// tandem queueing network [HKMKS99]
// gxn/dxp 25/01/00

ctmc

const int c = 5; // queue capacity

const double lambda = 4*c;
const double mu1a = 0.1*2;
const double mu1b = 0.9*2;
const double mu2 = 2;
const double kappa = 4;

module serverC
	
	sc : [0..c];
	ph : [1..2];
	
	[] (sc<c) -> lambda: (sc'=sc+1); 
	[route] (sc>0) & (ph=1) -> mu1b: (sc'=sc-1);
	[] (sc>0) & (ph=1) -> mu1a: (ph'=2); 
	[route] (sc>0) & (ph=2) -> mu2: (ph'=1) & (sc'=sc-1);
	
endmodule  

module serverM
	
	sm : [0..c];
	
	[route]	(sm<c) -> 1: (sm'=sm+1);
	[] (sm>0) -> kappa: (sm'=sm-1);
	
endmodule

// reward - number of customers in network
rewards "customers"
	true : sc + sm;
endrewards

label "network_full" = sc=c&sm=c&ph=2;
label "first_queue_full" = sc=c;
label "second_queue_full" = sm=c;