# HG changeset patch # User mmarzolla # Date 1331395427 0 # Node ID cdf1dbf20cd46cfce8a7c8e961be271bb4638fab # Parent bd7fb43a670e674a7686edcd6a8e850f7d994f1f fixed bug in texinfo documentation diff -r bd7fb43a670e -r cdf1dbf20cd4 main/queueing/doc/queueing.html --- a/main/queueing/doc/queueing.html Sat Mar 10 16:00:45 2012 +0000 +++ b/main/queueing/doc/queueing.html Sat Mar 10 16:03:47 2012 +0000 @@ -1100,36 +1100,46 @@

-— Function File: L = ctmc_exps (Q, tt, p)
+— Function File: L = ctmc_exps (Q, tt, p )
+— Function File: L = ctmc_exps (Q, p)
-

-Compute the expected total time L(t,j) spent in state -j during the time interval [0,tt(t)), assuming -that at time 0 the state occupancy probability was p. +

+With three arguments, compute the expected time L(t,j) +spent in each state j during the time interval +[0,tt(t)), assuming that at time 0 the state occupancy +probability was p. With two arguments, compute the expected +time L(j) spent in each state j until absorption.

INPUTS

-
Q
Infinitesimal generator matrix. Q(i,j) is the transition -rate from state i to state j, -1 ≤ i \neq j ≤ N. The matrix Q must also satisfy the -condition sum(Q,2) == 0 +
Q
N \times N infinitesimal generator matrix. Q(i,j) +is the transition rate from state i to state j, 1 +≤ i \neq j ≤ N. The matrix Q must also satisfy the +condition \sum_j=1^N Q_ij = 0.
tt
This parameter is a vector used for numerical integration. The first element tt(1) must be 0, and the last element tt(end) must be the upper bound of the interval [0,t) of interest (tt(end) == t). -
p
p(i) is the probability that at time 0 the system was in -state i, for all i = 1, ..., N +
p
Initial occupancy probability vector; p(i) is the +probability the system is in state i at time 0, i = 1, +..., N

OUTPUTS

-
L
L(t,j) is the expected time spent in state j -during the interval [0,tt(t)). 1 ≤ t ≤ length(tt) +
L
If this function is called with three arguments, L is a matrix +of size [length(tt), N] where L(t,j) is the +expected time spent in state j during the interval +[0,tt(t)]. If this function is called with two +arguments, L is a vector with N elements where +L(j) is the expected time spent in state j until +absorption, if j is a transient state. If j +is an absorbing state, L(j) = 0.
@@ -1175,9 +1185,9 @@

-— Function File: M = ctmc_taexps (Q, tt, p)
+— Function File: M = ctmc_taexps (Q, tt, p)
-

+

Compute the time-averaged sojourn time M(t,j), defined as the fraction of the time interval [0,tt(t)) spent in state j, assuming that at time 0 the state occupancy @@ -1264,12 +1274,13 @@

-— Function File: t = ctmc_mtta (Q, p)
+— Function File: t = ctmc_mtta (Q, p)
-

-Compute the Mean-Time to Absorption (MTTA) starting from initial -occupancy probability p at time 0. If there are no absorbing -states, this function fails with an error. +

+Compute the Mean-Time to Absorption (MTTA) of the CTMC described by +the infinitesimal generator matrix Q, starting from initial +occupancy probability p. If there are no absorbing states, this +function fails with an error.

INPUTS @@ -1326,7 +1337,7 @@ Performance Evaluation with Computer Science Applications, Wiley, 1998. -

+

@@ -1340,10 +1351,10 @@

-— Function File: M = ctmc_fpt (Q)
-— Function File: m = ctmc_fpt (Q, i, j)
+— Function File: M = ctmc_fpt (Q)
+— Function File: m = ctmc_fpt (Q, i, j)
-

+

If called with a single argument, computes the mean first passage times M(i,j), the average times before state j is reached, starting from state i, for all 1 \leq i, j \leq @@ -1449,9 +1460,9 @@

-— Function File: [U, R, Q, X, p0] = qnmm1 (lambda, mu)
+— Function File: [U, R, Q, X, p0] = qnmm1 (lambda, mu)
-

+

Compute utilization, response time, average number of requests and throughput for a M/M/1 queue. @@ -1496,7 +1507,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998, Section 6.3. -

+

@@ -1522,10 +1533,10 @@

-— Function File: [U, R, Q, X, p0, pm] = qnmmm (lambda, mu)
-— Function File: [U, R, Q, X, p0, pm] = qnmmm (lambda, mu, m)
+— Function File: [U, R, Q, X, p0, pm] = qnmmm (lambda, mu)
+— Function File: [U, R, Q, X, p0, pm] = qnmmm (lambda, mu, m)
-

+

Compute utilization, response time, average number of requests in service and throughput for a M/M/m queue, a queueing system with m identical service centers connected to a single queue. @@ -1577,7 +1588,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998, Section 6.5. -

+

@@ -1600,7 +1611,7 @@

-— Function File: [U, R, Q, X, p0] = qnmminf (lambda, mu)
+— Function File: [U, R, Q, X, p0] = qnmminf (lambda, mu)

Compute utilization, response time, average number of requests and throughput for a M/M/\infty queue. This is a system with an @@ -1608,7 +1619,7 @@ system is always stable, regardless the values of the arrival and service rates. -

+

INPUTS @@ -1626,7 +1637,7 @@ different from the utilization, which in the case of M/M/\infty centers is always zero. -

+


R
Service center response time.
Q
Average number of requests in the system (which is equal to the @@ -1654,7 +1665,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998, Section 6.4. -

+

@@ -1678,9 +1689,9 @@

-— Function File: [U, R, Q, X, p0, pK] = qnmm1k (lambda, mu, K)
+— Function File: [U, R, Q, X, p0, pK] = qnmm1k (lambda, mu, K)
-

+

Compute utilization, response time, average number of requests and throughput for a M/M/1/K finite capacity system. In a M/M/1/K queue there is a single server; the maximum number of @@ -1747,9 +1758,9 @@

-— Function File: [U, R, Q, X, p0, pK] = qnmmmk (lambda, mu, m, K)
+— Function File: [U, R, Q, X, p0, pK] = qnmmmk (lambda, mu, m, K)
-

+

Compute utilization, response time, average number of requests and throughput for a M/M/m/K finite capacity system. In a M/M/m/K system there are m \geq 1 identical service @@ -1807,7 +1818,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998, Section 6.6. -

+

@@ -1829,9 +1840,9 @@

-— Function File: [U, R, Q, X] = qnammm (lambda, mu)
+— Function File: [U, R, Q, X] = qnammm (lambda, mu)
-

+

Compute approximate utilization, response time, average number of requests in service and throughput for an asymmetric M/M/m queue. In this system there are m different service centers @@ -1878,7 +1889,7 @@ and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998 -

+

@@ -1894,9 +1905,9 @@

-— Function File: [U, R, Q, X, p0] = qnmg1 (lambda, xavg, x2nd)
+— Function File: [U, R, Q, X, p0] = qnmg1 (lambda, xavg, x2nd)
-

+

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 xavg, and by its second moment @@ -1953,9 +1964,9 @@

-— Function File: [U, R, Q, X, p0] = qnmh1 (lambda, mu, alpha)
+— Function File: [U, R, Q, X, p0] = qnmh1 (lambda, mu, alpha)
-

+

Compute utilization, response time, average number of requests and throughput for a M/H_m/1 system. In this system, the customer service times have hyper-exponential distribution: @@ -2037,7 +2048,7 @@

  • Utility functions: Utility functions to compute miscellaneous quantities -

    +

    @@ -2298,13 +2309,13 @@

    -— Function File: Q = qnmknode ("m/m/m-fcfs", S)
    -— Function File: Q = qnmknode ("m/m/m-fcfs", S, m)
    -— Function File: Q = qnmknode ("m/m/1-lcfs-pr", S)
    -— Function File: Q = qnmknode ("-/g/1-ps", S)
    -— Function File: Q = qnmknode ("-/g/1-ps", S, s2)
    -— Function File: Q = qnmknode ("-/g/inf", S)
    -— Function File: Q = qnmknode ("-/g/inf", S, s2)
    +— Function File: Q = qnmknode ("m/m/m-fcfs", S)
    +— Function File: Q = qnmknode ("m/m/m-fcfs", S, m)
    +— Function File: Q = qnmknode ("m/m/1-lcfs-pr", S)
    +— Function File: Q = qnmknode ("-/g/1-ps", S)
    +— Function File: Q = qnmknode ("-/g/1-ps", S, s2)
    +— Function File: Q = qnmknode ("-/g/inf", S)
    +— Function File: Q = qnmknode ("-/g/inf", S, s2)

    Creates a node; this function can be used together with qnsolve. It is possible to create either single-class nodes @@ -2373,10 +2384,10 @@

    -— Function File: [U, R, Q, X] = qnsolve ("closed", N, QQ, V)
    -— Function File: [U, R, Q, X] = qnsolve ("closed", N, QQ, V, Z)
    -— Function File: [U, R, Q, X] = qnsolve ("open", lambda, QQ, V)
    -— Function File: [U, R, Q, X] = qnsolve ("mixed", lambda, N, QQ, V)
    +— Function File: [U, R, Q, X] = qnsolve ("closed", N, QQ, V)
    +— Function File: [U, R, Q, X] = qnsolve ("closed", N, QQ, V, Z)
    +— Function File: [U, R, Q, X] = qnsolve ("open", lambda, QQ, V)
    +— Function File: [U, R, Q, X] = qnsolve ("mixed", lambda, N, QQ, V)

    General evaluator of QN models. Networks can be open, closed or mixed; single as well as multiclass networks are supported. @@ -2554,11 +2565,11 @@

    -— Function File: [U, R, Q, X] = qnjackson (lambda, S, P )
    -— Function File: [U, R, Q, X] = qnjackson (lambda, S, P, m )
    -— Function File: pr = qnjackson (lambda, S, P, m, k)
    +— Function File: [U, R, Q, X] = qnjackson (lambda, S, P )
    +— Function File: [U, R, Q, X] = qnjackson (lambda, S, P, m )
    +— Function File: pr = qnjackson (lambda, S, P, m, k)
    -

    +

    With three or four input parameters, this function computes the steady-state occupancy probabilities for a Jackson network. With five input parameters, this function computes the steady-state probability @@ -2640,7 +2651,7 @@ Performance Evaluation with Computer Science Applications, Wiley, 1998, pp. 284–287. -

    +

    6.3.2 The Convolution Algorithm

    @@ -2674,10 +2685,10 @@

    -— Function File: [U, R, Q, X, G] = qnconvolution (N, S, V)
    -— Function File: [U, R, Q, X, G] = qnconvolution (N, S, V, m)
    +— Function File: [U, R, Q, X, G] = qnconvolution (N, S, V)
    +— Function File: [U, R, Q, X, G] = qnconvolution (N, S, V, m)
    -

    +

    This function implements the convolution algorithm for computing steady-state performance measures of product-form, single-class closed queueing networks. Load-independent service @@ -2768,20 +2779,20 @@ 16, number 9, september 1973, pp. 527–531. http://doi.acm.org/10.1145/362342.362345 -

    +

    This implementation is based on G. Bolch, S. Greiner, H. de Meer and K. Trivedi, Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998, pp. 313–317. -

    +

    -— Function File: [U, R, Q, X, G] = qnconvolutionld (N, S, V)
    +— Function File: [U, R, Q, X, G] = qnconvolutionld (N, S, V)
    -

    +

    This function implements the convolution algorithm for product-form, single-class closed queueing networks with general load-dependent service centers. @@ -2841,7 +2852,7 @@ Purdue University, feb, 1981 (revised). http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-354.pdf -

    +

    M. Reiser, H. Kobayashi, On The Convolution Algorithm for Separable Queueing Networks, In Proceedings of the 1976 ACM SIGMETRICS Conference on Computer Performance Modeling Measurement and @@ -2849,7 +2860,7 @@ 1976). SIGMETRICS '76. ACM, New York, NY, pp. 109–117. http://doi.acm.org/10.1145/800200.806187 -

    +

    This implementation is based on G. Bolch, S. Greiner, H. de Meer and K. Trivedi, Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, @@ -2861,7 +2872,7 @@ function f_i defined in Schwetman, Some Computational Aspects of Queueing Network Models. -

    +

    6.3.3 Open networks

    @@ -2869,10 +2880,10 @@

    -— Function File: [U, R, Q, X] = qnopensingle (lambda, S, V)
    -— Function File: [U, R, Q, X] = qnopensingle (lambda, S, V, m)
    +— Function File: [U, R, Q, X] = qnopensingle (lambda, S, V)
    +— Function File: [U, R, Q, X] = qnopensingle (lambda, S, V, m)
    -

    +

    Analyze open, single class BCMP queueing networks.

    This function works for a subset of BCMP single-class open networks @@ -2965,16 +2976,16 @@ Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998. -

    +

    -— Function File: [U, R, Q, X] = qnopenmulti (lambda, S, V)
    -— Function File: [U, R, Q, X] = qnopenmulti (lambda, S, V, m)
    +— Function File: [U, R, Q, X] = qnopenmulti (lambda, S, V)
    +— Function File: [U, R, Q, X] = qnopenmulti (lambda, S, V, m)
    -

    +

    Exact analysis of open, multiple-class BCMP networks. The network can be made of single-server queueing centers (FCFS, LCFS-PR or PS) or delay centers (IS). This function assumes a network with @@ -3039,7 +3050,7 @@ 1984. http://www.cs.washington.edu/homes/lazowska/qsp/. In particular, see section 7.4.1 ("Open Model Solution Techniques"). -

    +

    6.3.4 Closed Networks

    @@ -3047,11 +3058,11 @@

    -— Function File: [U, R, Q, X, G] = qnclosedsinglemva (N, S, V)
    -— Function File: [U, R, Q, X, G] = qnclosedsinglemva (N, S, V, m)
    -— Function File: [U, R, Q, X, G] = qnclosedsinglemva (N, S, V, m, Z)
    +— Function File: [U, R, Q, X, G] = qnclosedsinglemva (N, S, V)
    +— Function File: [U, R, Q, X, G] = qnclosedsinglemva (N, S, V, m)
    +— Function File: [U, R, Q, X, G] = qnclosedsinglemva (N, S, V, m, Z)
    -

    +

    Analyze closed, single class queueing networks using the exact Mean Value Analysis (MVA) algorithm. The following queueing disciplines are supported: FCFS, LCFS-PR, PS and IS (Infinite Server). This @@ -3097,8 +3108,11 @@ X(k)*S(k).

    R
    R(k) is the response time at center k. +The Residence Time at center k is +R(k) * V(k). The system response time Rsys -can be computed as Rsys = N/Xsys - Z +can be computed either as Rsys = N/Xsys - Z +or as Rsys = dot(R,V)
    Q
    Q(k) is the average number of requests at center k. The number of requests in the system can be computed @@ -3149,7 +3163,7 @@ Multichain Queuing Networks, Journal of the ACM, vol. 27, n. 2, April 1980, pp. 313–322. http://doi.acm.org/10.1145/322186.322195 -

    +

    This implementation is described in R. Jain , The Art of Computer Systems Performance Analysis, Wiley, 1991, p. 577. Multi-server nodes @@ -3158,15 +3172,15 @@ Performance Evaluation with Computer Science Applications, Wiley, 1998, Section 8.2.1, "Single Class Queueing Networks". -

    +

    -— Function File: [U, R, Q, X] = qnclosedsinglemvald (N, S, V)
    -— Function File: [U, R, Q, X] = qnclosedsinglemvald (N, S, V, Z)
    +— Function File: [U, R, Q, X] = qnclosedsinglemvald (N, S, V)
    +— Function File: [U, R, Q, X] = qnclosedsinglemvald (N, S, V, Z)
    -

    +

    Exact MVA algorithm for closed, single class queueing networks with load-dependent service centers. This function supports FCFS, LCFS-PR, PS and IS nodes. For networks with only fixed-rate @@ -3224,15 +3238,15 @@ 1998, Section 8.2.4.1, “Networks with Load-Deèpendent Service: Closed Networks”. -

    +

    -— Function File: [U, R, Q, X] = qncmva (N, S, Sld, V)
    -— Function File: [U, R, Q, X] = qncmva (N, S, Sld, V, Z)
    +— Function File: [U, R, Q, X] = qncmva (N, S, Sld, V)
    +— Function File: [U, R, Q, X] = qncmva (N, S, Sld, V, Z)
    -

    +

    Implementation of the Conditional MVA (CMVA) algorithm, a numerically stable variant of MVA for load-dependent servers. CMVA is described in G. Casale, A Note on Stable Flow-Equivalent Aggregation in @@ -3286,19 +3300,19 @@ closed networks. Queueing Syst. Theory Appl., 60:193–202, December 2008. -

    +

    -— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V)
    -— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V, m)
    -— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V, m, Z)
    -— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V, m, Z, tol)
    -— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V, m, Z, tol, iter_max)
    +— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V)
    +— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V, m)
    +— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V, m, Z)
    +— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V, m, Z, tol)
    +— Function File: [U, R, Q, X] = qnclosedsinglemvaapprox (N, S, V, m, Z, tol, iter_max)
    -

    +

    Analyze closed, single class queueing networks using the Approximate Mean Value Analysis (MVA) algorithm. This function is based on approximating the number of customers seen at center k when a @@ -3377,20 +3391,20 @@ 1984. http://www.cs.washington.edu/homes/lazowska/qsp/. In particular, see section 6.4.2.2 ("Approximate Solution Techniques"). -

    +

    -— Function File: [U, R, Q, X] = qnclosedmultimva (N, S )
    -— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, V)
    -— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, V, m)
    -— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, V, m, Z)
    -— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, P)
    -— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, P, m)
    +— Function File: [U, R, Q, X] = qnclosedmultimva (N, S )
    +— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, V)
    +— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, V, m)
    +— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, V, m, Z)
    +— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, P)
    +— Function File: [U, R, Q, X] = qnclosedmultimva (N, S, P, m)
    -

    +

    Analyze closed, multiclass queueing networks with K service centers and C independent customer classes (chains) using the Mean Value Analysys (MVA) algorithm. @@ -3477,8 +3491,10 @@ defined as U(c,k) = X(c,k)*S(c,k).

    R
    R(c,k) is the class c response time at -center k. The total class c system response time -can be computed as dot(R, V, 2). +center k. The class c residence time +at center k is R(c,k) * C(c,k). +The total class c system response time +is dot(R, V, 2).
    Q
    Q(c,k) is the average number of class c requests at center k. The total number of @@ -3518,7 +3534,7 @@ Multichain Queuing Networks, Journal of the ACM, vol. 27, n. 2, April 1980, pp. 313–322. http://doi.acm.org/10.1145/322186.322195 -

    +

    This implementation is based on G. Bolch, S. Greiner, H. de Meer and K. Trivedi, Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, @@ -3528,18 +3544,18 @@ 1984. http://www.cs.washington.edu/homes/lazowska/qsp/. In particular, see section 7.4.2.1 ("Exact Solution Techniques"). -

    +

    -— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V)
    -— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V, m)
    -— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V, m, Z)
    -— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V, m, Z, tol)
    -— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V, m, Z, tol, iter_max)
    +— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V)
    +— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V, m)
    +— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V, m, Z)
    +— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V, m, Z, tol)
    +— Function File: [U, R, Q, X] = qnclosedmultimvaapprox (N, S, V, m, Z, tol, iter_max)
    -

    +

    Analyze closed, multiclass queueing networks with K service centers and C customer classes using the approximate Mean Value Analysys (MVA) algorithm. @@ -3624,12 +3640,12 @@ proc. 4th Int. Symp. on Modelling and Performance Evaluation of Computer Systems, feb. 1979, pp. 51–62. -

    +

    P. Schweitzer, Approximate Analysis of Multiclass Closed Networks of Queues, Proc. Int. Conf. on Stochastic Control and Optimization, jun 1979, pp. 25–29. -

    +

    This implementation is based on Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queueing Network Models, @@ -3640,7 +3656,7 @@ described above, as it computes the average response times R instead of the residence times. -

    +

    6.3.5 Mixed Networks

    @@ -3648,9 +3664,9 @@

    -— Function File: [U, R, Q, X] = qnmix (lambda, N, S, V, m)
    +— Function File: [U, R, Q, X] = qnmix (lambda, N, S, V, m)
    -

    +

    Solution of mixed queueing networks through MVA. The network consists of K service centers (single-server or delay centers) and C independent customer chains. Both open and closed chains @@ -3741,14 +3757,14 @@ Note that in this function we compute the mean response time R instead of the mean residence time as in the reference. -

    +

    Herb Schwetman, Implementing the Mean Value Algorithm for the Solution of Queueing Network Models, Technical Report CSD-TR-355, Department of Computer Sciences, Purdue University, feb 15, 1982, available at http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-355.pdf -

    +

    @@ -3767,9 +3783,9 @@

    -— Function File: [U, R, Q, X] = qnmvablo (N, S, M, P)
    +— Function File: [U, R, Q, X] = qnmvablo (N, S, M, P)
    -

    +

    MVA algorithm for closed queueing networks with blocking. qnmvablo computes approximate utilization, response time and mean queue length for closed, single class queueing networks with blocking. @@ -3824,16 +3840,16 @@ Networks, IEEE Transactions on Software Engineering, vol. 14, n. 2, april 1988, pp. 418–428. http://dx.doi.org/10.1109/32.4663 -

    +

    -— Function File: [U, R, Q, X] = qnmarkov (lambda, S, C, P)
    -— Function File: [U, R, Q, X] = qnmarkov (lambda, S, C, P, m)
    -— Function File: [U, R, Q, X] = qnmarkov (N, S, C, P)
    -— Function File: [U, R, Q, X] = qnmarkov (N, S, C, P, m)
    +— Function File: [U, R, Q, X] = qnmarkov (lambda, S, C, P)
    +— Function File: [U, R, Q, X] = qnmarkov (lambda, S, C, P, m)
    +— Function File: [U, R, Q, X] = qnmarkov (N, S, C, P)
    +— Function File: [U, R, Q, X] = qnmarkov (N, S, C, P, m)
    -

    +

    Compute utilization, response time, average queue length and throughput for open or closed queueing networks with finite capacity. Blocking type is Repetitive-Service (RS). This function explicitly @@ -3943,9 +3959,9 @@

    -— Function File: [Xu, Rl] = qnopenab (lambda, D)
    +— Function File: [Xu, Rl] = qnopenab (lambda, D)
    -

    +

    Compute Asymptotic Bounds for single-class, open Queueing Networks with K service centers. @@ -3985,14 +4001,14 @@ 1984. http://www.cs.washington.edu/homes/lazowska/qsp/. In particular, see section 5.2 ("Asymptotic Bounds"). -

    +

    -— Function File: [Xl, Xu, Rl, Ru] = qnclosedab (N, D)
    -— Function File: [Xl, Xu, Rl, Ru] = qnclosedab (N, D, Z)
    +— Function File: [Xl, Xu, Rl, Ru] = qnclosedab (N, D)
    +— Function File: [Xl, Xu, Rl, Ru] = qnclosedab (N, D, Z)
    -

    +

    Compute Asymptotic Bounds for single-class, closed Queueing Networks with K service centers. @@ -4033,14 +4049,14 @@ 1984. http://www.cs.washington.edu/homes/lazowska/qsp/. In particular, see section 5.2 ("Asymptotic Bounds"). -

    +

    -— Function File: [Xu, Rl, Ru] = qnopenbsb (lambda, D)
    +— Function File: [Xu, Rl, Ru] = qnopenbsb (lambda, D)
    -

    +

    Compute Balanced System Bounds for single-class, open Queueing Networks with K service centers. @@ -4080,14 +4096,14 @@ 1984. http://www.cs.washington.edu/homes/lazowska/qsp/. In particular, see section 5.4 ("Balanced Systems Bounds"). -

    +

    -— Function File: [Xl, Xu, Rl, Ru] = qnclosedbsb (N, D)
    -— Function File: [Xl, Xu, Rl, Ru] = qnclosedbsb (N, D, Z)
    +— Function File: [Xl, Xu, Rl, Ru] = qnclosedbsb (N, D)
    +— Function File: [Xl, Xu, Rl, Ru] = qnclosedbsb (N, D, Z)
    -

    +

    Compute Balanced System Bounds for single-class, closed Queueing Networks with K service centers. @@ -4123,7 +4139,7 @@

    -— Function File: [Xl, Xu] = qnclosedpb (N, D )
    +— Function File: [Xl, Xu] = qnclosedpb (N, D )

    Compute PB Bounds (C. H. Hsieh and S. Lam, 1987) for single-class, closed Queueing Networks @@ -4167,13 +4183,13 @@ Non-Iterative Analysis Technique for Closed Queueing Networks, IEEE Transactions on Computers, 57(6):780-794, June 2008. -

    +

    -— Function File: [Xl, Xu, Ql, Qu] = qnclosedgb (N, D, Z)
    +— Function File: [Xl, Xu, Ql, Qu] = qnclosedgb (N, D, Z)
    -

    +

    Compute Geometric Bounds (GB) for single-class, closed Queueing Networks.

    INPUTS @@ -4214,7 +4230,7 @@ Queueing Networks, IEEE Transactions on Computers, 57(6):780-794, June 2008. http://doi.ieeecomputersociety.org/10.1109/TC.2008.37 -

    +

    In this implementation we set X^+ and X^- as the upper and lower Asymptotic Bounds as computed by the qnclosedab function, respectively. @@ -4234,9 +4250,9 @@

    -— Function File: [U, R, Q, X] = qnclosed (N, S, V, ...)
    +— Function File: [U, R, Q, X] = qnclosed (N, S, V, ...)
    -

    +

    This function computes steady-state performance measures of closed queueing networks using the Mean Value Analysis (MVA) algorithm. The qneneing network is allowed to contain fixed-capacity centers, delay @@ -4303,9 +4319,9 @@

    -— Function File: [U, R, Q, X] = qnopen (lambda, S, V, ...)
    +— Function File: [U, R, Q, X] = qnopen (lambda, S, V, ...)
    -

    +

    Compute utilization, response time, average number of requests in the system, and throughput for open queueing networks. If lambda is a scalar, the network is considered a single-class QN and is solved @@ -4358,8 +4374,8 @@

    -— Function File: [V ch] = qnvisits (P)
    -— Function File: V = qnvisits (P, lambda)
    +— Function File: [V ch] = qnvisits (P)
    +— Function File: V = qnvisits (P, lambda)

    Compute the average number of visits to the service centers of a single class, open or closed Queueing Network with N service @@ -4421,9 +4437,9 @@

    -— Function File: pop_mix = population_mix (k, N)
    +— Function File: pop_mix = population_mix (k, N)
    -

    +

    Return the set of valid population mixes with exactly k customers, for a closed multiclass Queueing Network with population vector N. More specifically, given a multiclass Queueing @@ -4485,13 +4501,13 @@ Indices for a Complex Summation, unpublished report, available at http://arantxa.ii.uam.es/~ssantini/writing/notes/s668_summation.pdf -

    +

    -— Function File: H = qnmvapop (N)
    +— Function File: H = qnmvapop (N)
    -

    +

    Given a network with C customer classes, this function computes the number of valid population mixes H(r,n) that can be constructed by the multiclass MVA algorithm by allocating n @@ -4528,7 +4544,7 @@ Perform. Eval. Rev. 10, 3 (Sep. 1981), 80-85. DOI http://doi.acm.org/10.1145/1010629.805477 -

    +

    @@ -4639,7 +4655,7 @@

    Appendix C GNU GENERAL PUBLIC LICENSE

    -

    +

    Version 3, 29 June 2007
         Copyright © 2007 Free Software Foundation, Inc. http://fsf.org/
@@ -5346,69 +5362,69 @@
 
    Concept Index
    
 
 
    
 
 
    
@@ -5426,46 +5442,46 @@
 
  • ctmc: CTMC Stationary Probability
    • 
 
  • ctmc_bd: Birth-Death process
    • 
 
  • ctmc_exps: Expected Sojourn Time
    • 
-
  • ctmc_fpt: CTMC First Passage Times
    • 
-
  • ctmc_mtta: Expected Time to Absorption
    • 
-
  • ctmc_taexps: Time-Averaged Expected Sojourn Time
    • 
+
  • ctmc_fpt: CTMC First Passage Times
    • 
+
  • ctmc_mtta: Expected Time to Absorption
    • 
+
  • ctmc_taexps: Time-Averaged Expected Sojourn Time
    • 
 
  • dtmc: Discrete-Time Markov Chains
    • 
 
  • dtmc_fpt: Discrete-Time Markov Chains
    • 
-
  • population_mix: Utility functions
    • 
-
  • qnammm: The Asymmetric M/M/m System
    • 
-
  • qnclosed: Utility functions
    • 
-
  • qnclosedab: Bounds on performance
    • 
-
  • qnclosedbsb: Bounds on performance
    • 
-
  • qnclosedgb: Bounds on performance
    • 
-
  • qnclosedmultimva: Algorithms for Product-Form QNs
    • 
-
  • qnclosedmultimvaapprox: Algorithms for Product-Form QNs
    • 
-
  • qnclosedpb: Bounds on performance
    • 
-
  • qnclosedsinglemva: Algorithms for Product-Form QNs
    • 
-
  • qnclosedsinglemvaapprox: Algorithms for Product-Form QNs
    • 
-
  • qnclosedsinglemvald: Algorithms for Product-Form QNs
    • 
-
  • qncmva: Algorithms for Product-Form QNs
    • 
-
  • qnconvolution: Algorithms for Product-Form QNs
    • 
-
  • qnconvolutionld: Algorithms for Product-Form QNs
    • 
-
  • qnjackson: Algorithms for Product-Form QNs
    • 
-
  • qnmarkov: Algorithms for non Product-form QNs
    • 
-
  • qnmg1: The M/G/1 System
    • 
-
  • qnmh1: The M/Hm/1 System
    • 
-
  • qnmix: Algorithms for Product-Form QNs
    • 
-
  • qnmknode: Generic Algorithms
    • 
-
  • qnmm1: The M/M/1 System
    • 
-
  • qnmm1k: The M/M/1/K System
    • 
-
  • qnmminf: The M/M/inf System
    • 
-
  • qnmmm: The M/M/m System
    • 
-
  • qnmmmk: The M/M/m/K System
    • 
-
  • qnmvablo: Algorithms for non Product-form QNs
    • 
-
  • qnmvapop: Utility functions
    • 
-
  • qnopen: Utility functions
    • 
-
  • qnopenab: Bounds on performance
    • 
-
  • qnopenbsb: Bounds on performance
    • 
-
  • qnopenmulti: Algorithms for Product-Form QNs
    • 
-
  • qnopensingle: Algorithms for Product-Form QNs
    • 
-
  • qnsolve: Generic Algorithms
    • 
-
  • qnvisits: Utility functions
    • 
+
  • population_mix: Utility functions
    • 
+
  • qnammm: The Asymmetric M/M/m System
    • 
+
  • qnclosed: Utility functions
    • 
+
  • qnclosedab: Bounds on performance
    • 
+
  • qnclosedbsb: Bounds on performance
    • 
+
  • qnclosedgb: Bounds on performance
    • 
+
  • qnclosedmultimva: Algorithms for Product-Form QNs
    • 
+
  • qnclosedmultimvaapprox: Algorithms for Product-Form QNs
    • 
+
  • qnclosedpb: Bounds on performance
    • 
+
  • qnclosedsinglemva: Algorithms for Product-Form QNs
    • 
+
  • qnclosedsinglemvaapprox: Algorithms for Product-Form QNs
    • 
+
  • qnclosedsinglemvald: Algorithms for Product-Form QNs
    • 
+
  • qncmva: Algorithms for Product-Form QNs
    • 
+
  • qnconvolution: Algorithms for Product-Form QNs
    • 
+
  • qnconvolutionld: Algorithms for Product-Form QNs
    • 
+
  • qnjackson: Algorithms for Product-Form QNs
    • 
+
  • qnmarkov: Algorithms for non Product-form QNs
    • 
+
  • qnmg1: The M/G/1 System
    • 
+
  • qnmh1: The M/Hm/1 System
    • 
+
  • qnmix: Algorithms for Product-Form QNs
    • 
+
  • qnmknode: Generic Algorithms
    • 
+
  • qnmm1: The M/M/1 System
    • 
+
  • qnmm1k: The M/M/1/K System
    • 
+
  • qnmminf: The M/M/inf System
    • 
+
  • qnmmm: The M/M/m System
    • 
+
  • qnmmmk: The M/M/m/K System
    • 
+
  • qnmvablo: Algorithms for non Product-form QNs
    • 
+
  • qnmvapop: Utility functions
    • 
+
  • qnopen: Utility functions
    • 
+
  • qnopenab: Bounds on performance
    • 
+
  • qnopenbsb: Bounds on performance
    • 
+
  • qnopenmulti: Algorithms for Product-Form QNs
    • 
+
  • qnopensingle: Algorithms for Product-Form QNs
    • 
+
  • qnsolve: Generic Algorithms
    • 
+
  • qnvisits: Utility functions
    • 
    
    
 
 
    
@@ -5479,60 +5495,60 @@
 
 
 
 
diff -r bd7fb43a670e -r cdf1dbf20cd4 main/queueing/doc/queueing.pdf
Binary file main/queueing/doc/queueing.pdf has changed
diff -r bd7fb43a670e -r cdf1dbf20cd4 main/queueing/inst/ctmc_exps.m
--- a/main/queueing/inst/ctmc_exps.m	Sat Mar 10 16:00:45 2012 +0000
+++ b/main/queueing/inst/ctmc_exps.m	Sat Mar 10 16:03:47 2012 +0000
@@ -27,7 +27,7 @@
 ## spent in each state @math{j} during the time interval
 ## @code{[0,@var{tt}(t))}, assuming that at time 0 the state occupancy
 ## probability was @var{p}. With two arguments, compute the expected
-## time @code{@var{L}(j}} spent in each state @math{j} until absorption.
+## time @code{@var{L}(j)} spent in each state @math{j} until absorption.
 ##
 ## @strong{INPUTS}
 ##