init_state_fcfs_nonexp.m

clear node jobclass solver;
 
model = Network('model');
 
node{1} = Delay(model, 'Delay');
node{2} = Queue(model, 'Queue1', SchedStrategy.FCFS);
jobclass{1} = ClosedClass(model, 'Class1', 3, node{2}, 0);
jobclass{2} = ClosedClass(model, 'Class2', 2, node{2}, 0);
node{2}.setNumServers(3);
 
node{1}.setService(jobclass{1}, Exp(1));
node{1}.setService(jobclass{2}, Exp(1));
node{2}.setService(jobclass{1}, Exp(1.2));
node{2}.setService(jobclass{2}, Erlang.fitMeanAndSCV(1.0,0.5));
 
M = model.getNumberOfStations();
K = model.getNumberOfClasses();
 
P = cell(K,K);
P{1,1} = [0.3,0.1; 0.2,0];
P{1,2} = [0.6,0; 0.8,0];
P{2,2} = [0,1; 0,0];
P{2,1} = [0,0; 1,0];
 
model.link(P);
[Qt,Ut,Tt] = model.getTranHandles();
options = Solver.defaultOptions;
options.verbose=1;
options.samples=1e4;
options.stiff=true;
options.timespan = [0,5];
%% This part illustrates the execution of different solvers
solver{1} = CTMC(model,options);
%solver{end+1} = JMT(model,options);
%solver{end+1} = SSA(model,options);
solver{end+1} = FLD(model,options);
%solver{end+1} = MVA(model,options);
dashing = {'-','--'};
 
sn = model.getStruct();
%%
disp('Prior 1: prior all on default initialization')
model.initDefault;
disp('Initial state is:')
[sn.space{1}(1,:),sn.space{2}(1,:)]
for s=1:length(solver)
    fprintf(1,'SOLVER: %s\n',strrep(solver{s}.getName(),'Solver',''));
    [QNt,UNt,TNt] = solver{s}.getTranAvg(Qt,Ut,Tt);
    fprintf('SteadyStateQLen[%s/Prior1]: %.6f\n', strrep(solver{s}.getName(),'Solver',''), QNt{2,1}.metric(end));
    subplot(3,1,1);
    plot(QNt{2,1}.t,QNt{2,1}.metric,dashing{s}); hold on
    solver{s}.reset();
end
title('Prior on default state');
ylabel('QLen- station 2, class 1');
ylim([0,5])
xlabel('Time t');
xlim(options.timespan)
legend('ctmc','fluid')
%%
disp('Prior 2: prior all on first found state with the same number of jobs')
model.initFromMarginal([0,0;4,1]);
sn = model.getStruct;
disp('Initial state is:')
[sn.space{1}(1,:),sn.space{2}(1,:)]
for s=1:length(solver)
    solver{s}.reset();
    fprintf(1,'SOLVER: %s\n',strrep(solver{s}.getName(),'Solver',''));
    [QNt_marg,UNt_marg,TNt_marg] = solver{s}.getTranAvg(Qt,Ut,Tt);
    fprintf('SteadyStateQLen[%s/Prior2]: %.6f\n', strrep(solver{s}.getName(),'Solver',''), QNt_marg{2,1}.metric(end));
    subplot(3,1,2);
    plot(QNt_marg{2,1}.t,QNt_marg{2,1}.metric,dashing{s}); hold on
    solver{s}.reset();
end
title('Prior on first state with the same number of jobs');
ylabel('QLen- station 2, class 1');
ylim([0,5])
xlabel('Time t');
xlim(options.timespan)
legend('ctmc','fluid')
%%
disp('Prior 3: uniform prior over all states with the same number of jobs')
model.initFromMarginal([0,0;4,1]);
disp('Initial states are:')
space=sn.space;
[repmat(space{1}(1,:),size(space{2},1),1),space{2}]
prior = node{2}.getStatePrior;
prior = 0*prior; prior=ones(size(prior))/length(prior);
node{2}.setStatePrior(prior);
for s=1:length(solver)
    solver{s}.reset();
    %fprintf(1,'SOLVER: %s\n',strrep(solver{s}.getName(),'Solver',''));
    [QNt_unif,UNt_unif,TNt_unif] = solver{s}.getTranAvg(Qt,Ut,Tt);
    fprintf('SteadyStateQLen[%s/Prior3]: %.6f\n', strrep(solver{s}.getName(),'Solver',''), QNt_unif{2,1}.metric(end));
    subplot(3,1,3);
    plot(QNt_unif{2,1}.t,QNt_unif{2,1}.metric,dashing{s}); hold on
end
title('Uniform prior on states with the same number of jobs');
ylabel('QLen- station 2, class 1');
ylim([0,5])
xlabel('Time t');
xlim(options.timespan)
legend('ctmc','fluid')
hold off