ag_jackson_network.m

%% Jackson Network with MAM
%
% This example demonstrates MAM with RCAT methods on an open Jackson network with
% probabilistic routing. The RCAT algorithm models job transfers between
% queues as synchronization actions between interacting processes.
%
% Reference: Jackson, J.R. (1957). "Networks of waiting lines"
%
% Copyright (c) 2012-2025, Imperial College London
% All rights reserved.
 
clear; clc;
 
%% Parameters
lambda = 1.0;   % External arrival rate
mu = [2.0, 3.0, 2.5];  % Service rates
 
% Routing probabilities
p12 = 0.4;  % Queue1 -> Queue2
p13 = 0.3;  % Queue1 -> Queue3
p1s = 0.3;  % Queue1 -> Sink
p21 = 0.2;  % Queue2 -> Queue1
p23 = 0.3;  % Queue2 -> Queue3
p2s = 0.5;  % Queue2 -> Sink
p3s = 1.0;  % Queue3 -> Sink
 
%% Create model
model = Network('Jackson-3Q');
 
source = Source(model, 'Source');
queue1 = Queue(model, 'Queue1', SchedStrategy.FCFS);
queue2 = Queue(model, 'Queue2', SchedStrategy.FCFS);
queue3 = Queue(model, 'Queue3', SchedStrategy.FCFS);
sink = Sink(model, 'Sink');
 
oclass = OpenClass(model, 'Class1');
source.setArrival(oclass, Exp(lambda));
queue1.setService(oclass, Exp(mu(1)));
queue2.setService(oclass, Exp(mu(2)));
queue3.setService(oclass, Exp(mu(3)));
 
% Set routing matrix
P = model.initRoutingMatrix();
P{1,1}(source, queue1) = 1.0;
P{1,1}(queue1, queue2) = p12;
P{1,1}(queue1, queue3) = p13;
P{1,1}(queue1, sink) = p1s;
P{1,1}(queue2, queue1) = p21;
P{1,1}(queue2, queue3) = p23;
P{1,1}(queue2, sink) = p2s;
P{1,1}(queue3, sink) = p3s;
model.link(P);
 
%% Solve with MAM using INAP method (default)
solverINAP = MAM(model, 'method', 'inap');
avgTableINAP = solverINAP.getAvgTable()
 
%% Solve with MAM using exact method (AutoCAT)
solverExact = MAM(model, 'method', 'exact');
avgTableExact = solverExact.getAvgTable()
 
%% Solve with MVA for comparison
solverMVA = MVA(model);
avgTableMVA = solverMVA.getAvgTable()