Mercurial > forge
changeset 9692:dee7b9b17fae octave-forge
updated documentation
| author | mmarzolla |
|---|---|
| date | Wed, 14 Mar 2012 09:00:49 +0000 |
| parents | 617395740b29 |
| children | ae1a6c55972e |
| files | main/queueing/doc/queueing.html main/queueing/doc/queueing.pdf |
| diffstat | 2 files changed, 300 insertions(+), 296 deletions(-) [+] |
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--- a/main/queueing/doc/queueing.html Wed Mar 14 06:59:32 2012 +0000 +++ b/main/queueing/doc/queueing.html Wed Mar 14 09:00:49 2012 +0000 @@ -1337,12 +1337,13 @@ <div class="defun"> — Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, t, p</var>)<var><a name="index-ctmc_005ftaexps-35"></a></var><br> +— Function File: <var>M</var> = <b>ctmc_taexps</b> (<var>Q, p</var>)<var><a name="index-ctmc_005ftaexps-36"></a></var><br> <blockquote> - <p><a name="index-Markov-chain_002c-continuous-time-36"></a><a name="index-Time_002dalveraged-sojourn-time-37"></a> + <p><a name="index-Markov-chain_002c-continuous-time-37"></a><a name="index-Time_002dalveraged-sojourn-time-38"></a> Compute the <em>time-averaged sojourn time</em> <var>M</var><code>(i)</code>, -defined as the fraction of the time interval [0,t] spent in -state i, assuming that the state occupancy probabilities at -time 0 are <var>p</var>. +defined as the fraction of the time interval [0,t] (or until +absorption) spent in state i, assuming that the state +occupancy probabilities at time 0 are <var>p</var>. <p><strong>INPUTS</strong> @@ -1352,7 +1353,7 @@ 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>t</var><dd>Time + <br><dt><var>t</var><dd>Time. If omitted, the results are computed until absorption. <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 @@ -1362,9 +1363,12 @@ <p><strong>OUTPUTS</strong> <dl> -<dt><var>M</var><dd><var>M</var><code>(i)</code> is the expected fraction of time spent in state -i during the interval [0,t] assuming that the state -occupancy probability at time zero is <var>p</var>. +<dt><var>M</var><dd>If this function is called with three parameters, <var>M</var><code>(i)</code> +is the expected fraction of the interval 0,t] spent in state +i assuming that the state occupancy probability at time zero +is <var>p</var>. If this function is called with two parameters, +<var>M</var><code>(i)</code> is the expected fraction of time until absorption +spent in state i. </dl> @@ -1421,9 +1425,9 @@ <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-38"></a></var><br> +— Function File: <var>t</var> = <b>ctmc_mtta</b> (<var>Q, p</var>)<var><a name="index-ctmc_005fmtta-39"></a></var><br> <blockquote> - <p><a name="index-Markov-chain_002c-continuous-time-39"></a><a name="index-Mean-time-to-absorption-40"></a> + <p><a name="index-Markov-chain_002c-continuous-time-40"></a><a name="index-Mean-time-to-absorption-41"></a> Compute the Mean-Time to Absorption (MTTA) of the CTMC described by the infinitesimal generator matrix <var>Q</var>, starting from initial occupancy probabilities <var>p</var>. If there are no absorbing states, this @@ -1484,7 +1488,7 @@ Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998. - <p><a name="index-Bolch_002c-G_002e-41"></a><a name="index-Greiner_002c-S_002e-42"></a><a name="index-de-Meer_002c-H_002e-43"></a><a name="index-Trivedi_002c-K_002e-44"></a> + <p><a name="index-Bolch_002c-G_002e-42"></a><a name="index-Greiner_002c-S_002e-43"></a><a name="index-de-Meer_002c-H_002e-44"></a><a name="index-Trivedi_002c-K_002e-45"></a> <div class="node"> <a name="First-Passage-Times"></a> <p><hr> @@ -1498,10 +1502,10 @@ <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-45"></a></var><br> -— Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-46"></a></var><br> +— Function File: <var>M</var> = <b>ctmc_fpt</b> (<var>Q</var>)<var><a name="index-ctmc_005ffpt-46"></a></var><br> +— Function File: <var>m</var> = <b>ctmc_fpt</b> (<var>Q, i, j</var>)<var><a name="index-ctmc_005ffpt-47"></a></var><br> <blockquote> - <p><a name="index-Markov-chain_002c-continuous-time-47"></a><a name="index-First-passage-times-48"></a> + <p><a name="index-Markov-chain_002c-continuous-time-48"></a><a name="index-First-passage-times-49"></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 @@ -1607,9 +1611,9 @@ <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-qnmm1-49"></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-qnmm1-50"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-50"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002f1_007d-system-51"></a> Compute utilization, response time, average number of requests and throughput for a M/M/1 queue. @@ -1654,7 +1658,7 @@ 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-51"></a><a name="index-Greiner_002c-S_002e-52"></a><a name="index-de-Meer_002c-H_002e-53"></a><a name="index-Trivedi_002c-K_002e-54"></a> + <p><a name="index-Bolch_002c-G_002e-52"></a><a name="index-Greiner_002c-S_002e-53"></a><a name="index-de-Meer_002c-H_002e-54"></a><a name="index-Trivedi_002c-K_002e-55"></a> <!-- M/M/m --> <div class="node"> <a name="The-M%2fM%2fm-System"></a> @@ -1680,10 +1684,10 @@ <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-55"></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-56"></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-56"></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-57"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-57"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002fm_007d-system-58"></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. @@ -1735,7 +1739,7 @@ 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-58"></a><a name="index-Greiner_002c-S_002e-59"></a><a name="index-de-Meer_002c-H_002e-60"></a><a name="index-Trivedi_002c-K_002e-61"></a> + <p><a name="index-Bolch_002c-G_002e-59"></a><a name="index-Greiner_002c-S_002e-60"></a><a name="index-de-Meer_002c-H_002e-61"></a><a name="index-Trivedi_002c-K_002e-62"></a> <!-- M/M/inf --> <div class="node"> <a name="The-M%2fM%2finf-System"></a> @@ -1758,7 +1762,7 @@ <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-62"></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-63"></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 @@ -1766,7 +1770,7 @@ 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-63"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002f_007dinf-system-64"></a> <p><strong>INPUTS</strong> @@ -1784,7 +1788,7 @@ different from the utilization, which in the case of M/M/\infty centers is always zero. - <p><a name="index-traffic-intensity-64"></a> + <p><a name="index-traffic-intensity-65"></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 @@ -1812,7 +1816,7 @@ 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-65"></a><a name="index-Greiner_002c-S_002e-66"></a><a name="index-de-Meer_002c-H_002e-67"></a><a name="index-Trivedi_002c-K_002e-68"></a> + <p><a name="index-Bolch_002c-G_002e-66"></a><a name="index-Greiner_002c-S_002e-67"></a><a name="index-de-Meer_002c-H_002e-68"></a><a name="index-Trivedi_002c-K_002e-69"></a> <!-- M/M/1/k --> <div class="node"> <a name="The-M%2fM%2f1%2fK-System"></a> @@ -1836,9 +1840,9 @@ <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-69"></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-70"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-70"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002f1_002fK_007d-system-71"></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 @@ -1905,9 +1909,9 @@ <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-71"></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-72"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-72"></a> + <p><a name="index-g_t_0040math_007bM_002fM_002fm_002fK_007d-system-73"></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 @@ -1965,7 +1969,7 @@ 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-73"></a><a name="index-Greiner_002c-S_002e-74"></a><a name="index-de-Meer_002c-H_002e-75"></a><a name="index-Trivedi_002c-K_002e-76"></a> + <p><a name="index-Bolch_002c-G_002e-74"></a><a name="index-Greiner_002c-S_002e-75"></a><a name="index-de-Meer_002c-H_002e-76"></a><a name="index-Trivedi_002c-K_002e-77"></a> <!-- Approximate M/M/m --> <div class="node"> @@ -1987,9 +1991,9 @@ <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-77"></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-78"></a></var><br> <blockquote> - <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-78"></a> + <p><a name="index-Asymmetric-_0040math_007bM_002fM_002fm_007d-system-79"></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 @@ -2036,7 +2040,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998 - <p><a name="index-Bolch_002c-G_002e-79"></a><a name="index-Greiner_002c-S_002e-80"></a><a name="index-de-Meer_002c-H_002e-81"></a><a name="index-Trivedi_002c-K_002e-82"></a> + <p><a name="index-Bolch_002c-G_002e-80"></a><a name="index-Greiner_002c-S_002e-81"></a><a name="index-de-Meer_002c-H_002e-82"></a><a name="index-Trivedi_002c-K_002e-83"></a> <div class="node"> <a name="The-M%2fG%2f1-System"></a> <a name="The-M_002fG_002f1-System"></a> @@ -2052,9 +2056,9 @@ <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-qnmg1-83"></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-qnmg1-84"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-84"></a> + <p><a name="index-g_t_0040math_007bM_002fG_002f1_007d-system-85"></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 @@ -2111,9 +2115,9 @@ <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-qnmh1-85"></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-qnmh1-86"></a></var><br> <blockquote> - <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-86"></a> + <p><a name="index-g_t_0040math_007bM_002fH_005fm_002f1_007d-system-87"></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: @@ -2195,7 +2199,7 @@ <li><a accesskey="6" href="#Utility-functions">Utility functions</a>: Utility functions to compute miscellaneous quantities </ul> -<p><a name="index-queueing-networks-87"></a> +<p><a name="index-queueing-networks-88"></a> <!-- INTRODUCTION --> <div class="node"> <a name="Introduction-to-QNs"></a> @@ -2456,13 +2460,13 @@ <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-88"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-89"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-90"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-91"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-92"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-93"></a></var><br> -— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-94"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S</var>)<var><a name="index-qnmknode-89"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/m-fcfs", S, m</var>)<var><a name="index-qnmknode-90"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"m/m/1-lcfs-pr", S</var>)<var><a name="index-qnmknode-91"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S</var>)<var><a name="index-qnmknode-92"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/1-ps", S, s2</var>)<var><a name="index-qnmknode-93"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S</var>)<var><a name="index-qnmknode-94"></a></var><br> +— Function File: <var>Q</var> = <b>qnmknode</b> (<var>"-/g/inf", S, s2</var>)<var><a name="index-qnmknode-95"></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 @@ -2531,10 +2535,10 @@ <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-95"></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-96"></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-97"></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-98"></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-96"></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-97"></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-98"></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-99"></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. @@ -2712,11 +2716,11 @@ <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-99"></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-100"></a></var><br> -— Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-101"></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-100"></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-101"></a></var><br> +— Function File: <var>pr</var> = <b>qnjackson</b> (<var>lambda, S, P, m, k</var>)<var><a name="index-qnjackson-102"></a></var><br> <blockquote> - <p><a name="index-open-network_002c-single-class-102"></a><a name="index-Jackson-network-103"></a> + <p><a name="index-open-network_002c-single-class-103"></a><a name="index-Jackson-network-104"></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 @@ -2798,7 +2802,7 @@ Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998, pp. 284–287. - <p><a name="index-Bolch_002c-G_002e-104"></a><a name="index-Greiner_002c-S_002e-105"></a><a name="index-de-Meer_002c-H_002e-106"></a><a name="index-Trivedi_002c-K_002e-107"></a> + <p><a name="index-Bolch_002c-G_002e-105"></a><a name="index-Greiner_002c-S_002e-106"></a><a name="index-de-Meer_002c-H_002e-107"></a><a name="index-Trivedi_002c-K_002e-108"></a> <h4 class="subsection">6.3.2 The Convolution Algorithm</h4> @@ -2832,10 +2836,10 @@ <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-108"></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-109"></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-109"></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-110"></a></var><br> <blockquote> - <p><a name="index-closed-network-110"></a><a name="index-normalization-constant-111"></a><a name="index-convolution-algorithm-112"></a> + <p><a name="index-closed-network-111"></a><a name="index-normalization-constant-112"></a><a name="index-convolution-algorithm-113"></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 @@ -2926,20 +2930,20 @@ 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-113"></a> + <p><a name="index-Buzen_002c-J_002e-P_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, 1998, pp. 313–317. - <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> <!-- 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-118"></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-119"></a></var><br> <blockquote> - <p><a name="index-closed-network-119"></a><a name="index-normalization-constant-120"></a><a name="index-convolution-algorithm-121"></a><a name="index-load_002ddependent-service-center-122"></a> + <p><a name="index-closed-network-120"></a><a name="index-normalization-constant-121"></a><a name="index-convolution-algorithm-122"></a><a name="index-load_002ddependent-service-center-123"></a> This function implements the <em>convolution algorithm</em> for product-form, single-class closed queueing networks with general load-dependent service centers. @@ -2999,7 +3003,7 @@ 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-123"></a> + <p><a name="index-Schwetman_002c-H_002e-124"></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 @@ -3007,7 +3011,7 @@ 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-124"></a><a name="index-Kobayashi_002c-H_002e-125"></a> + <p><a name="index-Reiser_002c-M_002e-125"></a><a name="index-Kobayashi_002c-H_002e-126"></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, @@ -3019,7 +3023,7 @@ function f_i defined in Schwetman, <code>Some Computational Aspects of Queueing Network Models</code>. - <p><a name="index-Bolch_002c-G_002e-126"></a><a name="index-Greiner_002c-S_002e-127"></a><a name="index-de-Meer_002c-H_002e-128"></a><a name="index-Trivedi_002c-K_002e-129"></a> + <p><a name="index-Bolch_002c-G_002e-127"></a><a name="index-Greiner_002c-S_002e-128"></a><a name="index-de-Meer_002c-H_002e-129"></a><a name="index-Trivedi_002c-K_002e-130"></a> <h4 class="subsection">6.3.3 Open networks</h4> @@ -3027,10 +3031,10 @@ <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-130"></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-131"></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-131"></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-132"></a></var><br> <blockquote> - <p><a name="index-open-network_002c-single-class-132"></a><a name="index-BCMP-network-133"></a> + <p><a name="index-open-network_002c-single-class-133"></a><a name="index-BCMP-network-134"></a> Analyze open, single class BCMP queueing networks. <p>This function works for a subset of BCMP single-class open networks @@ -3123,16 +3127,16 @@ Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications</cite>, Wiley, 1998. - <p><a name="index-Bolch_002c-G_002e-134"></a><a name="index-Greiner_002c-S_002e-135"></a><a name="index-de-Meer_002c-H_002e-136"></a><a name="index-Trivedi_002c-K_002e-137"></a> + <p><a name="index-Bolch_002c-G_002e-135"></a><a name="index-Greiner_002c-S_002e-136"></a><a name="index-de-Meer_002c-H_002e-137"></a><a name="index-Trivedi_002c-K_002e-138"></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-138"></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-139"></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-139"></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-140"></a></var><br> <blockquote> - <p><a name="index-open-network_002c-multiple-classes-140"></a> + <p><a name="index-open-network_002c-multiple-classes-141"></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 @@ -3197,7 +3201,7 @@ 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-141"></a><a name="index-Zahorjan_002c-J_002e-142"></a><a name="index-Graham_002c-G_002e-S_002e-143"></a><a name="index-Sevcik_002c-K_002e-C_002e-144"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-142"></a><a name="index-Zahorjan_002c-J_002e-143"></a><a name="index-Graham_002c-G_002e-S_002e-144"></a><a name="index-Sevcik_002c-K_002e-C_002e-145"></a> <h4 class="subsection">6.3.4 Closed Networks</h4> @@ -3205,11 +3209,11 @@ <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-145"></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-146"></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-147"></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-146"></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-147"></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-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-normalization-constant-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-normalization-constant-151"></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 @@ -3310,7 +3314,7 @@ 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-151"></a><a name="index-Lavenberg_002c-S_002e-S_002e-152"></a> + <p><a name="index-Reiser_002c-M_002e-152"></a><a name="index-Lavenberg_002c-S_002e-S_002e-153"></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)}, --> @@ -3319,15 +3323,15 @@ 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-153"></a><a name="index-Bolch_002c-G_002e-154"></a><a name="index-Greiner_002c-S_002e-155"></a><a name="index-de-Meer_002c-H_002e-156"></a><a name="index-Trivedi_002c-K_002e-157"></a> + <p><a name="index-Jain_002c-R_002e-154"></a><a name="index-Bolch_002c-G_002e-155"></a><a name="index-Greiner_002c-S_002e-156"></a><a name="index-de-Meer_002c-H_002e-157"></a><a name="index-Trivedi_002c-K_002e-158"></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-158"></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-159"></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-159"></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-160"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-160"></a><a name="index-closed-network_002c-single-class-161"></a><a name="index-load_002ddependent-service-center-162"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-161"></a><a name="index-closed-network_002c-single-class-162"></a><a name="index-load_002ddependent-service-center-163"></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 @@ -3385,15 +3389,15 @@ 1998, Section 8.2.4.1, “Networks with Load-Deèpendent Service: Closed Networks”. - <p><a name="index-Bolch_002c-G_002e-163"></a><a name="index-Greiner_002c-S_002e-164"></a><a name="index-de-Meer_002c-H_002e-165"></a><a name="index-Trivedi_002c-K_002e-166"></a> + <p><a name="index-Bolch_002c-G_002e-164"></a><a name="index-Greiner_002c-S_002e-165"></a><a name="index-de-Meer_002c-H_002e-166"></a><a name="index-Trivedi_002c-K_002e-167"></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-167"></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-168"></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-168"></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-169"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-169"></a><a name="index-CMVA-170"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-170"></a><a name="index-CMVA-171"></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 @@ -3447,19 +3451,19 @@ closed networks</cite>. Queueing Syst. Theory Appl., 60:193–202, December 2008. - <p><a name="index-Casale_002c-G_002e-171"></a> + <p><a name="index-Casale_002c-G_002e-172"></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-172"></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-173"></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-174"></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-175"></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-176"></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-173"></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-174"></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-175"></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-176"></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-177"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-177"></a><a name="index-Approximate-MVA-178"></a><a name="index-Closed-network_002c-single-class-179"></a><a name="index-Closed-network_002c-approximate-analysis-180"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-178"></a><a name="index-Approximate-MVA-179"></a><a name="index-Closed-network_002c-single-class-180"></a><a name="index-Closed-network_002c-approximate-analysis-181"></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 @@ -3538,20 +3542,20 @@ 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-181"></a><a name="index-Zahorjan_002c-J_002e-182"></a><a name="index-Graham_002c-G_002e-S_002e-183"></a><a name="index-Sevcik_002c-K_002e-C_002e-184"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-182"></a><a name="index-Zahorjan_002c-J_002e-183"></a><a name="index-Graham_002c-G_002e-S_002e-184"></a><a name="index-Sevcik_002c-K_002e-C_002e-185"></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-185"></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-186"></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-187"></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-188"></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-189"></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-190"></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-186"></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-187"></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-188"></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-189"></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-190"></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-191"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-191"></a><a name="index-closed-network_002c-multiple-classes-192"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-192"></a><a name="index-closed-network_002c-multiple-classes-193"></a> Analyze closed, multiclass queueing networks with K service centers and C independent customer classes (chains) using the Mean Value Analysys (MVA) algorithm. @@ -3681,7 +3685,7 @@ 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-193"></a><a name="index-Lavenberg_002c-S_002e-S_002e-194"></a> + <p><a name="index-Reiser_002c-M_002e-194"></a><a name="index-Lavenberg_002c-S_002e-S_002e-195"></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, @@ -3691,18 +3695,18 @@ 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-195"></a><a name="index-Greiner_002c-S_002e-196"></a><a name="index-de-Meer_002c-H_002e-197"></a><a name="index-Trivedi_002c-K_002e-198"></a><a name="index-Lazowska_002c-E_002e-D_002e-199"></a><a name="index-Zahorjan_002c-J_002e-200"></a><a name="index-Graham_002c-G_002e-S_002e-201"></a><a name="index-Sevcik_002c-K_002e-C_002e-202"></a> + <p><a name="index-Bolch_002c-G_002e-196"></a><a name="index-Greiner_002c-S_002e-197"></a><a name="index-de-Meer_002c-H_002e-198"></a><a name="index-Trivedi_002c-K_002e-199"></a><a name="index-Lazowska_002c-E_002e-D_002e-200"></a><a name="index-Zahorjan_002c-J_002e-201"></a><a name="index-Graham_002c-G_002e-S_002e-202"></a><a name="index-Sevcik_002c-K_002e-C_002e-203"></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-203"></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-204"></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-205"></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-206"></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-207"></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-204"></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-205"></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-206"></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-207"></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-208"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-208"></a><a name="index-Approximate-MVA-209"></a><a name="index-Closed-network_002c-multiple-classes-210"></a><a name="index-Closed-network_002c-approximate-analysis-211"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029_002c-approximate-209"></a><a name="index-Approximate-MVA-210"></a><a name="index-Closed-network_002c-multiple-classes-211"></a><a name="index-Closed-network_002c-approximate-analysis-212"></a> Analyze closed, multiclass queueing networks with K service centers and C customer classes using the approximate Mean Value Analysys (MVA) algorithm. @@ -3787,12 +3791,12 @@ 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-212"></a> + <p><a name="index-Bard_002c-Y_002e-213"></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-213"></a> + <p><a name="index-Schweitzer_002c-P_002e-214"></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>, @@ -3803,7 +3807,7 @@ 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-214"></a><a name="index-Zahorjan_002c-J_002e-215"></a><a name="index-Graham_002c-G_002e-S_002e-216"></a><a name="index-Sevcik_002c-K_002e-C_002e-217"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-215"></a><a name="index-Zahorjan_002c-J_002e-216"></a><a name="index-Graham_002c-G_002e-S_002e-217"></a><a name="index-Sevcik_002c-K_002e-C_002e-218"></a> <h4 class="subsection">6.3.5 Mixed Networks</h4> @@ -3811,9 +3815,9 @@ <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-218"></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-219"></a></var><br> <blockquote> - <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-219"></a><a name="index-mixed-network-220"></a> + <p><a name="index-Mean-Value-Analysys-_0028MVA_0029-220"></a><a name="index-mixed-network-221"></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 @@ -3904,14 +3908,14 @@ 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-221"></a><a name="index-Zahorjan_002c-J_002e-222"></a><a name="index-Graham_002c-G_002e-S_002e-223"></a><a name="index-Sevcik_002c-K_002e-C_002e-224"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-222"></a><a name="index-Zahorjan_002c-J_002e-223"></a><a name="index-Graham_002c-G_002e-S_002e-224"></a><a name="index-Sevcik_002c-K_002e-C_002e-225"></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-225"></a> + <p><a name="index-Schwetman_002c-H_002e-226"></a> <div class="node"> <a name="Algorithms-for-non-Product-form-QNs"></a> @@ -3930,9 +3934,9 @@ <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-226"></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-227"></a></var><br> <blockquote> - <p><a name="index-queueing-network-with-blocking-227"></a><a name="index-blocking-queueing-network-228"></a><a name="index-closed-network_002c-finite-capacity-229"></a> + <p><a name="index-queueing-network-with-blocking-228"></a><a name="index-blocking-queueing-network-229"></a><a name="index-closed-network_002c-finite-capacity-230"></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. @@ -3987,16 +3991,16 @@ 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-230"></a> + <p><a name="index-Akyildiz_002c-I_002e-F_002e-231"></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-231"></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-232"></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-233"></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-234"></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-232"></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-233"></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-234"></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-235"></a></var><br> <blockquote> - <p><a name="index-closed-network_002c-multiple-classes-235"></a><a name="index-closed-network_002c-finite-capacity-236"></a><a name="index-blocking-queueing-network-237"></a><a name="index-RS-blocking-238"></a> + <p><a name="index-closed-network_002c-multiple-classes-236"></a><a name="index-closed-network_002c-finite-capacity-237"></a><a name="index-blocking-queueing-network-238"></a><a name="index-RS-blocking-239"></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 @@ -4106,9 +4110,9 @@ <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-239"></a></var><br> +— Function File: [<var>Xu</var>, <var>Rl</var>] = <b>qnopenab</b> (<var>lambda, D</var>)<var><a name="index-qnopenab-240"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-asymptotic-240"></a><a name="index-open-network-241"></a> + <p><a name="index-bounds_002c-asymptotic-241"></a><a name="index-open-network-242"></a> Compute Asymptotic Bounds for single-class, open Queueing Networks with K service centers. @@ -4148,14 +4152,14 @@ 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-242"></a><a name="index-Zahorjan_002c-J_002e-243"></a><a name="index-Graham_002c-G_002e-S_002e-244"></a><a name="index-Sevcik_002c-K_002e-C_002e-245"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-243"></a><a name="index-Zahorjan_002c-J_002e-244"></a><a name="index-Graham_002c-G_002e-S_002e-245"></a><a name="index-Sevcik_002c-K_002e-C_002e-246"></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-246"></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-247"></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-247"></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-248"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-asymptotic-248"></a><a name="index-closed-network-249"></a> + <p><a name="index-bounds_002c-asymptotic-249"></a><a name="index-closed-network-250"></a> Compute Asymptotic Bounds for single-class, closed Queueing Networks with K service centers. @@ -4196,14 +4200,14 @@ 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-250"></a><a name="index-Zahorjan_002c-J_002e-251"></a><a name="index-Graham_002c-G_002e-S_002e-252"></a><a name="index-Sevcik_002c-K_002e-C_002e-253"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-251"></a><a name="index-Zahorjan_002c-J_002e-252"></a><a name="index-Graham_002c-G_002e-S_002e-253"></a><a name="index-Sevcik_002c-K_002e-C_002e-254"></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-254"></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-255"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-balanced-system-255"></a><a name="index-open-network-256"></a> + <p><a name="index-bounds_002c-balanced-system-256"></a><a name="index-open-network-257"></a> Compute Balanced System Bounds for single-class, open Queueing Networks with K service centers. @@ -4243,14 +4247,14 @@ 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-257"></a><a name="index-Zahorjan_002c-J_002e-258"></a><a name="index-Graham_002c-G_002e-S_002e-259"></a><a name="index-Sevcik_002c-K_002e-C_002e-260"></a> + <p><a name="index-Lazowska_002c-E_002e-D_002e-258"></a><a name="index-Zahorjan_002c-J_002e-259"></a><a name="index-Graham_002c-G_002e-S_002e-260"></a><a name="index-Sevcik_002c-K_002e-C_002e-261"></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-261"></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-262"></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-262"></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-263"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-balanced-system-263"></a><a name="index-closed-network-264"></a> + <p><a name="index-bounds_002c-balanced-system-264"></a><a name="index-closed-network-265"></a> Compute Balanced System Bounds for single-class, closed Queueing Networks with K service centers. @@ -4286,7 +4290,7 @@ <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-265"></a></var><br> +— Function File: [<var>Xl</var>, <var>Xu</var>] = <b>qnclosedpb</b> (<var>N, D </var>)<var><a name="index-qnclosedpb-266"></a></var><br> <blockquote> <p>Compute PB Bounds (C. H. Hsieh and S. Lam, 1987) for single-class, closed Queueing Networks @@ -4330,13 +4334,13 @@ 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-266"></a><a name="index-Lam_002c-S_002e-267"></a><a name="index-Casale_002c-G_002e-268"></a><a name="index-Muntz_002c-R_002e-R_002e-269"></a><a name="index-Serazzi_002c-G_002e-270"></a> + <p><a name="index-Hsieh_002c-C_002e-H-267"></a><a name="index-Lam_002c-S_002e-268"></a><a name="index-Casale_002c-G_002e-269"></a><a name="index-Muntz_002c-R_002e-R_002e-270"></a><a name="index-Serazzi_002c-G_002e-271"></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-271"></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-272"></a></var><br> <blockquote> - <p><a name="index-bounds_002c-geometric-272"></a><a name="index-closed-network-273"></a> + <p><a name="index-bounds_002c-geometric-273"></a><a name="index-closed-network-274"></a> Compute Geometric Bounds (GB) for single-class, closed Queueing Networks. <p><strong>INPUTS</strong> @@ -4377,7 +4381,7 @@ 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-274"></a><a name="index-Muntz_002c-R_002e-R_002e-275"></a><a name="index-Serazzi_002c-G_002e-276"></a> + <p><a name="index-Casale_002c-G_002e-275"></a><a name="index-Muntz_002c-R_002e-R_002e-276"></a><a name="index-Serazzi_002c-G_002e-277"></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. @@ -4397,9 +4401,9 @@ <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-277"></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-278"></a></var><br> <blockquote> - <p><a name="index-closed-network-278"></a> + <p><a name="index-closed-network-279"></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 @@ -4466,9 +4470,9 @@ <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-279"></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-280"></a></var><br> <blockquote> - <p><a name="index-open-network-280"></a> + <p><a name="index-open-network-281"></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 @@ -4521,8 +4525,8 @@ <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-281"></a></var><br> -— Function File: <var>V</var> = <b>qnvisits</b> (<var>P, lambda</var>)<var><a name="index-qnvisits-282"></a></var><br> +— Function File: [<var>V</var> <var>ch</var>] = <b>qnvisits</b> (<var>P</var>)<var><a name="index-qnvisits-282"></a></var><br> +— Function File: <var>V</var> = <b>qnvisits</b> (<var>P, lambda</var>)<var><a name="index-qnvisits-283"></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 @@ -4584,9 +4588,9 @@ <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-283"></a></var><br> +— Function File: pop_mix = <b>population_mix</b> (<var>k, N</var>)<var><a name="index-population_005fmix-284"></a></var><br> <blockquote> - <p><a name="index-population-mix-284"></a><a name="index-closed-network_002c-multiple-classes-285"></a> + <p><a name="index-population-mix-285"></a><a name="index-closed-network_002c-multiple-classes-286"></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 @@ -4648,13 +4652,13 @@ 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-286"></a><a name="index-Santini_002c-S_002e-287"></a> + <p><a name="index-Schwetman_002c-H_002e-287"></a><a name="index-Santini_002c-S_002e-288"></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-288"></a></var><br> +— Function File: <var>H</var> = <b>qnmvapop</b> (<var>N</var>)<var><a name="index-qnmvapop-289"></a></var><br> <blockquote> - <p><a name="index-population-mix-289"></a><a name="index-closed-network_002c-multiple-classes-290"></a> + <p><a name="index-population-mix-290"></a><a name="index-closed-network_002c-multiple-classes-291"></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 @@ -4691,7 +4695,7 @@ 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-291"></a><a name="index-Wong_002c-E_002e-292"></a> + <p><a name="index-Zahorjan_002c-J_002e-292"></a><a name="index-Wong_002c-E_002e-293"></a> <!-- Appendix starts here --> <!-- DO NOT EDIT! Generated automatically by munge-texi. --> @@ -4802,7 +4806,7 @@ <h2 class="appendix">Appendix C GNU GENERAL PUBLIC LICENSE</h2> -<p><a name="index-warranty-293"></a><a name="index-copyright-294"></a> +<p><a name="index-warranty-294"></a><a name="index-copyright-295"></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> @@ -5509,46 +5513,46 @@ <h2 class="unnumbered">Concept Index</h2> <ul class="index-cp" compact> -<li><a href="#index-Approximate-MVA-178">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-78">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-133">BCMP network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-Approximate-MVA-179">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-79">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-134">BCMP network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> <li><a href="#index-Birth_002ddeath-process-30">Birth-death process</a>: <a href="#Birth_002dDeath-process">Birth-Death process</a></li> <li><a href="#index-Birth_002ddeath-process-11">Birth-death process</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-blocking-queueing-network-228">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-240">bounds, asymptotic</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-bounds_002c-balanced-system-255">bounds, balanced system</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-bounds_002c-geometric-272">bounds, geometric</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-closed-network-278">closed network</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-closed-network-249">closed network</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-closed-network-110">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-180">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-229">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-285">closed network, multiple classes</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-closed-network_002c-multiple-classes-235">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-210">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-192">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-179">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-149">closed network, single class</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-CMVA-170">CMVA</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-blocking-queueing-network-229">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-241">bounds, asymptotic</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-bounds_002c-balanced-system-256">bounds, balanced system</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-bounds_002c-geometric-273">bounds, geometric</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-closed-network-279">closed network</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-closed-network-250">closed network</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-closed-network-111">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-181">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-230">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-286">closed network, multiple classes</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-closed-network_002c-multiple-classes-236">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-211">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-193">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-180">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-150">closed network, single class</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-CMVA-171">CMVA</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> <li><a href="#index-Continuous-time-Markov-chain-25">Continuous time Markov chain</a>: <a href="#State-occupancy-probabilities">State occupancy probabilities</a></li> -<li><a href="#index-convolution-algorithm-112">convolution algorithm</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-copyright-294">copyright</a>: <a href="#Copying">Copying</a></li> +<li><a href="#index-convolution-algorithm-113">convolution algorithm</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-copyright-295">copyright</a>: <a href="#Copying">Copying</a></li> <li><a href="#index-Discrete-time-Markov-chain-6">Discrete time Markov chain</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> <li><a href="#index-Expected-sojourn-time-34">Expected sojourn time</a>: <a href="#Expected-Sojourn-Time">Expected Sojourn Time</a></li> -<li><a href="#index-First-passage-times-48">First passage times</a>: <a href="#First-Passage-Times">First Passage Times</a></li> +<li><a href="#index-First-passage-times-49">First passage times</a>: <a href="#First-Passage-Times">First Passage Times</a></li> <li><a href="#index-First-passage-times-15">First passage times</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-Jackson-network-103">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-122">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-84">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-86">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-50">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-70">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-63">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-57">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-72">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-47">Markov chain, continuous time</a>: <a href="#First-Passage-Times">First Passage Times</a></li> -<li><a href="#index-Markov-chain_002c-continuous-time-39">Markov chain, continuous time</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> -<li><a href="#index-Markov-chain_002c-continuous-time-36">Markov chain, continuous time</a>: <a href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a></li> +<li><a href="#index-Jackson-network-104">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-123">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-85">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-87">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-51">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-71">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-64">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-58">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-73">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-48">Markov chain, continuous time</a>: <a href="#First-Passage-Times">First Passage Times</a></li> +<li><a href="#index-Markov-chain_002c-continuous-time-40">Markov chain, continuous time</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> +<li><a href="#index-Markov-chain_002c-continuous-time-37">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-33">Markov chain, continuous time</a>: <a href="#Expected-Sojourn-Time">Expected Sojourn Time</a></li> <li><a href="#index-Markov-chain_002c-continuous-time-29">Markov chain, continuous time</a>: <a href="#Birth_002dDeath-process">Birth-Death process</a></li> <li><a href="#index-Markov-chain_002c-continuous-time-24">Markov chain, continuous time</a>: <a href="#State-occupancy-probabilities">State occupancy probabilities</a></li> @@ -5557,25 +5561,25 @@ <li><a href="#index-Markov-chain_002c-disctete-time-18">Markov chain, disctete time</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> <li><a href="#index-Markov-chain_002c-state-occupancy-probabilities-26">Markov chain, state occupancy probabilities</a>: <a href="#State-occupancy-probabilities">State occupancy probabilities</a></li> <li><a href="#index-Markov-chain_002c-stationary-probabilities-7">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-40">Mean time to absorption</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> +<li><a href="#index-Mean-time-to-absorption-41">Mean time to absorption</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> <li><a href="#index-Mean-time-to-absorption-19">Mean time to absorption</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-Mean-Value-Analysys-_0028MVA_0029-148">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-177">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-220">mixed network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-normalization-constant-111">normalization constant</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-open-network-280">open network</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-open-network-241">open network</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-open-network_002c-multiple-classes-140">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-102">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-284">population mix</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-queueing-network-with-blocking-227">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-87">queueing networks</a>: <a href="#Queueing-Networks">Queueing Networks</a></li> -<li><a href="#index-RS-blocking-238">RS blocking</a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-Mean-Value-Analysys-_0028MVA_0029-149">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-178">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-221">mixed network</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-normalization-constant-112">normalization constant</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-open-network-281">open network</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-open-network-242">open network</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-open-network_002c-multiple-classes-141">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-103">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-285">population mix</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-queueing-network-with-blocking-228">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-88">queueing networks</a>: <a href="#Queueing-Networks">Queueing Networks</a></li> +<li><a href="#index-RS-blocking-239">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-27">Stationary probabilities</a>: <a href="#State-occupancy-probabilities">State occupancy probabilities</a></li> <li><a href="#index-Stationary-probabilities-8">Stationary probabilities</a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-Time_002dalveraged-sojourn-time-37">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-64">traffic intensity</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-warranty-293">warranty</a>: <a href="#Copying">Copying</a></li> +<li><a href="#index-Time_002dalveraged-sojourn-time-38">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-65">traffic intensity</a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-warranty-294">warranty</a>: <a href="#Copying">Copying</a></li> </ul><div class="node"> <a name="Function-Index"></a> <p><hr> @@ -5594,49 +5598,49 @@ <li><a href="#index-ctmc_005fbd-28"><code>ctmc_bd</code></a>: <a href="#Birth_002dDeath-process">Birth-Death process</a></li> <li><a href="#index-ctmc_005fcheck_005fQ-20"><code>ctmc_check_Q</code></a>: <a href="#Continuous_002dTime-Markov-Chains">Continuous-Time Markov Chains</a></li> <li><a href="#index-ctmc_005fexps-31"><code>ctmc_exps</code></a>: <a href="#Expected-Sojourn-Time">Expected Sojourn Time</a></li> -<li><a href="#index-ctmc_005ffpt-45"><code>ctmc_fpt</code></a>: <a href="#First-Passage-Times">First Passage Times</a></li> -<li><a href="#index-ctmc_005fmtta-38"><code>ctmc_mtta</code></a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> +<li><a href="#index-ctmc_005ffpt-46"><code>ctmc_fpt</code></a>: <a href="#First-Passage-Times">First Passage Times</a></li> +<li><a href="#index-ctmc_005fmtta-39"><code>ctmc_mtta</code></a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> <li><a href="#index-ctmc_005ftaexps-35"><code>ctmc_taexps</code></a>: <a href="#Time_002dAveraged-Expected-Sojourn-Time">Time-Averaged Expected Sojourn Time</a></li> <li><a href="#index-dtmc-3"><code>dtmc</code></a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> <li><a href="#index-dtmc_005fbd-9"><code>dtmc_bd</code></a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> <li><a href="#index-dtmc_005fcheck_005fP-1"><code>dtmc_check_P</code></a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> <li><a href="#index-dtmc_005ffpt-12"><code>dtmc_fpt</code></a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> <li><a href="#index-dtmc_005fmtta-16"><code>dtmc_mtta</code></a>: <a href="#Discrete_002dTime-Markov-Chains">Discrete-Time Markov Chains</a></li> -<li><a href="#index-population_005fmix-283"><code>population_mix</code></a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-qnammm-77"><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-277"><code>qnclosed</code></a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-qnclosedab-246"><code>qnclosedab</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnclosedbsb-261"><code>qnclosedbsb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnclosedgb-271"><code>qnclosedgb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnclosedmultimva-185"><code>qnclosedmultimva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnclosedmultimvaapprox-203"><code>qnclosedmultimvaapprox</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnclosedpb-265"><code>qnclosedpb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnclosedsinglemva-145"><code>qnclosedsinglemva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnclosedsinglemvaapprox-172"><code>qnclosedsinglemvaapprox</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnclosedsinglemvald-158"><code>qnclosedsinglemvald</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qncmva-167"><code>qncmva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnconvolution-108"><code>qnconvolution</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnconvolutionld-118"><code>qnconvolutionld</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnjackson-99"><code>qnjackson</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnmarkov-231"><code>qnmarkov</code></a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> -<li><a href="#index-qnmg1-83"><code>qnmg1</code></a>: <a href="#The-M_002fG_002f1-System">The M/G/1 System</a></li> -<li><a href="#index-qnmh1-85"><code>qnmh1</code></a>: <a href="#The-M_002fHm_002f1-System">The M/Hm/1 System</a></li> -<li><a href="#index-qnmix-218"><code>qnmix</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnmknode-88"><code>qnmknode</code></a>: <a href="#Generic-Algorithms">Generic Algorithms</a></li> -<li><a href="#index-qnmm1-49"><code>qnmm1</code></a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> -<li><a href="#index-qnmm1k-69"><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-62"><code>qnmminf</code></a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> -<li><a href="#index-qnmmm-55"><code>qnmmm</code></a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> -<li><a href="#index-qnmmmk-71"><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-226"><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-288"><code>qnmvapop</code></a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-qnopen-279"><code>qnopen</code></a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-qnopenab-239"><code>qnopenab</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnopenbsb-254"><code>qnopenbsb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-qnopenmulti-138"><code>qnopenmulti</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnopensingle-130"><code>qnopensingle</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> -<li><a href="#index-qnsolve-95"><code>qnsolve</code></a>: <a href="#Generic-Algorithms">Generic Algorithms</a></li> -<li><a href="#index-qnvisits-281"><code>qnvisits</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-population_005fmix-284"><code>population_mix</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-qnammm-78"><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-278"><code>qnclosed</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-qnclosedab-247"><code>qnclosedab</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnclosedbsb-262"><code>qnclosedbsb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnclosedgb-272"><code>qnclosedgb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnclosedmultimva-186"><code>qnclosedmultimva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnclosedmultimvaapprox-204"><code>qnclosedmultimvaapprox</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnclosedpb-266"><code>qnclosedpb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnclosedsinglemva-146"><code>qnclosedsinglemva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnclosedsinglemvaapprox-173"><code>qnclosedsinglemvaapprox</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnclosedsinglemvald-159"><code>qnclosedsinglemvald</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qncmva-168"><code>qncmva</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnconvolution-109"><code>qnconvolution</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnconvolutionld-119"><code>qnconvolutionld</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnjackson-100"><code>qnjackson</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnmarkov-232"><code>qnmarkov</code></a>: <a href="#Algorithms-for-non-Product_002dform-QNs">Algorithms for non Product-form QNs</a></li> +<li><a href="#index-qnmg1-84"><code>qnmg1</code></a>: <a href="#The-M_002fG_002f1-System">The M/G/1 System</a></li> +<li><a href="#index-qnmh1-86"><code>qnmh1</code></a>: <a href="#The-M_002fHm_002f1-System">The M/Hm/1 System</a></li> +<li><a href="#index-qnmix-219"><code>qnmix</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnmknode-89"><code>qnmknode</code></a>: <a href="#Generic-Algorithms">Generic Algorithms</a></li> +<li><a href="#index-qnmm1-50"><code>qnmm1</code></a>: <a href="#The-M_002fM_002f1-System">The M/M/1 System</a></li> +<li><a href="#index-qnmm1k-70"><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-63"><code>qnmminf</code></a>: <a href="#The-M_002fM_002finf-System">The M/M/inf System</a></li> +<li><a href="#index-qnmmm-56"><code>qnmmm</code></a>: <a href="#The-M_002fM_002fm-System">The M/M/m System</a></li> +<li><a href="#index-qnmmmk-72"><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-227"><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-289"><code>qnmvapop</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-qnopen-280"><code>qnopen</code></a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-qnopenab-240"><code>qnopenab</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnopenbsb-255"><code>qnopenbsb</code></a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-qnopenmulti-139"><code>qnopenmulti</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnopensingle-131"><code>qnopensingle</code></a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> +<li><a href="#index-qnsolve-96"><code>qnsolve</code></a>: <a href="#Generic-Algorithms">Generic Algorithms</a></li> +<li><a href="#index-qnvisits-282"><code>qnvisits</code></a>: <a href="#Utility-functions">Utility functions</a></li> </ul><div class="node"> <a name="Author-Index"></a> <p><hr> @@ -5650,60 +5654,60 @@ <ul class="index-au" compact> -<li><a href="#index-Akyildiz_002c-I_002e-F_002e-230">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-212">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-104">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-79">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-73">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-65">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-58">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-51">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-41">Bolch, G.</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> -<li><a href="#index-Buzen_002c-J_002e-P_002e-113">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-268">Casale, G.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Casale_002c-G_002e-171">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-106">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-81">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-75">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-67">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-60">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-53">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-43">de Meer, H.</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> -<li><a href="#index-Graham_002c-G_002e-S_002e-244">Graham, G. S.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Graham_002c-G_002e-S_002e-143">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-105">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-80">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-74">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-66">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-59">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-52">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-42">Greiner, S.</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> -<li><a href="#index-Hsieh_002c-C_002e-H-266">Hsieh, C. H</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Jain_002c-R_002e-153">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-125">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-267">Lam, S.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Lavenberg_002c-S_002e-S_002e-152">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-242">Lazowska, E. D.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Lazowska_002c-E_002e-D_002e-141">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-269">Muntz, R. R.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Reiser_002c-M_002e-124">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-287">Santini, S.</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-Schweitzer_002c-P_002e-213">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-286">Schwetman, H.</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-Schwetman_002c-H_002e-123">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-270">Serazzi, G.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Sevcik_002c-K_002e-C_002e-245">Sevcik, K. C.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Sevcik_002c-K_002e-C_002e-144">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-107">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-82">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-76">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-68">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-61">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-54">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-44">Trivedi, K.</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> -<li><a href="#index-Wong_002c-E_002e-292">Wong, E.</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-Zahorjan_002c-J_002e-291">Zahorjan, J.</a>: <a href="#Utility-functions">Utility functions</a></li> -<li><a href="#index-Zahorjan_002c-J_002e-243">Zahorjan, J.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> -<li><a href="#index-Zahorjan_002c-J_002e-142">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-231">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-213">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-105">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-80">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-74">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-66">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-59">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-52">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-42">Bolch, G.</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> +<li><a href="#index-Buzen_002c-J_002e-P_002e-114">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-269">Casale, G.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Casale_002c-G_002e-172">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-107">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-82">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-76">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-68">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-61">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-54">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-44">de Meer, H.</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> +<li><a href="#index-Graham_002c-G_002e-S_002e-245">Graham, G. S.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Graham_002c-G_002e-S_002e-144">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-106">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-81">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-75">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-67">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-60">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-53">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-43">Greiner, S.</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> +<li><a href="#index-Hsieh_002c-C_002e-H-267">Hsieh, C. H</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Jain_002c-R_002e-154">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-126">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-268">Lam, S.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Lavenberg_002c-S_002e-S_002e-153">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-243">Lazowska, E. D.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Lazowska_002c-E_002e-D_002e-142">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-270">Muntz, R. R.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Reiser_002c-M_002e-125">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-288">Santini, S.</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-Schweitzer_002c-P_002e-214">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-287">Schwetman, H.</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-Schwetman_002c-H_002e-124">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-271">Serazzi, G.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Sevcik_002c-K_002e-C_002e-246">Sevcik, K. C.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Sevcik_002c-K_002e-C_002e-145">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-108">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-83">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-77">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-69">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-62">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-55">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-45">Trivedi, K.</a>: <a href="#Mean-Time-to-Absorption">Mean Time to Absorption</a></li> +<li><a href="#index-Wong_002c-E_002e-293">Wong, E.</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-Zahorjan_002c-J_002e-292">Zahorjan, J.</a>: <a href="#Utility-functions">Utility functions</a></li> +<li><a href="#index-Zahorjan_002c-J_002e-244">Zahorjan, J.</a>: <a href="#Bounds-on-performance">Bounds on performance</a></li> +<li><a href="#index-Zahorjan_002c-J_002e-143">Zahorjan, J.</a>: <a href="#Algorithms-for-Product_002dForm-QNs">Algorithms for Product-Form QNs</a></li> </ul></body></html>