail( "ctmcisir(Q)" ); +***** test + Q = [-1 1 0; .5 -.5 0; 0 0 0]; + [r s] = ctmcisir(Q); + assert( r == 0 ); + assert( max(s), 2 ); + assert( min(s), 1 ); +***** test + Q = [-.5 .5 0; .2 -.7 .5; .2 0 -.2]; + [r s] = ctmcisir(Q); + assert( r == 1 ); + assert( max(s), 1 ); + assert( min(s), 1 ); +3 tests, 3 passed, 0 known failure, 0 skipped +[inst/qnclosedbsb.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnclosedbsb.m +***** test + fail("qnclosedbsb(-1,0)", "N must be"); + fail("qnclosedbsb(1,[])", "nonempty"); + fail("qnclosedbsb(1,[-1 2])", "nonnegative"); + fail("qnclosedbsb(1,[1 2 3],-1)", "nonnegative"); +warning: qnclosedbsb is deprecated. Please use qncsbsb instead +1 test, 1 passed, 0 known failure, 0 skipped +[inst/qsmminf.m] +>>>>> /build/octave-queueing-1.2.6/inst/qsmminf.m +***** test + fail( "qsmminf( [1 2], [1 2 3] )", "incompatible size"); + fail( "qsmminf( [-1 -1], [1 1] )", ">0" ); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/dtmc_fpt.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmc_fpt.m +***** test + P = [1 1 1; 1 1 1]; + fail( "dtmc_fpt(P)" ); +warning: dtmc_fpt is deprecated. Please use dtmcfpt instead +***** test + P = dtmc_bd([1 1 1], [0 0 0] ); + fail( "dtmc_fpt(P)", "absorbing" ); +***** test + P = [ 0.0 0.9 0.1; ... + 0.1 0.0 0.9; ... + 0.9 0.1 0.0 ]; + p = dtmc(P); + M = dtmc_fpt(P); + assert( diag(M)', 1./p, 1e-8 ); +***** test + P = [ 0 1 0 0 0; ... + .25 .0 .75 0 0; ... + 0 .5 0 .5 0; ... + 0 0 .75 0 .25; ... + 0 0 0 1 0 ]; + M = dtmc_fpt(P); + assert( M, [16 1 2.6667 6.3333 21.3333; ... + 15 4 1.6667 5.3333 20.3333; ... + 18.6667 3.6667 2.6667 3.6667 18.6667; ... + 20.3333 5.3333 1.6667 4 15; ... + 21.3333 6.3333 2.6667 1 16 ], 1e-4 ); +***** test + sz = 10; + P = reshape( 1:sz^2, sz, sz ); + normP = repmat(sum(P,2),1,columns(P)); + P = P./normP; + M = dtmc_fpt(P); + for i=1:rows(P) + for j=1:columns(P) + assert( M(i,j), 1 + dot(P(i,:), M(:,j)) - P(i,j)*M(j,j), 1e-8); + endfor + endfor +***** test + P = zeros(9,9); + P(1,[2 4]) = .5; + P(2,[1 5 3]) = 1/3; + P(3,[2 6]) = .5; + P(4,[1 5 7]) = 1/3; + P(5,[2 4 6 8]) = 1/4; + P(6,[3 5 9]) = 1/3; + P(7,[4 8]) = .5; + P(8,[7 5 9]) = 1/3; + P(9,[6 8]) = .5; + M = dtmc_fpt(P); + assert( M(1:9 != 5,5)', [6 5 6 5 5 6 5 6], 100*eps ); +6 tests, 6 passed, 0 known failure, 0 skipped +[inst/qncsbsb.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncsbsb.m +***** test + fail("qncsbsb(-1,0)", "N must be"); + fail("qncsbsb(1,[])", "nonempty"); + fail("qncsbsb(1,[-1 2])", "nonnegative"); + fail("qncsbsb(1,[1 2],[1 2 3])", "incompatible size"); + fail("qncsbsb(1,[1 2 3],[1 2 3],[1 2])", "incompatible size"); + fail("qncsbsb(1,[1 2 3],[1 2 3],[1 2 1])", "M/M/1 servers"); + fail("qncsbsb(1,[1 2 3],[1 2 3],[1 1 1],-1)", "nonnegative"); + fail("qncsbsb(1,[1 2 3],[1 2 3],[1 1 1],[0 0])", "scalar"); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/qnsolve.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnsolve.m +***** test + # Example 8.7 p. 349 Bolch et al. + N = 3; + Q1 = qnmknode( "m/m/m-fcfs", .5, 2 ); + Q2 = qnmknode( "m/m/m-fcfs", 1/1.667 ); + Q3 = qnmknode( "m/m/m-fcfs", 1/1.25 ); + Q4 = qnmknode( "m/m/m-fcfs", 1./[1 2 3] ); + V = [ 1 .5 .5 1 ]; + [U R Q X] = qnsolve("closed",N, { Q1, Q2, Q3, Q4 }, V); + assert( Q, [0.624 0.473 0.686 1.217], 1e-3 ); + assert( R, [0.512 0.776 1.127 1], 1e-3 ); +***** test + # Example 8.7 p. 349 Bolch et al. + N = 3; + Q1 = qnmknode( "m/m/m-fcfs", 1/2, 2 ); + Q2 = qnmknode( "m/m/m-fcfs", 1/1.667 ); + Q3 = qnmknode( "m/m/m-fcfs", 1/1.25 ); + Q4 = qnmknode( "-/g/inf", 1 ); + V = [ 1 .5 .5 1 ]; + [U R Q X] = qnsolve("closed",N, { Q1, Q2, Q3, Q4 }, V); + assert( Q, [0.624 0.473 0.686 1.217], 1e-3 ); + assert( R, [0.512 0.776 1.127 1], 1e-3 ); +***** test + # Example 8.4 p. 333 Bolch et al. + N = 3; + Q1 = qnmknode( "m/m/m-fcfs", .5, 2 ); + Q2 = qnmknode( "m/m/m-fcfs", .6 ); + Q3 = qnmknode( "m/m/m-fcfs", .8 ); + Q4 = qnmknode( "-/g/inf", 1 ); + V = [ 1 .5 .5 1 ]; + [U R Q X] = qnsolve("closed",N, { Q1, Q2, Q3, Q4 }, V); + assert( U(1:3), [.304 .365 .487], 1e-3 ); + assert( X, [1.218 0.609 0.609 1.218], 1e-3 ); +***** test + # Same as above, with center 1 replaced with a load-dependent service center + N = 3; + Q1 = qnmknode( "m/m/m-fcfs", [.5 .25 .25] ); + Q2 = qnmknode( "m/m/m-fcfs", .6 ); + Q3 = qnmknode( "m/m/m-fcfs", .8 ); + Q4 = qnmknode( "m/m/m-fcfs", [1 1/2 1/3] ); + V = [ 1 .5 .5 1 ]; + [U R Q X] = qnsolve("closed",N, { Q1, Q2, Q3, Q4 }, V); + assert( U(2:3), [.365 .487], 1e-3 ); ## NOTE: Utilization U(1) is computed differently from M/M/m nodes and load-dependent M/M/1 nodes + assert( X, [1.218 0.609 0.609 1.218], 1e-3 ); +***** test + # Example 7.4 p. 287 Bolch et al. + QQ = { qnmknode( "m/m/m-fcfs", 0.04 ), ... + qnmknode( "m/m/m-fcfs", 0.03 ), ... + qnmknode( "m/m/m-fcfs", 0.06 ), ... + qnmknode( "m/m/m-fcfs", 0.05 ) }; + P = [ 0 0.5 0.5 0; 1 0 0 0; 0.6 0 0 0; 1 0 0 0 ]; + lambda = [0 0 0 4]; + [U R Q X] = qnsolve("open", sum(lambda), QQ, qnosvisits(P,lambda) ); + assert( X, [20 10 10 4], 1e-4 ); + assert( U, [0.8 0.3 0.6 0.2], 1e-2 ); + assert( R, [0.2 0.043 0.15 0.0625], 1e-3 ); + assert( Q, [4, 0.429 1.5 0.25], 1e-3 ); +***** test + V = [1 1; 1 1]; + Q1 = qnmknode( "m/m/m-fcfs", [1;2] ); + Q2 = qnmknode( "m/m/m-fcfs", [3;4] ); + lambda = [3/19 2/19]; + [U R Q] = qnsolve("open", lambda, { Q1, Q2 }, diag( lambda / sum(lambda) ) * V); + assert( U(1,1), 3/19, 1e-6 ); + assert( U(2,1), 4/19, 1e-6 ); + assert( R(1,1), 19/12, 1e-6 ); + assert( R(1,2), 57/2, 1e-6 ); + assert( Q(1,1), .25, 1e-6 ); +***** test + QQ = { qnmknode( "m/m/m-fcfs", [0.2; 0.2], 2 ), ... + qnmknode( "-/g/1-ps", [0.4; 0.6] ), ... + qnmknode( "-/g/inf", [1; 2] ) }; + V = [ 1 0.6 0.4; 1 0.3 0.7 ]; + N = [ 2 1 ]; + [U R Q X] = qnsolve( "closed", N, QQ, V ); + assert( Q, [ 0.428 0.726 0.845; 0.108 0.158 0.734 ], 1e-3 ); + assert( X(1,1), 2.113, 1e-3 ); # CHECK + assert( X(2,1), 0.524, 1e-3 ); # CHECK + assert( all( all(U(:,[1,2])<=1) ) ); +***** test + QQ = { qnmknode( "m/m/m-fcfs", [0.2 0.1 0.1; 0.2 0.1 0.1] ), ... + qnmknode( "-/g/1-ps", [0.4; 0.6] ), ... + qnmknode( "-/g/inf", [1; 2] ) }; + V = [ 1 0.6 0.4; 1 0.3 0.7 ]; + N = [ 2 1 ]; + [U R Q X] = qnsolve( "closed", N, QQ, V ); + assert( Q, [ 0.428 0.726 0.845; 0.108 0.158 0.734 ], 1e-3 ); + assert( X(1,1), 2.113, 1e-3 ); # CHECK + assert( X(2,1), 0.524, 1e-3 ); # CHECK + assert( all( all(U(:,[1,2])<=1) ) ); +***** test + # example p. 26 Schwetman + QQ = { qnmknode( "m/m/m-fcfs", [.25; .25] ), + qnmknode( "-/g/1-ps", [0; .1] ) }; + V = [1 0; 1 1]; + lambda = [1 0]; + N = [0 3]; + [U R Q X] = qnsolve( "mixed", lambda, N, QQ, V ); + assert( U(1,1), .25, 1e-3 ); + assert( X(1,1), 1.0, 1e-3 ); + assert( [R(1,1) R(2,1) R(2,2)], [1.201 0.885 0.135], 1e-3 ); +***** demo + QQ = { qnmknode( "m/m/m-fcfs", [0.2 0.1 0.1; 0.2 0.1 0.1] ), ... + qnmknode( "-/g/1-ps", [0.4; 0.6] ), ... + qnmknode( "-/g/inf", [1; 2] ) }; + V = [ 1 0.6 0.4; ... + 1 0.3 0.7 ]; + N = [ 2 1 ]; + [U R Q X] = qnsolve( "closed", N, QQ, V ); +9 tests, 9 passed, 0 known failure, 0 skipped +[inst/ctmc_bd.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmc_bd.m +***** test + birth = [ 1 1 1 ]; + death = [ 2 2 2 ]; + Q = ctmc_bd( birth, death ); + assert( ctmc(Q), [ 8/15 4/15 2/15 1/15 ], 1e-5 ); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/dtmc_mtta.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmc_mtta.m +***** test + fail( "dtmc_mtta(1,2,3)" ); + fail( "dtmc_mtta()" ); +***** test + P = dtmcbd([0 .5 .5 .5], [.5 .5 .5 0]); + [t N B] = dtmc_mtta(P); + assert( t, [0 3 4 3 0], 10*eps ); + assert( B([2 3 4],[1 5]), [3/4 1/4; 1/2 1/2; 1/4 3/4], 10*eps ); + assert( B(1,1), 1 ); + assert( B(5,5), 1 ); +***** test + P = dtmcbd([0 .5 .5 .5], [.5 .5 .5 0]); + [t N B] = dtmc_mtta(P); + assert( t(3), 4, 10*eps ); + assert( B(3,1), 0.5, 10*eps ); + assert( B(3,5), 0.5, 10*eps ); +***** test + P = dtmcbd([0 .5 .5 .5 .5], [.5 .5 .5 .5 0]); + [t N B] = dtmc_mtta(P); + assert( t(2:5), [4 6 6 4], 100*eps ); + assert( B(2:5,1), [.8 .6 .4 .2]', 100*eps ); + assert( B(2:5,6), [.2 .4 .6 .8]', 100*eps ); +***** test + P = zeros(9,9); + P(1,[2 4]) = .5; + P(2,[1 5 3]) = 1/3; + P(3,[2 6]) = .5; + P(4,[1 5 7]) = 1/3; + P(5,:) = 0; P(5,5) = 1; + P(6,[3 5 9]) = 1/3; + P(7,[4 8]) = .5; + P(8,[7 5 9]) = 1/3; + P(9,[6 8]) = .5; + t = dtmc_mtta(P); + assert( t, [6 5 6 5 0 5 6 5 6], 10*eps ); +5 tests, 5 passed, 0 known failure, 0 skipped [inst/dtmcmtta.m] >>>>> /build/octave-queueing-1.2.6/inst/dtmcmtta.m ***** test @@ -5921,6 +5783,178 @@ t = dtmcmtta(P); assert( t, [6 5 6 5 0 5 6 5 6], 10*eps ); 5 tests, 5 passed, 0 known failure, 0 skipped +[inst/qnmminf.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnmminf.m +***** test + fail( "qnmminf( [1 2], [1 2 3] )", "incompatible size"); + fail( "qnmminf( [-1 -1], [1 1] )", ">0" ); +warning: qnmminf is deprecated. Please use qsmminf instead +1 test, 1 passed, 0 known failure, 0 skipped +[inst/qncmnpop.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncmnpop.m +***** test + H = qncmnpop( [1 2 2] ); + assert( H, [1 1 0 0 0 0; 1 2 2 1 0 0; 1 3 5 5 3 1] ); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/ctmcmtta.m] +>>>>> /build/octave-queueing-1.2.6/inst/ctmcmtta.m +***** test + Q = [0 1 0; 1 0 1; 0 1 0 ]; Q -= diag( sum(Q,2) ); + fail( "ctmcmtta(Q,[1 0 0])", "no absorbing"); +***** test + Q = [0 1 0; 1 0 1; 0 0 0; 0 0 0 ]; + fail( "ctmcmtta(Q,[1 0 0])", "square matrix"); +***** test + Q = [0 1 0; 1 0 1; 0 0 0 ]; + fail( "ctmcmtta(Q,[1 0 0])", "infinitesimal"); +***** test + Q = [ 0 0.1 0 0; ... + 0.9 0 0.1 0; ... + 0 0.9 0 0.1; ... + 0 0 0 0 ]; + Q -= diag( sum(Q,2) ); + assert( ctmcmtta( Q,[0 0 0 1] ), 0 ); # state 4 is absorbing +***** test + Q = [-1 1; 0 0]; + assert( ctmcmtta( Q, [0 1] ), 0 ); # state 2 is absorbing + assert( ctmcmtta( Q, [1 0] ), 1 ); # the result has been computed by hand +***** demo + mu = 0.01; + death = [ 3 4 5 ] * mu; + birth = 0*death; + Q = ctmcbd(birth,death); + t = ctmcmtta(Q,[0 0 0 1]) +***** demo + N = 100; + birth = death = ones(1,N-1); birth(1) = death(N-1) = 0; + Q = diag(birth,1)+diag(death,-1); + Q -= diag(sum(Q,2)); + t = zeros(1,N/2); + initial_state = 1:(N/2); + for i=initial_state + p = zeros(1,N); p(i) = 1; + t(i) = ctmcmtta(Q,p); + endfor + plot(initial_state,t,"+"); + xlabel("Initial state"); + ylabel("MTTA"); +5 tests, 5 passed, 0 known failure, 0 skipped +[inst/dtmc_bd.m] +>>>>> /build/octave-queueing-1.2.6/inst/dtmc_bd.m +***** test + birth = [.5 .5 .3]; + death = [.6 .2 .3]; + fail("dtmc_bd(birth,death)","must be"); +1 test, 1 passed, 0 known failure, 0 skipped +[inst/qnmvablo.m] +>>>>> /build/octave-queueing-1.2.6/inst/qnmvablo.m +***** test + fail( "qnmvablo( 10, [1 1], [4 5], [0 1; 1 0] )", "capacity"); + fail( "qnmvablo( 6, [1 1], [4 5], [0 1; 1 1] )", "stochastic"); + fail( "qnmvablo( 5, [1 1 1], [1 1], [0 1; 1 1] )", "3 elements"); +warning: qnmvablo is deprecated. Please use qncsmvablo instead +***** test + # This is the example on section v) p. 422 of the reference paper + M = [12 10 14]; + P = [0 1 0; 0 0 1; 1 0 0]; + S = [1/1 1/2 1/3]; + K = 27; + [U R Q X]=qnmvablo( K, S, M, P ); + assert( R, [11.80 1.66 14.4], 1e-2 ); +***** test + # This is example 2, i) and ii) p. 424 of the reference paper + M = [4 5 5]; + S = [1.5 2 1]; + P = [0 1 0; 0 0 1; 1 0 0]; + K = 10; + [U R Q X]=qnmvablo( K, S, M, P ); + assert( R, [6.925 8.061 4.185], 1e-3 ); + K = 12; + [U R Q X]=qnmvablo( K, S, M, P ); + assert( R, [7.967 9.019 8.011], 1e-3 ); +***** test + # This is example 3, i) and ii) p. 424 of the reference paper + M = [8 7 6]; + S = [0.2 1.2 1.4]; + P = [ 0 0.5 0.5; 1 0 0; 1 0 0 ]; + K = 10; + [U R Q X] = qnmvablo( K, S, M, P ); + assert( R, [1.674 5.007 7.639], 1e-3 ); + K = 12; + [U R Q X] = qnmvablo( K, S, M, P ); + assert( R, [2.166 5.372 6.567], 1e-3 ); +***** test + # Network which never blocks, central server model + M = [50 50 50]; + S = [1 1/0.8 1/0.4]; + P = [0 0.7 0.3; 1 0 0; 1 0 0]; + K = 40; + [U1 R1 Q1] = qnmvablo( K, S, M, P ); + V = qncsvisits(P); + [U2 R2 Q2] = qnclosedsinglemva( K, S, V ); + assert( U1, U2, 1e-5 ); + assert( R1, R2, 1e-5 ); + assert( Q1, Q2, 1e-5 ); +warning: qnclosedsinglemva is deprecated. Please use qncsmva instead +5 tests, 5 passed, 0 known failure, 0 skipped +[inst/qncsconvld.m] +>>>>> /build/octave-queueing-1.2.6/inst/qncsconvld.m +***** test + K=3; + S = [ 1 1 1; 1 1 1 ]; + V = [ 1 .667 .2 ]; + fail( "qncsconvld(K,S,V)", "size mismatch" ); +***** test + # Example 8.1 p. 318 Bolch et al. + K=3; + S = [ 1/0.8 ./ [1 2 2]; + 1/0.6 ./ [1 2 3]; + 1/0.4 ./ [1 1 1] ]; + V = [ 1 .667 .2 ]; + [U R Q X G] = qncsconvld( K, S, V ); + assert( G, [1 2.861 4.218 4.465], 5e-3 ); + assert( X, [0.945 0.630 0.189], 1e-3 ); + assert( Q, [1.290 1.050 0.660], 1e-3 ); + assert( R, [1.366 1.667 3.496], 1e-3 ); +***** test + # Example 8.3 p. 331 Bolch et al. + # compare results of convolution with those of mva + K = 6; + S = [ 0.02 0.2 0.4 0.6 ]; + V = [ 1 0.4 0.2 0.1 ]; + [U_mva R_mva Q_mva X_mva] = qncsmva(K, S, V); + [U_con R_con Q_con X_con G] = qncsconvld(K, repmat(S',1,K), V ); + assert( U_mva, U_con, 1e-5 ); + assert( R_mva, R_con, 1e-5 ); + assert( Q_mva, Q_con, 1e-5 ); + assert( X_mva, X_con, 1e-5 ); +***** test + # Compare the results of convolution to those of mva + S = [ 0.02 0.2 0.4 0.6 ]; + K = 6; + V = [ 1 0.4 0.2 0.1 ]; + m = [ 1 5 2 1 ]; + [U_mva R_mva Q_mva X_mva] = qncsmva(K, S, V); + [U_con R_con Q_con X_con G] = qncsconvld(K, repmat(S',1,K), V); + assert( U_mva, U_con, 1e-5 ); + assert( R_mva, R_con, 1e-5 ); + assert( Q_mva, Q_con, 1e-5 ); + assert( X_mva, X_con, 1e-5 ); +***** function r = S_function(k,n) + M = [ 1/0.8 ./ [1 2 2]; + 1/0.6 ./ [1 2 3]; + 1/0.4 ./ [1 1 1] ]; + r = M(k,n); +***** test + # Example 8.1 p. 318 Bolch et al. + K=3; + V = [ 1 .667 .2 ]; + [U R Q X G] = qncsconvld( K, @S_function, V ); + assert( G, [1 2.861 4.218 4.465], 5e-3 ); + assert( X, [0.945 0.630 0.189], 1e-3 ); + assert( Q, [1.290 1.050 0.660], 1e-3 ); + assert( R, [1.366 1.667 3.496], 1e-3 ); +5 tests, 5 passed, 0 known failure, 0 skipped Checking C++ files ... Summary: 270 tests, 267 passed, 3 known failures, 0 skipped dh_octave_substvar -O--buildsystem=octave @@ -5949,12 +5983,14 @@ dpkg-source: info: using options from octave-queueing-1.2.6/debian/source/options: --extend-diff-ignore=doc/INSTALL|doc/.*\.png|doc/.*\.pdf|doc/queueing\.html dpkg-buildpackage: info: binary-only upload (no source included) I: copying local configuration +I: user script /srv/workspace/pbuilder/19078/tmp/hooks/B01_cleanup starting +I: user script /srv/workspace/pbuilder/19078/tmp/hooks/B01_cleanup finished I: unmounting dev/ptmx filesystem I: unmounting dev/pts filesystem I: unmounting dev/shm filesystem I: unmounting proc filesystem I: unmounting sys filesystem I: cleaning the build env -I: removing directory /srv/workspace/pbuilder/50668 and its subdirectories -I: Current time: Fri Jul 23 15:47:04 -12 2021 -I: pbuilder-time-stamp: 1627098424 +I: removing directory /srv/workspace/pbuilder/19078 and its subdirectories +I: Current time: Sun Jun 21 11:34:27 +14 2020 +I: pbuilder-time-stamp: 1592688867