Example session to illustrate use of the Multiclass [Ph(t)/Ph(t)/infinity]^K Maple Software

August 1, 2000

These routines for the single-node case provide the essential computational engines

> read(`PhPhInfSymbolic.txt`):

Warning, new definition for norm

Warning, new definition for trace

> read(`PhPhInfNumericEmpty.txt`):

> read(`PhPhInfNumericInit.txt`):

> read(`PhPhInfMoments.txt`):

> read(`PhPhInfSojourn.txt`):

These routines handle the single arrival source, multiple queue case

> read(`PhPhInfNetSymbolic.txt`):

> read(`PhPhInfNetNumeric.txt`):

> read(`PhPhInfNetMoments.txt`):

> read(`PhPhInfNetSojourn.txt`):

These are the most general multiclass routines; and are what the user would typically call

> read(`PhPhInfMCNSymbolic.txt`):

> read(`PhPhInfMCNNumeric.txt`):

> read(`PhPhInfMCNMoments.txt`):

> read(`PhPhInfMCNSojourn.txt`):

>

First create the input parameters for the example: Markov routine matrix Pr, Phase arrival process (1 class) A, lambda,

and two-node queueing network, B, mu

> Pr := matrix(3,3, [1/2 + 1/2*sin(Pi*t/4), 1/2 - 1/2*sin(Pi*t/4), 0,

> 0.15, 0, 0.85, 0.7, 0.3, 0]);

> A := matrix(4,4, [ 0, 1/3 + 1/3*cos(Pi*t/4), 2/3 - 1/3*cos(Pi*t/4), 0,

> 0,0,0,1, 0,0.3,0,0.7, 0.8,0.2,0,0]);

> lambda := vector(3, [5, 8, 10 + 5*sin(Pi*t/5)]);

> B := vector(2);

Create B matrix for node 1

> B[1] := matrix(4,4, [0,0.4,0.6,0, 0,0, 1/4 + 1/4*sin(Pi*t/6), 3/4 - 1/4*sin(Pi*t/6),

> 0,0,0.2,0.8, 0.5,0,.5,0]);

Create B matrix for node 2

> B[2] := matrix(4,4, [0,0.5,0.5,0, 0,0,2/3,1/3, 0,1/3,1/3,1/3,

> .5, 0, .5, 0]);

> mu := vector(2, [ [3,4,7.5], [2,2,2] ]);

>

Plot the mean and variance of number in the network, and in each node, from time 0 to 10

> mplots := PhPhInfMCNMoments(A, lambda, 1, B, mu, 2, Pr, [1,2], 0, 10):

Print out time-dependent mean number in network and at each node

> mplots[1];

Print out time-dependent variance of the number in network and at each node

> mplots[2];

Determine the mean, variance, and cdf for a virtual customer arriving to the network at time 5

> sojourn := PhPhInfMCNSojourn(A, lambda, 1, B, mu, 2, Pr, 5):

mean

> sojourn[1];

variance

> sojourn[2];

cdf

> sojourn[3];

>

Finally, display the moment differential equations for this model

> PhPhInfMCNSymbolic(A, lambda, 1, B, mu, 2, Pr);

>