Mercurial > forge
changeset 9622:cdf1dbf20cd4 octave-forge
fixed bug in texinfo documentation
| author | mmarzolla |
|---|---|
| date | Sat, 10 Mar 2012 16:03:47 +0000 |
| parents | bd7fb43a670e |
| children | 40a1e6b36726 |
| files | main/queueing/doc/queueing.html main/queueing/doc/queueing.pdf main/queueing/inst/ctmc_exps.m |
| diffstat | 3 files changed, 329 insertions(+), 313 deletions(-) [+] |
line wrap: on
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--- a/main/queueing/doc/queueing.html Sat Mar 10 16:00:45 2012 +0000 +++ b/main/queueing/doc/queueing.html Sat Mar 10 16:03:47 2012 +0000 @@ -1100,36 +1100,46 @@ <p><a name="doc_002dctmc_005fexps"></a> <div class="defun"> -— Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, tt, p</var>)<var><a name="index-ctmc_005fexps-20"></a></var><br> +— Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, tt, p </var>)<var><a name="index-ctmc_005fexps-20"></a></var><br> +— Function File: <var>L</var> = <b>ctmc_exps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fexps-21"></a></var><br> <blockquote> - <p><a name="index-Markov-chain_002c-continuous-time-21"></a><a name="index-Expected-sojourn-time-22"></a> -Compute the expected total time <var>L</var><code>(t,j)</code> spent in state -j during the time interval <code>[0,</code><var>tt</var><code>(t))</code>, assuming -that at time 0 the state occupancy probability was <var>p</var>. + <p><a name="index-Markov-chain_002c-continuous-time-22"></a><a name="index-Expected-sojourn-time-23"></a> +With three arguments, compute the expected time <var>L</var><code>(t,j)</code> +spent in each state j during the time interval +<code>[0,</code><var>tt</var><code>(t))</code>, assuming that at time 0 the state occupancy +probability was <var>p</var>. With two arguments, compute the expected +time <var>L</var><code>(j)</code> spent in each state j until absorption. <p><strong>INPUTS</strong> <dl> -<dt><var>Q</var><dd>Infinitesimal generator matrix. <var>Q</var><code>(i,j)</code> is the transition -rate from state i to state j, -1 ≤ i \neq j ≤ N. The matrix <var>Q</var> must also satisfy the -condition <code>sum(</code><var>Q</var><code>,2) == 0</code> +<dt><var>Q</var><dd>N \times N infinitesimal generator matrix. <var>Q</var><code>(i,j)</code> +is the transition rate from state i to state j, 1 +≤ i \neq j ≤ N. The matrix <var>Q</var> must also satisfy the +condition \sum_j=1^N Q_ij = 0. <br><dt><var>tt</var><dd>This parameter is a vector used for numerical integration. The first element <var>tt</var><code>(1)</code> must be 0, and the last element <var>tt</var><code>(end)</code> must be the upper bound of the interval [0,t) of interest (<var>tt</var><code>(end) == t</code>). - <br><dt><var>p</var><dd><var>p</var><code>(i)</code> is the probability that at time 0 the system was in -state i, for all i = 1, <small class="dots">...</small>, N + <br><dt><var>p</var><dd>Initial occupancy probability vector; <var>p</var><code>(i)</code> is the +probability the system is in state i at time 0, i = 1, +<small class="dots">...</small>, N </dl> <p><strong>OUTPUTS</strong> <dl> -<dt><var>L</var><dd><var>L</var><code>(t,j)</code> is the expected time spent in state j -during the interval <code>[0,</code><var>tt</var><code>(t))</code>. <code>1 ≤ </code><var>t</var><code> ≤ length(</code><var>tt</var><code>)</code> +<dt><var>L</var><dd>If this function is called with three arguments, <var>L</var> is a matrix +of size <code>[length(</code><var>tt</var><code>), N]</code> where <var>L</var><code>(t,j)</code> is the +expected time spent in state j during the interval +<code>[0,</code><var>tt</var><code>(t)]</code>. If this function is called with two +arguments, <var>L</var> is a vector with N elements where +<var>L</var><code>(j)</code> is the expected time spent in state j until +absorption, if j is a transient state. If j +is an absorbing state, <var>L</var><code>(j) = 0</code>. </dl> @@ -1175,9 +1185,9 @@ <p><a name="doc_002dctmc_005ftaexps"></a> <div class="defun"> -— Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, tt, p</var>)<var><a name="index-ctmc_005ftaexps-23"></a></var><br> +— Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, tt, p</var>)<var><a name="index-ctmc_005ftaexps-24"></a></var><br> <blockquote> - <p><a name="index-Markov-chain_002c-continuous-time-24"></a><a name="index-Time_002dalveraged-sojourn-time-25"></a> + <p><a name="index-Markov-chain_002c-continuous-time-25"></a><a name="index-Time_002dalveraged-sojourn-time-26"></a> Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(t,j)</code>, defined as the fraction of the time interval <code>[0,</code><var>tt</var><code>(t))</code> spent in state j, assuming that at time 0 the state occupancy @@ -1264,12 +1274,13 @@ <p><a name="doc_002dctmc_005fmtta"></a> <div class="defun"> -— Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-26"></a></var><br> +— Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-27"></a></var><br> <blockquote> - <p><a name="index-Markov-chain_002c-continuous-time-27"></a><a name="index-Mean-time-to-absorption-28"></a> -Compute the Mean-Time to Absorption (MTTA) starting from initial -occupancy probability <var>p</var> at time 0. If there are no absorbing -states, this function fails with an error. + <p><a name="index-Markov-chain_002c-continuous-time-28"></a><a name="index-Mean-time-to-absorption-29"></a> +Compute the Mean-Time to Absorption (MTTA) of the CTMC described by +the infinitesimal generator matrix <var>Q</var>, starting from initial +occupancy probability <var>p</var>. If there are no absorbing states, this +function fails with an error. <p><strong>INPUTS</strong> @@ -1326,7 +1337,7 @@ Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998. - <p><a name="index-Bolch_002c-G_002e-29"></a><a name="index-Greiner_002c-S_002e-30"></a><a name="index-de-Meer_002c-H_002e-31"></a><a name="index-Trivedi_002c-K_002e-32"></a> + <p><a name="index-Bolch_002c-G_002e-30"></a><a name="index-Greiner_002c-S_002e-31"></a><a name="index-de-Meer_002c-H_002e-32"></a><a name="index-Trivedi_002c-K_002e-33"></a> <div class="node"> <a name="CTMC-First-Passage-Times"></a> <p><hr> @@ -1340,10 +1351,10 @@ <p><a name="doc_002dctmc_005ffpt"></a> <div class="defun"> -— Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-33"></a></var><br> -— Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-34"></a></var><br> +— Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-34"></a></var><br> +— Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-35"></a></var><br> <blockquote> - <p><a name="index-Markov-chain_002c-continuous-time-35"></a><a name="index-First-passage-times-36"></a> + <p><a name="index-Markov-chain_002c-continuous-time-36"></a><a name="index-First-passage-times-37"></a> If called with a single argument, computes the mean first passage times <var>M</var><code>(i,j)</code>, the average times before state <var>j</var> is reached, starting from state <var>i</var>, for all 1 \leq i, j \leq @@ -1449,9 +1460,9 @@ <p><a name="doc_002dqnmm1"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-37"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmm1</b> (<var>lambda, mu</var>)<var><a name="index-qnmm1-38"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-38"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-39"></a> Compute utilization, response time, average number of requests and throughput for a M/M/1 queue. @@ -1496,7 +1507,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998, Section 6.3. - <p><a name="index-Bolch_002c-G_002e-39"></a><a name="index-Greiner_002c-S_002e-40"></a><a name="index-de-Meer_002c-H_002e-41"></a><a name="index-Trivedi_002c-K_002e-42"></a> + <p><a name="index-Bolch_002c-G_002e-40"></a><a name="index-Greiner_002c-S_002e-41"></a><a name="index-de-Meer_002c-H_002e-42"></a><a name="index-Trivedi_002c-K_002e-43"></a> <!-- M/M/m --> <div class="node"> <a name="The-M%2fM%2fm-System"></a> @@ -1522,10 +1533,10 @@ <p><a name="doc_002dqnmmm"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-43"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-44"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu</var>)<var><a name="index-qnmmm-44"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pm</var>] = <b>qnmmm</b> (<var>lambda, mu, m</var>)<var><a name="index-qnmmm-45"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-45"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-46"></a> Compute utilization, response time, average number of requests in service and throughput for a M/M/m queue, a queueing system with m identical service centers connected to a single queue. @@ -1577,7 +1588,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998, Section 6.5. - <p><a name="index-Bolch_002c-G_002e-46"></a><a name="index-Greiner_002c-S_002e-47"></a><a name="index-de-Meer_002c-H_002e-48"></a><a name="index-Trivedi_002c-K_002e-49"></a> + <p><a name="index-Bolch_002c-G_002e-47"></a><a name="index-Greiner_002c-S_002e-48"></a><a name="index-de-Meer_002c-H_002e-49"></a><a name="index-Trivedi_002c-K_002e-50"></a> <!-- M/M/inf --> <div class="node"> <a name="The-M%2fM%2finf-System"></a> @@ -1600,7 +1611,7 @@ <p><a name="doc_002dqnmminf"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-50"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmminf</b> (<var>lambda, mu</var>)<var><a name="index-qnmminf-51"></a></var><br> <blockquote> <p>Compute utilization, response time, average number of requests and throughput for a M/M/\infty queue. This is a system with an @@ -1608,7 +1619,7 @@ system is always stable, regardless the values of the arrival and service rates. - <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-51"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-52"></a> <p><strong>INPUTS</strong> @@ -1626,7 +1637,7 @@ different from the utilization, which in the case of M/M/\infty centers is always zero. - <p><a name="index-traffic-intensity-52"></a> + <p><a name="index-traffic-intensity-53"></a> <br><dt><var>R</var><dd>Service center response time. <br><dt><var>Q</var><dd>Average number of requests in the system (which is equal to the @@ -1654,7 +1665,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998, Section 6.4. - <p><a name="index-Bolch_002c-G_002e-53"></a><a name="index-Greiner_002c-S_002e-54"></a><a name="index-de-Meer_002c-H_002e-55"></a><a name="index-Trivedi_002c-K_002e-56"></a> + <p><a name="index-Bolch_002c-G_002e-54"></a><a name="index-Greiner_002c-S_002e-55"></a><a name="index-de-Meer_002c-H_002e-56"></a><a name="index-Trivedi_002c-K_002e-57"></a> <!-- M/M/1/k --> <div class="node"> <a name="The-M%2fM%2f1%2fK-System"></a> @@ -1678,9 +1689,9 @@ <p><a name="doc_002dqnmm1k"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-57"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmm1k</b> (<var>lambda, mu, K</var>)<var><a name="index-qnmm1k-58"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-58"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-59"></a> Compute utilization, response time, average number of requests and throughput for a M/M/1/K finite capacity system. In a M/M/1/K queue there is a single server; the maximum number of @@ -1747,9 +1758,9 @@ <p><a name="doc_002dqnmmmk"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-59"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>, <var>pK</var>] = <b>qnmmmk</b> (<var>lambda, mu, m, K</var>)<var><a name="index-qnmmmk-60"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-60"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-61"></a> Compute utilization, response time, average number of requests and throughput for a M/M/m/K finite capacity system. In a M/M/m/K system there are m \geq 1 identical service @@ -1807,7 +1818,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998, Section 6.6. - <p><a name="index-Bolch_002c-G_002e-61"></a><a name="index-Greiner_002c-S_002e-62"></a><a name="index-de-Meer_002c-H_002e-63"></a><a name="index-Trivedi_002c-K_002e-64"></a> + <p><a name="index-Bolch_002c-G_002e-62"></a><a name="index-Greiner_002c-S_002e-63"></a><a name="index-de-Meer_002c-H_002e-64"></a><a name="index-Trivedi_002c-K_002e-65"></a> <!-- Approximate M/M/m --> <div class="node"> @@ -1829,9 +1840,9 @@ <p><a name="doc_002dqnammm"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-65"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnammm</b> (<var>lambda, mu</var>)<var><a name="index-qnammm-66"></a></var><br> <blockquote> - <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-66"></a> + <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-67"></a> Compute <em>approximate</em> utilization, response time, average number of requests in service and throughput for an asymmetric M/M/m queue. In this system there are m different service centers @@ -1878,7 +1889,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998 - <p><a name="index-Bolch_002c-G_002e-67"></a><a name="index-Greiner_002c-S_002e-68"></a><a name="index-de-Meer_002c-H_002e-69"></a><a name="index-Trivedi_002c-K_002e-70"></a> + <p><a name="index-Bolch_002c-G_002e-68"></a><a name="index-Greiner_002c-S_002e-69"></a><a name="index-de-Meer_002c-H_002e-70"></a><a name="index-Trivedi_002c-K_002e-71"></a> <div class="node"> <a name="The-M%2fG%2f1-System"></a> <a name="The-M_002fG_002f1-System"></a> @@ -1894,9 +1905,9 @@ <p><a name="doc_002dqnmg1"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-71"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmg1</b> (<var>lambda, xavg, x2nd</var>)<var><a name="index-qnmg1-72"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-72"></a> + <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-73"></a> Compute utilization, response time, average number of requests and throughput for a M/G/1 system. The service time distribution is described by its mean <var>xavg</var>, and by its second moment @@ -1953,9 +1964,9 @@ <p><a name="doc_002dqnmh1"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-73"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>p0</var>] = <b>qnmh1</b> (<var>lambda, mu, alpha</var>)<var><a name="index-qnmh1-74"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-74"></a> + <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-75"></a> Compute utilization, response time, average number of requests and throughput for a M/H_m/1 system. In this system, the customer service times have hyper-exponential distribution: @@ -2037,7 +2048,7 @@ <li><a accesskey="6" href="#Utility-functions">Utility functions</a>: Utility functions to compute miscellaneous quantities </ul> -<p><a name="index-queueing-networks-75"></a> +<p><a name="index-queueing-networks-76"></a> <!-- INTRODUCTION --> <div class="node"> <a name="Introduction-to-QNs"></a> @@ -2298,13 +2309,13 @@ <p><a name="doc_002dqnmknode"></a> <div class="defun"> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-76"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-77"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-78"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-79"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-80"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-81"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-82"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-77"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-78"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-79"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-80"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-81"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-82"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-83"></a></var><br> <blockquote> <p>Creates a node; this function can be used together with <code>qnsolve</code>. It is possible to create either single-class nodes @@ -2373,10 +2384,10 @@ <p><a name="doc_002dqnsolve"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-83"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-84"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-85"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-86"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V</var>)<var><a name="index-qnsolve-84"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"closed", N, QQ, V, Z</var>)<var><a name="index-qnsolve-85"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"open", lambda, QQ, V</var>)<var><a name="index-qnsolve-86"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnsolve</b> (<var>"mixed", lambda, N, QQ, V</var>)<var><a name="index-qnsolve-87"></a></var><br> <blockquote> <p>General evaluator of QN models. Networks can be open, closed or mixed; single as well as multiclass networks are supported. @@ -2554,11 +2565,11 @@ <p><a name="doc_002dqnjackson"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-87"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-88"></a></var><br> -— Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-89"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P </var>)<var><a name="index-qnjackson-88"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnjackson</b> (<var>lambda, S, P, m </var>)<var><a name="index-qnjackson-89"></a></var><br> +— Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-90"></a></var><br> <blockquote> - <p><a name="index-open-network_002c-single-class-90"></a><a name="index-Jackson-network-91"></a> + <p><a name="index-open-network_002c-single-class-91"></a><a name="index-Jackson-network-92"></a> With three or four input parameters, this function computes the steady-state occupancy probabilities for a Jackson network. With five input parameters, this function computes the steady-state probability @@ -2640,7 +2651,7 @@ Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998, pp. 284–287. - <p><a name="index-Bolch_002c-G_002e-92"></a><a name="index-Greiner_002c-S_002e-93"></a><a name="index-de-Meer_002c-H_002e-94"></a><a name="index-Trivedi_002c-K_002e-95"></a> + <p><a name="index-Bolch_002c-G_002e-93"></a><a name="index-Greiner_002c-S_002e-94"></a><a name="index-de-Meer_002c-H_002e-95"></a><a name="index-Trivedi_002c-K_002e-96"></a> <h4 class="subsection">6.3.2 The Convolution Algorithm</h4> @@ -2674,10 +2685,10 @@ <p><a name="doc_002dqnconvolution"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-96"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-97"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V</var>)<var><a name="index-qnconvolution-97"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolution</b> (<var>N, S, V, m</var>)<var><a name="index-qnconvolution-98"></a></var><br> <blockquote> - <p><a name="index-closed-network-98"></a><a name="index-normalization-constant-99"></a><a name="index-convolution-algorithm-100"></a> + <p><a name="index-closed-network-99"></a><a name="index-normalization-constant-100"></a><a name="index-convolution-algorithm-101"></a> This function implements the <em>convolution algorithm</em> for computing steady-state performance measures of product-form, single-class closed queueing networks. Load-independent service @@ -2768,20 +2779,20 @@ 16, number 9, september 1973, pp. 527–531. <a href="http://doi.acm.org/10.1145/362342.362345">http://doi.acm.org/10.1145/362342.362345</a> - <p><a name="index-Buzen_002c-J_002e-P_002e-101"></a> + <p><a name="index-Buzen_002c-J_002e-P_002e-102"></a> This implementation is based on G. Bolch, S. Greiner, H. de Meer and K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998, pp. 313–317. - <p><a name="index-Bolch_002c-G_002e-102"></a><a name="index-Greiner_002c-S_002e-103"></a><a name="index-de-Meer_002c-H_002e-104"></a><a name="index-Trivedi_002c-K_002e-105"></a> + <p><a name="index-Bolch_002c-G_002e-103"></a><a name="index-Greiner_002c-S_002e-104"></a><a name="index-de-Meer_002c-H_002e-105"></a><a name="index-Trivedi_002c-K_002e-106"></a> <!-- Convolution for load-dependent service centers --> <a name="doc_002dqnconvolutionld"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-106"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnconvolutionld</b> (<var>N, S, V</var>)<var><a name="index-qnconvolutionld-107"></a></var><br> <blockquote> - <p><a name="index-closed-network-107"></a><a name="index-normalization-constant-108"></a><a name="index-convolution-algorithm-109"></a><a name="index-load_002ddependent-service-center-110"></a> + <p><a name="index-closed-network-108"></a><a name="index-normalization-constant-109"></a><a name="index-convolution-algorithm-110"></a><a name="index-load_002ddependent-service-center-111"></a> This function implements the <em>convolution algorithm</em> for product-form, single-class closed queueing networks with general load-dependent service centers. @@ -2841,7 +2852,7 @@ Purdue University, feb, 1981 (revised). <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf</a> - <p><a name="index-Schwetman_002c-H_002e-111"></a> + <p><a name="index-Schwetman_002c-H_002e-112"></a> M. Reiser, H. Kobayashi, <cite>On The Convolution Algorithm for Separable Queueing Networks</cite>, In Proceedings of the 1976 ACM SIGMETRICS Conference on Computer Performance Modeling Measurement and @@ -2849,7 +2860,7 @@ 1976). SIGMETRICS '76. ACM, New York, NY, pp. 109–117. <a href="http://doi.acm.org/10.1145/800200.806187">http://doi.acm.org/10.1145/800200.806187</a> - <p><a name="index-Reiser_002c-M_002e-112"></a><a name="index-Kobayashi_002c-H_002e-113"></a> + <p><a name="index-Reiser_002c-M_002e-113"></a><a name="index-Kobayashi_002c-H_002e-114"></a> This implementation is based on G. Bolch, S. Greiner, H. de Meer and K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, @@ -2861,7 +2872,7 @@ function f_i defined in Schwetman, <code>Some Computational Aspects of Queueing Network Models</code>. - <p><a name="index-Bolch_002c-G_002e-114"></a><a name="index-Greiner_002c-S_002e-115"></a><a name="index-de-Meer_002c-H_002e-116"></a><a name="index-Trivedi_002c-K_002e-117"></a> + <p><a name="index-Bolch_002c-G_002e-115"></a><a name="index-Greiner_002c-S_002e-116"></a><a name="index-de-Meer_002c-H_002e-117"></a><a name="index-Trivedi_002c-K_002e-118"></a> <h4 class="subsection">6.3.3 Open networks</h4> @@ -2869,10 +2880,10 @@ <p><a name="doc_002dqnopensingle"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-118"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-119"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V</var>)<var><a name="index-qnopensingle-119"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopensingle</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopensingle-120"></a></var><br> <blockquote> - <p><a name="index-open-network_002c-single-class-120"></a><a name="index-BCMP-network-121"></a> + <p><a name="index-open-network_002c-single-class-121"></a><a name="index-BCMP-network-122"></a> Analyze open, single class BCMP queueing networks. <p>This function works for a subset of BCMP single-class open networks @@ -2965,16 +2976,16 @@ Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998. - <p><a name="index-Bolch_002c-G_002e-122"></a><a name="index-Greiner_002c-S_002e-123"></a><a name="index-de-Meer_002c-H_002e-124"></a><a name="index-Trivedi_002c-K_002e-125"></a> + <p><a name="index-Bolch_002c-G_002e-123"></a><a name="index-Greiner_002c-S_002e-124"></a><a name="index-de-Meer_002c-H_002e-125"></a><a name="index-Trivedi_002c-K_002e-126"></a> <!-- Open network with multiple classes --> <p><a name="doc_002dqnopenmulti"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-126"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-127"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V</var>)<var><a name="index-qnopenmulti-127"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopenmulti</b> (<var>lambda, S, V, m</var>)<var><a name="index-qnopenmulti-128"></a></var><br> <blockquote> - <p><a name="index-open-network_002c-multiple-classes-128"></a> + <p><a name="index-open-network_002c-multiple-classes-129"></a> Exact analysis of open, multiple-class BCMP networks. The network can be made of <em>single-server</em> queueing centers (FCFS, LCFS-PR or PS) or delay centers (IS). This function assumes a network with @@ -3039,7 +3050,7 @@ 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In particular, see section 7.4.1 ("Open Model Solution Techniques"). - <p><a name="index-Lazowska_002c-E_002e-D_002e-129"></a><a name="index-Zahorjan_002c-J_002e-130"></a><a name="index-Graham_002c-G_002e-S_002e-131"></a><a name="index-Sevcik_002c-K_002e-C_002e-132"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-130"></a><a name="index-Zahorjan_002c-J_002e-131"></a><a name="index-Graham_002c-G_002e-S_002e-132"></a><a name="index-Sevcik_002c-K_002e-C_002e-133"></a> <h4 class="subsection">6.3.4 Closed Networks</h4> @@ -3047,11 +3058,11 @@ <p><a name="doc_002dqnclosedsinglemva"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-133"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-134"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-135"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemva-134"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemva-135"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>, <var>G</var>] = <b>qnclosedsinglemva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemva-136"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-136"></a><a name="index-closed-network_002c-single-class-137"></a><a name="index-normalization-constant-138"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-137"></a><a name="index-closed-network_002c-single-class-138"></a><a name="index-normalization-constant-139"></a> Analyze closed, single class queueing networks using the exact Mean Value Analysis (MVA) algorithm. The following queueing disciplines are supported: FCFS, LCFS-PR, PS and IS (Infinite Server). This @@ -3097,8 +3108,11 @@ <var>X</var><code>(k)*</code><var>S</var><code>(k)</code>. <br><dt><var>R</var><dd><var>R</var><code>(k)</code> is the response time at center k. +The <em>Residence Time</em> at center k is +<var>R</var><code>(k) * </code><var>V</var><code>(k)</code>. The system response time <var>Rsys</var> -can be computed as <var>Rsys</var><code> = </code><var>N</var><code>/</code><var>Xsys</var><code> - Z</code> +can be computed either as <var>Rsys</var><code> = </code><var>N</var><code>/</code><var>Xsys</var><code> - Z</code> +or as <var>Rsys</var><code> = dot(</code><var>R</var><code>,</code><var>V</var><code>)</code> <br><dt><var>Q</var><dd><var>Q</var><code>(k)</code> is the average number of requests at center k. The number of requests in the system can be computed @@ -3149,7 +3163,7 @@ Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April 1980, pp. 313–322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a> - <p><a name="index-Reiser_002c-M_002e-139"></a><a name="index-Lavenberg_002c-S_002e-S_002e-140"></a> + <p><a name="index-Reiser_002c-M_002e-140"></a><a name="index-Lavenberg_002c-S_002e-S_002e-141"></a> This implementation is described in R. Jain , <cite>The Art of Computer Systems Performance Analysis</cite>, Wiley, 1991, p. 577. Multi-server nodes <!-- and the computation of @math{G(N)}, --> @@ -3158,15 +3172,15 @@ Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998, Section 8.2.1, "Single Class Queueing Networks". - <p><a name="index-Jain_002c-R_002e-141"></a><a name="index-Bolch_002c-G_002e-142"></a><a name="index-Greiner_002c-S_002e-143"></a><a name="index-de-Meer_002c-H_002e-144"></a><a name="index-Trivedi_002c-K_002e-145"></a> + <p><a name="index-Jain_002c-R_002e-142"></a><a name="index-Bolch_002c-G_002e-143"></a><a name="index-Greiner_002c-S_002e-144"></a><a name="index-de-Meer_002c-H_002e-145"></a><a name="index-Trivedi_002c-K_002e-146"></a> <!-- MVA for single class, closed networks with load dependent servers --> <a name="doc_002dqnclosedsinglemvald"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-146"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-147"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvald-147"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvald</b> (<var>N, S, V, Z</var>)<var><a name="index-qnclosedsinglemvald-148"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-148"></a><a name="index-closed-network_002c-single-class-149"></a><a name="index-load_002ddependent-service-center-150"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-149"></a><a name="index-closed-network_002c-single-class-150"></a><a name="index-load_002ddependent-service-center-151"></a> Exact MVA algorithm for closed, single class queueing networks with load-dependent service centers. This function supports FCFS, LCFS-PR, PS and IS nodes. For networks with only fixed-rate @@ -3224,15 +3238,15 @@ 1998, Section 8.2.4.1, “Networks with Load-Deèpendent Service: Closed Networks”. - <p><a name="index-Bolch_002c-G_002e-151"></a><a name="index-Greiner_002c-S_002e-152"></a><a name="index-de-Meer_002c-H_002e-153"></a><a name="index-Trivedi_002c-K_002e-154"></a> + <p><a name="index-Bolch_002c-G_002e-152"></a><a name="index-Greiner_002c-S_002e-153"></a><a name="index-de-Meer_002c-H_002e-154"></a><a name="index-Trivedi_002c-K_002e-155"></a> <!-- CMVA for single class, closed networks with a single load dependent servers --> <a name="doc_002dqncmva"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-155"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-156"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V</var>)<var><a name="index-qncmva-156"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qncmva</b> (<var>N, S, Sld, V, Z</var>)<var><a name="index-qncmva-157"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-157"></a><a name="index-CMVA-158"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-158"></a><a name="index-CMVA-159"></a> Implementation of the Conditional MVA (CMVA) algorithm, a numerically stable variant of MVA for load-dependent servers. CMVA is described in G. Casale, <cite>A Note on Stable Flow-Equivalent Aggregation in @@ -3286,19 +3300,19 @@ closed networks</cite>. Queueing Syst. Theory Appl., 60:193–202, December 2008. - <p><a name="index-Casale_002c-G_002e-159"></a> + <p><a name="index-Casale_002c-G_002e-160"></a> <!-- Approximate MVA for single class, closed networks --> <p><a name="doc_002dqnclosedsinglemvaapprox"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-160"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-161"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-162"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-163"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-164"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedsinglemvaapprox-161"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedsinglemvaapprox-162"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedsinglemvaapprox-163"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedsinglemvaapprox-164"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedsinglemvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedsinglemvaapprox-165"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-165"></a><a name="index-Approximate-MVA-166"></a><a name="index-Closed-network_002c-single-class-167"></a><a name="index-Closed-network_002c-approximate-analysis-168"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-166"></a><a name="index-Approximate-MVA-167"></a><a name="index-Closed-network_002c-single-class-168"></a><a name="index-Closed-network_002c-approximate-analysis-169"></a> Analyze closed, single class queueing networks using the Approximate Mean Value Analysis (MVA) algorithm. This function is based on approximating the number of customers seen at center k when a @@ -3377,20 +3391,20 @@ 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In particular, see section 6.4.2.2 ("Approximate Solution Techniques"). - <p><a name="index-Lazowska_002c-E_002e-D_002e-169"></a><a name="index-Zahorjan_002c-J_002e-170"></a><a name="index-Graham_002c-G_002e-S_002e-171"></a><a name="index-Sevcik_002c-K_002e-C_002e-172"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-170"></a><a name="index-Zahorjan_002c-J_002e-171"></a><a name="index-Graham_002c-G_002e-S_002e-172"></a><a name="index-Sevcik_002c-K_002e-C_002e-173"></a> <!-- MVA for multiple class, closed networks --> <p><a name="doc_002dqnclosedmultimva"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-173"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-174"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-175"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-176"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-177"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-178"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S </var>)<var><a name="index-qnclosedmultimva-174"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimva-175"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimva-176"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimva-177"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P</var>)<var><a name="index-qnclosedmultimva-178"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimva</b> (<var>N, S, P, m</var>)<var><a name="index-qnclosedmultimva-179"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-179"></a><a name="index-closed-network_002c-multiple-classes-180"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-180"></a><a name="index-closed-network_002c-multiple-classes-181"></a> Analyze closed, multiclass queueing networks with K service centers and C independent customer classes (chains) using the Mean Value Analysys (MVA) algorithm. @@ -3477,8 +3491,10 @@ defined as <var>U</var><code>(c,k) = </code><var>X</var><code>(c,k)*</code><var>S</var><code>(c,k)</code>. <br><dt><var>R</var><dd><var>R</var><code>(c,k)</code> is the class c response time at -center k. The total class c system response time -can be computed as <code>dot(</code><var>R</var><code>, </code><var>V</var><code>, 2)</code>. +center k. The class c <em>residence time</em> +at center k is <var>R</var><code>(c,k) * </code><var>C</var><code>(c,k)</code>. +The total class c system response time +is <code>dot(</code><var>R</var><code>, </code><var>V</var><code>, 2)</code>. <br><dt><var>Q</var><dd><var>Q</var><code>(c,k)</code> is the average number of class c requests at center k. The total number of @@ -3518,7 +3534,7 @@ Multichain Queuing Networks</cite>, Journal of the ACM, vol. 27, n. 2, April 1980, pp. 313–322. <a href="http://doi.acm.org/10.1145/322186.322195">http://doi.acm.org/10.1145/322186.322195</a> - <p><a name="index-Reiser_002c-M_002e-181"></a><a name="index-Lavenberg_002c-S_002e-S_002e-182"></a> + <p><a name="index-Reiser_002c-M_002e-182"></a><a name="index-Lavenberg_002c-S_002e-S_002e-183"></a> This implementation is based on G. Bolch, S. Greiner, H. de Meer and K. Trivedi, <cite>Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, @@ -3528,18 +3544,18 @@ 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In particular, see section 7.4.2.1 ("Exact Solution Techniques"). - <p><a name="index-Bolch_002c-G_002e-183"></a><a name="index-Greiner_002c-S_002e-184"></a><a name="index-de-Meer_002c-H_002e-185"></a><a name="index-Trivedi_002c-K_002e-186"></a><a name="index-Lazowska_002c-E_002e-D_002e-187"></a><a name="index-Zahorjan_002c-J_002e-188"></a><a name="index-Graham_002c-G_002e-S_002e-189"></a><a name="index-Sevcik_002c-K_002e-C_002e-190"></a> + <p><a name="index-Bolch_002c-G_002e-184"></a><a name="index-Greiner_002c-S_002e-185"></a><a name="index-de-Meer_002c-H_002e-186"></a><a name="index-Trivedi_002c-K_002e-187"></a><a name="index-Lazowska_002c-E_002e-D_002e-188"></a><a name="index-Zahorjan_002c-J_002e-189"></a><a name="index-Graham_002c-G_002e-S_002e-190"></a><a name="index-Sevcik_002c-K_002e-C_002e-191"></a> <!-- Approximate MVA, with Bard-Schweitzer approximation --> <a name="doc_002dqnclosedmultimvaapprox"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-191"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-192"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-193"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-194"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-195"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V</var>)<var><a name="index-qnclosedmultimvaapprox-192"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m</var>)<var><a name="index-qnclosedmultimvaapprox-193"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z</var>)<var><a name="index-qnclosedmultimvaapprox-194"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol</var>)<var><a name="index-qnclosedmultimvaapprox-195"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosedmultimvaapprox</b> (<var>N, S, V, m, Z, tol, iter_max</var>)<var><a name="index-qnclosedmultimvaapprox-196"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-196"></a><a name="index-Approximate-MVA-197"></a><a name="index-Closed-network_002c-multiple-classes-198"></a><a name="index-Closed-network_002c-approximate-analysis-199"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-197"></a><a name="index-Approximate-MVA-198"></a><a name="index-Closed-network_002c-multiple-classes-199"></a><a name="index-Closed-network_002c-approximate-analysis-200"></a> Analyze closed, multiclass queueing networks with K service centers and C customer classes using the approximate Mean Value Analysys (MVA) algorithm. @@ -3624,12 +3640,12 @@ proc. 4th Int. Symp. on Modelling and Performance Evaluation of Computer Systems, feb. 1979, pp. 51–62. - <p><a name="index-Bard_002c-Y_002e-200"></a> + <p><a name="index-Bard_002c-Y_002e-201"></a> P. Schweitzer, <cite>Approximate Analysis of Multiclass Closed Networks of Queues</cite>, Proc. Int. Conf. on Stochastic Control and Optimization, jun 1979, pp. 25–29. - <p><a name="index-Schweitzer_002c-P_002e-201"></a> + <p><a name="index-Schweitzer_002c-P_002e-202"></a> This implementation is based on Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik, <cite>Quantitative System Performance: Computer System Analysis Using Queueing Network Models</cite>, @@ -3640,7 +3656,7 @@ described above, as it computes the average response times R instead of the residence times. - <p><a name="index-Lazowska_002c-E_002e-D_002e-202"></a><a name="index-Zahorjan_002c-J_002e-203"></a><a name="index-Graham_002c-G_002e-S_002e-204"></a><a name="index-Sevcik_002c-K_002e-C_002e-205"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-203"></a><a name="index-Zahorjan_002c-J_002e-204"></a><a name="index-Graham_002c-G_002e-S_002e-205"></a><a name="index-Sevcik_002c-K_002e-C_002e-206"></a> <h4 class="subsection">6.3.5 Mixed Networks</h4> @@ -3648,9 +3664,9 @@ <p><a name="doc_002dqnmix"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmix</b> (<var>lambda, N, S, V, m</var>)<var><a name="index-qnmix-206"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmix</b> (<var>lambda, N, S, V, m</var>)<var><a name="index-qnmix-207"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-207"></a><a name="index-mixed-network-208"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-208"></a><a name="index-mixed-network-209"></a> Solution of mixed queueing networks through MVA. The network consists of K service centers (single-server or delay centers) and C independent customer chains. Both open and closed chains @@ -3741,14 +3757,14 @@ Note that in this function we compute the mean response time R instead of the mean residence time as in the reference. - <p><a name="index-Lazowska_002c-E_002e-D_002e-209"></a><a name="index-Zahorjan_002c-J_002e-210"></a><a name="index-Graham_002c-G_002e-S_002e-211"></a><a name="index-Sevcik_002c-K_002e-C_002e-212"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-210"></a><a name="index-Zahorjan_002c-J_002e-211"></a><a name="index-Graham_002c-G_002e-S_002e-212"></a><a name="index-Sevcik_002c-K_002e-C_002e-213"></a> Herb Schwetman, <cite>Implementing the Mean Value Algorithm for the Solution of Queueing Network Models</cite>, Technical Report CSD-TR-355, Department of Computer Sciences, Purdue University, feb 15, 1982, available at <a href="http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf">http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf</a> - <p><a name="index-Schwetman_002c-H_002e-213"></a> + <p><a name="index-Schwetman_002c-H_002e-214"></a> <div class="node"> <a name="Algorithms-for-non-Product-form-QNs"></a> @@ -3767,9 +3783,9 @@ <p><a name="doc_002dqnmvablo"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmvablo</b> (<var>N, S, M, P</var>)<var><a name="index-qnmvablo-214"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmvablo</b> (<var>N, S, M, P</var>)<var><a name="index-qnmvablo-215"></a></var><br> <blockquote> - <p><a name="index-queueing-network-with-blocking-215"></a><a name="index-blocking-queueing-network-216"></a><a name="index-closed-network_002c-finite-capacity-217"></a> + <p><a name="index-queueing-network-with-blocking-216"></a><a name="index-blocking-queueing-network-217"></a><a name="index-closed-network_002c-finite-capacity-218"></a> MVA algorithm for closed queueing networks with blocking. <samp><span class="command">qnmvablo</span></samp> computes approximate utilization, response time and mean queue length for closed, single class queueing networks with blocking. @@ -3824,16 +3840,16 @@ Networks</cite>, IEEE Transactions on Software Engineering, vol. 14, n. 2, april 1988, pp. 418–428. <a href="http://dx.doi.org/10.1109/32.4663">http://dx.doi.org/10.1109/32.4663</a> - <p><a name="index-Akyildiz_002c-I_002e-F_002e-218"></a> + <p><a name="index-Akyildiz_002c-I_002e-F_002e-219"></a> <a name="doc_002dqnmarkov"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P</var>)<var><a name="index-qnmarkov-219"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P, m</var>)<var><a name="index-qnmarkov-220"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P</var>)<var><a name="index-qnmarkov-221"></a></var><br> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P, m</var>)<var><a name="index-qnmarkov-222"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P</var>)<var><a name="index-qnmarkov-220"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>lambda, S, C, P, m</var>)<var><a name="index-qnmarkov-221"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P</var>)<var><a name="index-qnmarkov-222"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnmarkov</b> (<var>N, S, C, P, m</var>)<var><a name="index-qnmarkov-223"></a></var><br> <blockquote> - <p><a name="index-closed-network_002c-multiple-classes-223"></a><a name="index-closed-network_002c-finite-capacity-224"></a><a name="index-blocking-queueing-network-225"></a><a name="index-RS-blocking-226"></a> + <p><a name="index-closed-network_002c-multiple-classes-224"></a><a name="index-closed-network_002c-finite-capacity-225"></a><a name="index-blocking-queueing-network-226"></a><a name="index-RS-blocking-227"></a> Compute utilization, response time, average queue length and throughput for open or closed queueing networks with finite capacity. Blocking type is Repetitive-Service (RS). This function explicitly @@ -3943,9 +3959,9 @@ <p><a name="doc_002dqnopenab"></a> <div class="defun"> -— Function File: [<var>Xu</var>, <var>Rl</var>] = <b>qnopenab</b> (<var>lambda, D</var>)<var><a name="index-qnopenab-227"></a></var><br> +— Function File: [<var>Xu</var>, <var>Rl</var>] = <b>qnopenab</b> (<var>lambda, D</var>)<var><a name="index-qnopenab-228"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-asymptotic-228"></a><a name="index-open-network-229"></a> + <p><a name="index-bounds_002c-asymptotic-229"></a><a name="index-open-network-230"></a> Compute Asymptotic Bounds for single-class, open Queueing Networks with K service centers. @@ -3985,14 +4001,14 @@ 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In particular, see section 5.2 ("Asymptotic Bounds"). - <p><a name="index-Lazowska_002c-E_002e-D_002e-230"></a><a name="index-Zahorjan_002c-J_002e-231"></a><a name="index-Graham_002c-G_002e-S_002e-232"></a><a name="index-Sevcik_002c-K_002e-C_002e-233"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-231"></a><a name="index-Zahorjan_002c-J_002e-232"></a><a name="index-Graham_002c-G_002e-S_002e-233"></a><a name="index-Sevcik_002c-K_002e-C_002e-234"></a> <a name="doc_002dqnclosedab"></a> <div class="defun"> -— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedab</b> (<var>N, D</var>)<var><a name="index-qnclosedab-234"></a></var><br> -— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedab</b> (<var>N, D, Z</var>)<var><a name="index-qnclosedab-235"></a></var><br> +— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedab</b> (<var>N, D</var>)<var><a name="index-qnclosedab-235"></a></var><br> +— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedab</b> (<var>N, D, Z</var>)<var><a name="index-qnclosedab-236"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-asymptotic-236"></a><a name="index-closed-network-237"></a> + <p><a name="index-bounds_002c-asymptotic-237"></a><a name="index-closed-network-238"></a> Compute Asymptotic Bounds for single-class, closed Queueing Networks with K service centers. @@ -4033,14 +4049,14 @@ 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In particular, see section 5.2 ("Asymptotic Bounds"). - <p><a name="index-Lazowska_002c-E_002e-D_002e-238"></a><a name="index-Zahorjan_002c-J_002e-239"></a><a name="index-Graham_002c-G_002e-S_002e-240"></a><a name="index-Sevcik_002c-K_002e-C_002e-241"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-239"></a><a name="index-Zahorjan_002c-J_002e-240"></a><a name="index-Graham_002c-G_002e-S_002e-241"></a><a name="index-Sevcik_002c-K_002e-C_002e-242"></a> <p><a name="doc_002dqnopenbsb"></a> <div class="defun"> -— Function File: [<var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnopenbsb</b> (<var>lambda, D</var>)<var><a name="index-qnopenbsb-242"></a></var><br> +— Function File: [<var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnopenbsb</b> (<var>lambda, D</var>)<var><a name="index-qnopenbsb-243"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-balanced-system-243"></a><a name="index-open-network-244"></a> + <p><a name="index-bounds_002c-balanced-system-244"></a><a name="index-open-network-245"></a> Compute Balanced System Bounds for single-class, open Queueing Networks with K service centers. @@ -4080,14 +4096,14 @@ 1984. <a href="http://www.cs.washington.edu/homes/lazowska/qsp/">http://www.cs.washington.edu/homes/lazowska/qsp/</a>. In particular, see section 5.4 ("Balanced Systems Bounds"). - <p><a name="index-Lazowska_002c-E_002e-D_002e-245"></a><a name="index-Zahorjan_002c-J_002e-246"></a><a name="index-Graham_002c-G_002e-S_002e-247"></a><a name="index-Sevcik_002c-K_002e-C_002e-248"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-246"></a><a name="index-Zahorjan_002c-J_002e-247"></a><a name="index-Graham_002c-G_002e-S_002e-248"></a><a name="index-Sevcik_002c-K_002e-C_002e-249"></a> <a name="doc_002dqnclosedbsb"></a> <div class="defun"> -— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedbsb</b> (<var>N, D</var>)<var><a name="index-qnclosedbsb-249"></a></var><br> -— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedbsb</b> (<var>N, D, Z</var>)<var><a name="index-qnclosedbsb-250"></a></var><br> +— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedbsb</b> (<var>N, D</var>)<var><a name="index-qnclosedbsb-250"></a></var><br> +— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Rl</var>, <var>Ru</var>] = <b>qnclosedbsb</b> (<var>N, D, Z</var>)<var><a name="index-qnclosedbsb-251"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-balanced-system-251"></a><a name="index-closed-network-252"></a> + <p><a name="index-bounds_002c-balanced-system-252"></a><a name="index-closed-network-253"></a> Compute Balanced System Bounds for single-class, closed Queueing Networks with K service centers. @@ -4123,7 +4139,7 @@ <p><a name="doc_002dqnclosedpb"></a> <div class="defun"> -— Function File: [<var>Xl</var>, <var>Xu</var>] = <b>qnclosedpb</b> (<var>N, D </var>)<var><a name="index-qnclosedpb-253"></a></var><br> +— Function File: [<var>Xl</var>, <var>Xu</var>] = <b>qnclosedpb</b> (<var>N, D </var>)<var><a name="index-qnclosedpb-254"></a></var><br> <blockquote> <p>Compute PB Bounds (C. H. Hsieh and S. Lam, 1987) for single-class, closed Queueing Networks @@ -4167,13 +4183,13 @@ Non-Iterative Analysis Technique for Closed Queueing Networks</cite>, IEEE Transactions on Computers, 57(6):780-794, June 2008. - <p><a name="index-Hsieh_002c-C_002e-H-254"></a><a name="index-Lam_002c-S_002e-255"></a><a name="index-Casale_002c-G_002e-256"></a><a name="index-Muntz_002c-R_002e-R_002e-257"></a><a name="index-Serazzi_002c-G_002e-258"></a> + <p><a name="index-Hsieh_002c-C_002e-H-255"></a><a name="index-Lam_002c-S_002e-256"></a><a name="index-Casale_002c-G_002e-257"></a><a name="index-Muntz_002c-R_002e-R_002e-258"></a><a name="index-Serazzi_002c-G_002e-259"></a> <a name="doc_002dqnclosedgb"></a> <div class="defun"> -— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Ql</var>, <var>Qu</var>] = <b>qnclosedgb</b> (<var>N, D, Z</var>)<var><a name="index-qnclosedgb-259"></a></var><br> +— Function File: [<var>Xl</var>, <var>Xu</var>, <var>Ql</var>, <var>Qu</var>] = <b>qnclosedgb</b> (<var>N, D, Z</var>)<var><a name="index-qnclosedgb-260"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-geometric-260"></a><a name="index-closed-network-261"></a> + <p><a name="index-bounds_002c-geometric-261"></a><a name="index-closed-network-262"></a> Compute Geometric Bounds (GB) for single-class, closed Queueing Networks. <p><strong>INPUTS</strong> @@ -4214,7 +4230,7 @@ Queueing Networks</cite>, IEEE Transactions on Computers, 57(6):780-794, June 2008. <a href="http://doi.ieeecomputersociety.org/10.1109/TC.2008.37">http://doi.ieeecomputersociety.org/10.1109/TC.2008.37</a> - <p><a name="index-Casale_002c-G_002e-262"></a><a name="index-Muntz_002c-R_002e-R_002e-263"></a><a name="index-Serazzi_002c-G_002e-264"></a> + <p><a name="index-Casale_002c-G_002e-263"></a><a name="index-Muntz_002c-R_002e-R_002e-264"></a><a name="index-Serazzi_002c-G_002e-265"></a> In this implementation we set X^+ and X^- as the upper and lower Asymptotic Bounds as computed by the <code>qnclosedab</code> function, respectively. @@ -4234,9 +4250,9 @@ <p><a name="doc_002dqnclosed"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosed</b> (<var>N, S, V, <small class="dots">...</small></var>)<var><a name="index-qnclosed-265"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnclosed</b> (<var>N, S, V, <small class="dots">...</small></var>)<var><a name="index-qnclosed-266"></a></var><br> <blockquote> - <p><a name="index-closed-network-266"></a> + <p><a name="index-closed-network-267"></a> This function computes steady-state performance measures of closed queueing networks using the Mean Value Analysis (MVA) algorithm. The qneneing network is allowed to contain fixed-capacity centers, delay @@ -4303,9 +4319,9 @@ <p><a name="doc_002dqnopen"></a> <div class="defun"> -— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopen</b> (<var>lambda, S, V, <small class="dots">...</small></var>)<var><a name="index-qnopen-267"></a></var><br> +— Function File: [<var>U</var>, <var>R</var>, <var>Q</var>, <var>X</var>] = <b>qnopen</b> (<var>lambda, S, V, <small class="dots">...</small></var>)<var><a name="index-qnopen-268"></a></var><br> <blockquote> - <p><a name="index-open-network-268"></a> + <p><a name="index-open-network-269"></a> Compute utilization, response time, average number of requests in the system, and throughput for open queueing networks. If <var>lambda</var> is a scalar, the network is considered a single-class QN and is solved @@ -4358,8 +4374,8 @@ <p><a name="doc_002dqnvisits"></a> <div class="defun"> -— Function File: [<var>V</var> <var>ch</var>] = <b>qnvisits</b> (<var>P</var>)<var><a name="index-qnvisits-269"></a></var><br> -— Function File: <var>V</var> = <b>qnvisits</b> (<var>P, lambda</var>)<var><a name="index-qnvisits-270"></a></var><br> +— Function File: [<var>V</var> <var>ch</var>] = <b>qnvisits</b> (<var>P</var>)<var><a name="index-qnvisits-270"></a></var><br> +— Function File: <var>V</var> = <b>qnvisits</b> (<var>P, lambda</var>)<var><a name="index-qnvisits-271"></a></var><br> <blockquote> <p>Compute the average number of visits to the service centers of a single class, open or closed Queueing Network with N service @@ -4421,9 +4437,9 @@ <p><a name="doc_002dpopulation_005fmix"></a> <div class="defun"> -— Function File: pop_mix = <b>population_mix</b> (<var>k, N</var>)<var><a name="index-population_005fmix-271"></a></var><br> +— Function File: pop_mix = <b>population_mix</b> (<var>k, N</var>)<var><a name="index-population_005fmix-272"></a></var><br> <blockquote> - <p><a name="index-population-mix-272"></a><a name="index-closed-network_002c-multiple-classes-273"></a> + <p><a name="index-population-mix-273"></a><a name="index-closed-network_002c-multiple-classes-274"></a> Return the set of valid population mixes with exactly <var>k</var> customers, for a closed multiclass Queueing Network with population vector <var>N</var>. More specifically, given a multiclass Queueing @@ -4485,13 +4501,13 @@ Indices for a Complex Summation</cite>, unpublished report, available at <a href="http://arantxa.ii.uam.es/~ssantini/writing/notes/s668_summation.pdf">http://arantxa.ii.uam.es/~ssantini/writing/notes/s668_summation.pdf</a> - <p><a name="index-Schwetman_002c-H_002e-274"></a><a name="index-Santini_002c-S_002e-275"></a> + <p><a name="index-Schwetman_002c-H_002e-275"></a><a name="index-Santini_002c-S_002e-276"></a> <a name="doc_002dqnmvapop"></a> <div class="defun"> -— Function File: <var>H</var> = <b>qnmvapop</b> (<var>N</var>)<var><a name="index-qnmvapop-276"></a></var><br> +— Function File: <var>H</var> = <b>qnmvapop</b> (<var>N</var>)<var><a name="index-qnmvapop-277"></a></var><br> <blockquote> - <p><a name="index-population-mix-277"></a><a name="index-closed-network_002c-multiple-classes-278"></a> + <p><a name="index-population-mix-278"></a><a name="index-closed-network_002c-multiple-classes-279"></a> Given a network with C customer classes, this function computes the number of valid population mixes <var>H</var><code>(r,n)</code> that can be constructed by the multiclass MVA algorithm by allocating n @@ -4528,7 +4544,7 @@ Perform. Eval. Rev. 10, 3 (Sep. 1981), 80-85. DOI <a href="http://doi.acm.org/10.1145/1010629.805477">http://doi.acm.org/10.1145/1010629.805477</a> - <p><a name="index-Zahorjan_002c-J_002e-279"></a><a name="index-Wong_002c-E_002e-280"></a> + <p><a name="index-Zahorjan_002c-J_002e-280"></a><a name="index-Wong_002c-E_002e-281"></a> <!-- Appendix starts here --> <!-- DO NOT EDIT! Generated automatically by munge-texi. --> @@ -4639,7 +4655,7 @@ <h2 class="appendix">Appendix C GNU GENERAL PUBLIC LICENSE</h2> -<p><a name="index-warranty-281"></a><a name="index-copyright-282"></a> +<p><a name="index-warranty-282"></a><a name="index-copyright-283"></a> <div align="center">Version 3, 29 June 2007</div> <pre class="display"> Copyright © 2007 Free Software Foundation, Inc. <a href="http://fsf.org/">http://fsf.org/</a> @@ -5346,69 +5362,69 @@ <h2 class="unnumbered">Concept Index</h2> <ul class="index-cp" compact> -<li><a href="#index-Approximate-MVA-166">Approximate MVA</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-66">Asymmetric M/M/m system</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> -<li><a href="#index-BCMP-network-121">BCMP network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Approximate-MVA-167">Approximate MVA</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-67">Asymmetric M/M/m system</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> +<li><a href="#index-BCMP-network-122">BCMP network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> <li><a href="#index-Birth_002ddeath-process-19">Birth-death process</a>: <a href="#Birth_002dDeath-process">Birth-Death process</a></li> -<li><a href="#index-blocking-queueing-network-216">blocking queueing network</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> -<li><a href="#index-bounds_002c-asymptotic-228">bounds, asymptotic</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-bounds_002c-balanced-system-243">bounds, balanced system</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-bounds_002c-geometric-260">bounds, geometric</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-closed-network-266">closed network</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-closed-network-237">closed network</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-closed-network-98">closed network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Closed-network_002c-approximate-analysis-168">Closed network, approximate analysis</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-closed-network_002c-finite-capacity-217">closed network, finite capacity</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> -<li><a href="#index-closed-network_002c-multiple-classes-273">closed network, multiple classes</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-closed-network_002c-multiple-classes-223">closed network, multiple classes</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> -<li><a href="#index-Closed-network_002c-multiple-classes-198">Closed network, multiple classes</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-closed-network_002c-multiple-classes-180">closed network, multiple classes</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Closed-network_002c-single-class-167">Closed network, single class</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-closed-network_002c-single-class-137">closed network, single class</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-CMVA-158">CMVA</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-blocking-queueing-network-217">blocking queueing network</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-bounds_002c-asymptotic-229">bounds, asymptotic</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-bounds_002c-balanced-system-244">bounds, balanced system</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-bounds_002c-geometric-261">bounds, geometric</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-closed-network-267">closed network</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-closed-network-238">closed network</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-closed-network-99">closed network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Closed-network_002c-approximate-analysis-169">Closed network, approximate analysis</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-closed-network_002c-finite-capacity-218">closed network, finite capacity</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-closed-network_002c-multiple-classes-274">closed network, multiple classes</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-closed-network_002c-multiple-classes-224">closed network, multiple classes</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-Closed-network_002c-multiple-classes-199">Closed network, multiple classes</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-closed-network_002c-multiple-classes-181">closed network, multiple classes</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Closed-network_002c-single-class-168">Closed network, single class</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-closed-network_002c-single-class-138">closed network, single class</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-CMVA-159">CMVA</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> <li><a href="#index-Continuous-time-Markov-chain-14">Continuous time Markov chain</a>: <a href="#CTMC-Stationary-Probability">CTMC Stationary Probability</a></li> -<li><a href="#index-convolution-algorithm-100">convolution algorithm</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-copyright-282">copyright</a>: <a href="#Copying">Copying</a></li> +<li><a href="#index-convolution-algorithm-101">convolution algorithm</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-copyright-283">copyright</a>: <a href="#Copying">Copying</a></li> <li><a href="#index-Discrete-time-Markov-chain-4">Discrete time Markov chain</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-Expected-sojourn-time-22">Expected sojourn time</a>: <a href="#Expected-Sojourn-Time">Expected Sojourn Time</a></li> -<li><a href="#index-First-passage-times-36">First passage times</a>: <a href="#CTMC-First-Passage-Times">CTMC First Passage Times</a></li> +<li><a href="#index-Expected-sojourn-time-23">Expected sojourn time</a>: <a href="#Expected-Sojourn-Time">Expected Sojourn Time</a></li> +<li><a href="#index-First-passage-times-37">First passage times</a>: <a href="#CTMC-First-Passage-Times">CTMC First Passage Times</a></li> <li><a href="#index-First-passage-times-10">First passage times</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-Jackson-network-91">Jackson network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-load_002ddependent-service-center-110">load-dependent service center</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-g_t_0040math_007bM_002fG_002f1_007d-system-72">M/G/1 system</a>: <a href="#The-M_002fG_002f1-System">The M/G/1 System</a></li> -<li><a href="#index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-74">M/H_m/1 system</a>: <a href="#The-M_002fHm_002f1-System">The M/Hm/1 System</a></li> -<li><a href="#index-g_t_0040math_007bM_002fM_002f1_007d-system-38">M/M/1 system</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> -<li><a href="#index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-58">M/M/1/K system</a>: <a href="#The-M_002fM_002f1_002fK-System">The M/M/1/K System</a></li> -<li><a href="#index-g_t_0040math_007bM_002fM_002f_007dinf-system-51">M/M/inf system</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-g_t_0040math_007bM_002fM_002fm_007d-system-45">M/M/m system</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> -<li><a href="#index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-60">M/M/m/K system</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> -<li><a href="#index-Markov-chain_002c-continuous-time-35">Markov chain, continuous time</a>: <a href="#CTMC-First-Passage-Times">CTMC First Passage Times</a></li> -<li><a href="#index-Markov-chain_002c-continuous-time-27">Markov chain, continuous time</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> -<li><a href="#index-Markov-chain_002c-continuous-time-24">Markov chain, continuous time</a>: <a href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a></li> -<li><a href="#index-Markov-chain_002c-continuous-time-21">Markov chain, continuous time</a>: <a href="#Expected-Sojourn-Time">Expected Sojourn Time</a></li> +<li><a href="#index-Jackson-network-92">Jackson network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-load_002ddependent-service-center-111">load-dependent service center</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-g_t_0040math_007bM_002fG_002f1_007d-system-73">M/G/1 system</a>: <a href="#The-M_002fG_002f1-System">The M/G/1 System</a></li> +<li><a href="#index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-75">M/H_m/1 system</a>: <a href="#The-M_002fHm_002f1-System">The M/Hm/1 System</a></li> +<li><a href="#index-g_t_0040math_007bM_002fM_002f1_007d-system-39">M/M/1 system</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> +<li><a href="#index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-59">M/M/1/K system</a>: <a href="#The-M_002fM_002f1_002fK-System">The M/M/1/K System</a></li> +<li><a href="#index-g_t_0040math_007bM_002fM_002f_007dinf-system-52">M/M/inf system</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-g_t_0040math_007bM_002fM_002fm_007d-system-46">M/M/m system</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> +<li><a href="#index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-61">M/M/m/K system</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> +<li><a href="#index-Markov-chain_002c-continuous-time-36">Markov chain, continuous time</a>: <a href="#CTMC-First-Passage-Times">CTMC First Passage Times</a></li> +<li><a href="#index-Markov-chain_002c-continuous-time-28">Markov chain, continuous time</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> +<li><a href="#index-Markov-chain_002c-continuous-time-25">Markov chain, continuous time</a>: <a href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a></li> +<li><a href="#index-Markov-chain_002c-continuous-time-22">Markov chain, continuous time</a>: <a href="#Expected-Sojourn-Time">Expected Sojourn Time</a></li> <li><a href="#index-Markov-chain_002c-continuous-time-18">Markov chain, continuous time</a>: <a href="#Birth_002dDeath-process">Birth-Death process</a></li> <li><a href="#index-Markov-chain_002c-continuous-time-13">Markov chain, continuous time</a>: <a href="#CTMC-Stationary-Probability">CTMC Stationary Probability</a></li> <li><a href="#index-Markov-chain_002c-discrete-time-3">Markov chain, discrete time</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> <li><a href="#index-Markov-chain_002c-state-occupancy-probabilities-15">Markov chain, state occupancy probabilities</a>: <a href="#CTMC-Stationary-Probability">CTMC Stationary Probability</a></li> <li><a href="#index-Markov-chain_002c-stationary-probabilities-5">Markov chain, stationary probabilities</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-Mean-time-to-absorption-28">Mean time to absorption</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> -<li><a href="#index-Mean-Value-Analysys-_0028MVA_0029-136">Mean Value Analysys (MVA)</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-165">Mean Value Analysys (MVA), approximate</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-mixed-network-208">mixed network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-normalization-constant-99">normalization constant</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-open-network-268">open network</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-open-network-229">open network</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-open-network_002c-multiple-classes-128">open network, multiple classes</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-open-network_002c-single-class-90">open network, single class</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-population-mix-272">population mix</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-queueing-network-with-blocking-215">queueing network with blocking</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> -<li><a href="#index-queueing-networks-75">queueing networks</a>: <a href="#Queueing-Networks">Queueing Networks</a></li> -<li><a href="#index-RS-blocking-226">RS blocking</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-Mean-time-to-absorption-29">Mean time to absorption</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> +<li><a href="#index-Mean-Value-Analysys-_0028MVA_0029-137">Mean Value Analysys (MVA)</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-166">Mean Value Analysys (MVA), approximate</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-mixed-network-209">mixed network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-normalization-constant-100">normalization constant</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-open-network-269">open network</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-open-network-230">open network</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-open-network_002c-multiple-classes-129">open network, multiple classes</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-open-network_002c-single-class-91">open network, single class</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-population-mix-273">population mix</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-queueing-network-with-blocking-216">queueing network with blocking</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-queueing-networks-76">queueing networks</a>: <a href="#Queueing-Networks">Queueing Networks</a></li> +<li><a href="#index-RS-blocking-227">RS blocking</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> <li><a href="#index-Stationary-probabilities-16">Stationary probabilities</a>: <a href="#CTMC-Stationary-Probability">CTMC Stationary Probability</a></li> <li><a href="#index-Stationary-probabilities-6">Stationary probabilities</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-Time_002dalveraged-sojourn-time-25">Time-alveraged sojourn time</a>: <a href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a></li> -<li><a href="#index-traffic-intensity-52">traffic intensity</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-warranty-281">warranty</a>: <a href="#Copying">Copying</a></li> +<li><a href="#index-Time_002dalveraged-sojourn-time-26">Time-alveraged sojourn time</a>: <a href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a></li> +<li><a href="#index-traffic-intensity-53">traffic intensity</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-warranty-282">warranty</a>: <a href="#Copying">Copying</a></li> </ul><div class="node"> <a name="Function-Index"></a> <p><hr> @@ -5426,46 +5442,46 @@ <li><a href="#index-ctmc-11"><code>ctmc</code></a>: <a href="#CTMC-Stationary-Probability">CTMC Stationary Probability</a></li> <li><a href="#index-ctmc_005fbd-17"><code>ctmc_bd</code></a>: <a href="#Birth_002dDeath-process">Birth-Death process</a></li> <li><a href="#index-ctmc_005fexps-20"><code>ctmc_exps</code></a>: <a href="#Expected-Sojourn-Time">Expected Sojourn Time</a></li> -<li><a href="#index-ctmc_005ffpt-33"><code>ctmc_fpt</code></a>: <a href="#CTMC-First-Passage-Times">CTMC First Passage Times</a></li> -<li><a href="#index-ctmc_005fmtta-26"><code>ctmc_mtta</code></a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> -<li><a href="#index-ctmc_005ftaexps-23"><code>ctmc_taexps</code></a>: <a href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a></li> +<li><a href="#index-ctmc_005ffpt-34"><code>ctmc_fpt</code></a>: <a href="#CTMC-First-Passage-Times">CTMC First Passage Times</a></li> +<li><a href="#index-ctmc_005fmtta-27"><code>ctmc_mtta</code></a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> +<li><a href="#index-ctmc_005ftaexps-24"><code>ctmc_taexps</code></a>: <a href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a></li> <li><a href="#index-dtmc-1"><code>dtmc</code></a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> <li><a href="#index-dtmc_005ffpt-7"><code>dtmc_fpt</code></a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-population_005fmix-271"><code>population_mix</code></a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-qnammm-65"><code>qnammm</code></a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> -<li><a href="#index-qnclosed-265"><code>qnclosed</code></a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-qnclosedab-234"><code>qnclosedab</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnclosedbsb-249"><code>qnclosedbsb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnclosedgb-259"><code>qnclosedgb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnclosedmultimva-173"><code>qnclosedmultimva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnclosedmultimvaapprox-191"><code>qnclosedmultimvaapprox</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnclosedpb-253"><code>qnclosedpb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnclosedsinglemva-133"><code>qnclosedsinglemva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnclosedsinglemvaapprox-160"><code>qnclosedsinglemvaapprox</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnclosedsinglemvald-146"><code>qnclosedsinglemvald</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qncmva-155"><code>qncmva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnconvolution-96"><code>qnconvolution</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnconvolutionld-106"><code>qnconvolutionld</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnjackson-87"><code>qnjackson</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnmarkov-219"><code>qnmarkov</code></a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> -<li><a href="#index-qnmg1-71"><code>qnmg1</code></a>: <a href="#The-M_002fG_002f1-System">The M/G/1 System</a></li> -<li><a href="#index-qnmh1-73"><code>qnmh1</code></a>: <a href="#The-M_002fHm_002f1-System">The M/Hm/1 System</a></li> -<li><a href="#index-qnmix-206"><code>qnmix</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnmknode-76"><code>qnmknode</code></a>: <a href="#Generic-Algorithms">Generic Algorithms</a></li> -<li><a href="#index-qnmm1-37"><code>qnmm1</code></a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> -<li><a href="#index-qnmm1k-57"><code>qnmm1k</code></a>: <a href="#The-M_002fM_002f1_002fK-System">The M/M/1/K System</a></li> -<li><a href="#index-qnmminf-50"><code>qnmminf</code></a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-qnmmm-43"><code>qnmmm</code></a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> -<li><a href="#index-qnmmmk-59"><code>qnmmmk</code></a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> -<li><a href="#index-qnmvablo-214"><code>qnmvablo</code></a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> -<li><a href="#index-qnmvapop-276"><code>qnmvapop</code></a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-qnopen-267"><code>qnopen</code></a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-qnopenab-227"><code>qnopenab</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnopenbsb-242"><code>qnopenbsb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnopenmulti-126"><code>qnopenmulti</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnopensingle-118"><code>qnopensingle</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnsolve-83"><code>qnsolve</code></a>: <a href="#Generic-Algorithms">Generic Algorithms</a></li> -<li><a href="#index-qnvisits-269"><code>qnvisits</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-population_005fmix-272"><code>population_mix</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-qnammm-66"><code>qnammm</code></a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> +<li><a href="#index-qnclosed-266"><code>qnclosed</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-qnclosedab-235"><code>qnclosedab</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnclosedbsb-250"><code>qnclosedbsb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnclosedgb-260"><code>qnclosedgb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnclosedmultimva-174"><code>qnclosedmultimva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnclosedmultimvaapprox-192"><code>qnclosedmultimvaapprox</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnclosedpb-254"><code>qnclosedpb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnclosedsinglemva-134"><code>qnclosedsinglemva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnclosedsinglemvaapprox-161"><code>qnclosedsinglemvaapprox</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnclosedsinglemvald-147"><code>qnclosedsinglemvald</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qncmva-156"><code>qncmva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnconvolution-97"><code>qnconvolution</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnconvolutionld-107"><code>qnconvolutionld</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnjackson-88"><code>qnjackson</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnmarkov-220"><code>qnmarkov</code></a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-qnmg1-72"><code>qnmg1</code></a>: <a href="#The-M_002fG_002f1-System">The M/G/1 System</a></li> +<li><a href="#index-qnmh1-74"><code>qnmh1</code></a>: <a href="#The-M_002fHm_002f1-System">The M/Hm/1 System</a></li> +<li><a href="#index-qnmix-207"><code>qnmix</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnmknode-77"><code>qnmknode</code></a>: <a href="#Generic-Algorithms">Generic Algorithms</a></li> +<li><a href="#index-qnmm1-38"><code>qnmm1</code></a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> +<li><a href="#index-qnmm1k-58"><code>qnmm1k</code></a>: <a href="#The-M_002fM_002f1_002fK-System">The M/M/1/K System</a></li> +<li><a href="#index-qnmminf-51"><code>qnmminf</code></a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-qnmmm-44"><code>qnmmm</code></a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> +<li><a href="#index-qnmmmk-60"><code>qnmmmk</code></a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> +<li><a href="#index-qnmvablo-215"><code>qnmvablo</code></a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-qnmvapop-277"><code>qnmvapop</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-qnopen-268"><code>qnopen</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-qnopenab-228"><code>qnopenab</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnopenbsb-243"><code>qnopenbsb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnopenmulti-127"><code>qnopenmulti</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnopensingle-119"><code>qnopensingle</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnsolve-84"><code>qnsolve</code></a>: <a href="#Generic-Algorithms">Generic Algorithms</a></li> +<li><a href="#index-qnvisits-270"><code>qnvisits</code></a>: <a href="#Utility-functions">Utility functions</a></li> </ul><div class="node"> <a name="Author-Index"></a> <p><hr> @@ -5479,60 +5495,60 @@ <ul class="index-au" compact> -<li><a href="#index-Akyildiz_002c-I_002e-F_002e-218">Akyildiz, I. F.</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> -<li><a href="#index-Bard_002c-Y_002e-200">Bard, Y.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Bolch_002c-G_002e-92">Bolch, G.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Bolch_002c-G_002e-67">Bolch, G.</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> -<li><a href="#index-Bolch_002c-G_002e-61">Bolch, G.</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> -<li><a href="#index-Bolch_002c-G_002e-53">Bolch, G.</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-Bolch_002c-G_002e-46">Bolch, G.</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> -<li><a href="#index-Bolch_002c-G_002e-39">Bolch, G.</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> -<li><a href="#index-Bolch_002c-G_002e-29">Bolch, G.</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> -<li><a href="#index-Buzen_002c-J_002e-P_002e-101">Buzen, J. P.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Casale_002c-G_002e-256">Casale, G.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Casale_002c-G_002e-159">Casale, G.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-de-Meer_002c-H_002e-94">de Meer, H.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-de-Meer_002c-H_002e-69">de Meer, H.</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> -<li><a href="#index-de-Meer_002c-H_002e-63">de Meer, H.</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> -<li><a href="#index-de-Meer_002c-H_002e-55">de Meer, H.</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-de-Meer_002c-H_002e-48">de Meer, H.</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> -<li><a href="#index-de-Meer_002c-H_002e-41">de Meer, H.</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> -<li><a href="#index-de-Meer_002c-H_002e-31">de Meer, H.</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> -<li><a href="#index-Graham_002c-G_002e-S_002e-232">Graham, G. S.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Graham_002c-G_002e-S_002e-131">Graham, G. S.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Greiner_002c-S_002e-93">Greiner, S.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Greiner_002c-S_002e-68">Greiner, S.</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> -<li><a href="#index-Greiner_002c-S_002e-62">Greiner, S.</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> -<li><a href="#index-Greiner_002c-S_002e-54">Greiner, S.</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-Greiner_002c-S_002e-47">Greiner, S.</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> -<li><a href="#index-Greiner_002c-S_002e-40">Greiner, S.</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> -<li><a href="#index-Greiner_002c-S_002e-30">Greiner, S.</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> -<li><a href="#index-Hsieh_002c-C_002e-H-254">Hsieh, C. H</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Jain_002c-R_002e-141">Jain, R.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Kobayashi_002c-H_002e-113">Kobayashi, H.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Lam_002c-S_002e-255">Lam, S.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Lavenberg_002c-S_002e-S_002e-140">Lavenberg, S. S.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Lazowska_002c-E_002e-D_002e-230">Lazowska, E. D.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Lazowska_002c-E_002e-D_002e-129">Lazowska, E. D.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Muntz_002c-R_002e-R_002e-257">Muntz, R. R.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Reiser_002c-M_002e-112">Reiser, M.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Santini_002c-S_002e-275">Santini, S.</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-Schweitzer_002c-P_002e-201">Schweitzer, P.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Schwetman_002c-H_002e-274">Schwetman, H.</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-Schwetman_002c-H_002e-111">Schwetman, H.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Serazzi_002c-G_002e-258">Serazzi, G.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Sevcik_002c-K_002e-C_002e-233">Sevcik, K. C.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Sevcik_002c-K_002e-C_002e-132">Sevcik, K. C.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Trivedi_002c-K_002e-95">Trivedi, K.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-Trivedi_002c-K_002e-70">Trivedi, K.</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> -<li><a href="#index-Trivedi_002c-K_002e-64">Trivedi, K.</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> -<li><a href="#index-Trivedi_002c-K_002e-56">Trivedi, K.</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-Trivedi_002c-K_002e-49">Trivedi, K.</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> -<li><a href="#index-Trivedi_002c-K_002e-42">Trivedi, K.</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> -<li><a href="#index-Trivedi_002c-K_002e-32">Trivedi, K.</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> -<li><a href="#index-Wong_002c-E_002e-280">Wong, E.</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-Zahorjan_002c-J_002e-279">Zahorjan, J.</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-Zahorjan_002c-J_002e-231">Zahorjan, J.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Zahorjan_002c-J_002e-130">Zahorjan, J.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Akyildiz_002c-I_002e-F_002e-219">Akyildiz, I. F.</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-Bard_002c-Y_002e-201">Bard, Y.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Bolch_002c-G_002e-93">Bolch, G.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Bolch_002c-G_002e-68">Bolch, G.</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> +<li><a href="#index-Bolch_002c-G_002e-62">Bolch, G.</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> +<li><a href="#index-Bolch_002c-G_002e-54">Bolch, G.</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-Bolch_002c-G_002e-47">Bolch, G.</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> +<li><a href="#index-Bolch_002c-G_002e-40">Bolch, G.</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> +<li><a href="#index-Bolch_002c-G_002e-30">Bolch, G.</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> +<li><a href="#index-Buzen_002c-J_002e-P_002e-102">Buzen, J. P.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Casale_002c-G_002e-257">Casale, G.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Casale_002c-G_002e-160">Casale, G.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-de-Meer_002c-H_002e-95">de Meer, H.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-de-Meer_002c-H_002e-70">de Meer, H.</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> +<li><a href="#index-de-Meer_002c-H_002e-64">de Meer, H.</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> +<li><a href="#index-de-Meer_002c-H_002e-56">de Meer, H.</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-de-Meer_002c-H_002e-49">de Meer, H.</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> +<li><a href="#index-de-Meer_002c-H_002e-42">de Meer, H.</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> +<li><a href="#index-de-Meer_002c-H_002e-32">de Meer, H.</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> +<li><a href="#index-Graham_002c-G_002e-S_002e-233">Graham, G. S.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Graham_002c-G_002e-S_002e-132">Graham, G. S.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Greiner_002c-S_002e-94">Greiner, S.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Greiner_002c-S_002e-69">Greiner, S.</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> +<li><a href="#index-Greiner_002c-S_002e-63">Greiner, S.</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> +<li><a href="#index-Greiner_002c-S_002e-55">Greiner, S.</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-Greiner_002c-S_002e-48">Greiner, S.</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> +<li><a href="#index-Greiner_002c-S_002e-41">Greiner, S.</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> +<li><a href="#index-Greiner_002c-S_002e-31">Greiner, S.</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> +<li><a href="#index-Hsieh_002c-C_002e-H-255">Hsieh, C. H</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Jain_002c-R_002e-142">Jain, R.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Kobayashi_002c-H_002e-114">Kobayashi, H.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Lam_002c-S_002e-256">Lam, S.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Lavenberg_002c-S_002e-S_002e-141">Lavenberg, S. S.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Lazowska_002c-E_002e-D_002e-231">Lazowska, E. D.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Lazowska_002c-E_002e-D_002e-130">Lazowska, E. D.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Muntz_002c-R_002e-R_002e-258">Muntz, R. R.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Reiser_002c-M_002e-113">Reiser, M.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Santini_002c-S_002e-276">Santini, S.</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-Schweitzer_002c-P_002e-202">Schweitzer, P.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Schwetman_002c-H_002e-275">Schwetman, H.</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-Schwetman_002c-H_002e-112">Schwetman, H.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Serazzi_002c-G_002e-259">Serazzi, G.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Sevcik_002c-K_002e-C_002e-234">Sevcik, K. C.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Sevcik_002c-K_002e-C_002e-133">Sevcik, K. C.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Trivedi_002c-K_002e-96">Trivedi, K.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Trivedi_002c-K_002e-71">Trivedi, K.</a>: <a href="#The-Asymmetric-M_002fM_002fm-System">The Asymmetric M/M/m System</a></li> +<li><a href="#index-Trivedi_002c-K_002e-65">Trivedi, K.</a>: <a href="#The-M_002fM_002fm_002fK-System">The M/M/m/K System</a></li> +<li><a href="#index-Trivedi_002c-K_002e-57">Trivedi, K.</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-Trivedi_002c-K_002e-50">Trivedi, K.</a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> +<li><a href="#index-Trivedi_002c-K_002e-43">Trivedi, K.</a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> +<li><a href="#index-Trivedi_002c-K_002e-33">Trivedi, K.</a>: <a href="#Expected-Time-to-Absorption">Expected Time to Absorption</a></li> +<li><a href="#index-Wong_002c-E_002e-281">Wong, E.</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-Zahorjan_002c-J_002e-280">Zahorjan, J.</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-Zahorjan_002c-J_002e-232">Zahorjan, J.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Zahorjan_002c-J_002e-131">Zahorjan, J.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> </ul></body></html>
--- a/main/queueing/inst/ctmc_exps.m Sat Mar 10 16:00:45 2012 +0000 +++ b/main/queueing/inst/ctmc_exps.m Sat Mar 10 16:03:47 2012 +0000 @@ -27,7 +27,7 @@ ## spent in each state @math{j} during the time interval ## @code{[0,@var{tt}(t))}, assuming that at time 0 the state occupancy ## probability was @var{p}. With two arguments, compute the expected -## time @code{@var{L}(j}} spent in each state @math{j} until absorption. +## time @code{@var{L}(j)} spent in each state @math{j} until absorption. ## ## @strong{INPUTS} ##