# copyright Barry L. Nelson and Michael R. Taaffe 2001

with(linalg):

MapPhInfMCNSymbolic := proc(A, vA, lambda, R, B, mu, K, Pr)

#
# this procedure returns a symbolic representation
# of the first and second moment differential
# equations for a [Map_t/Ph_t/Infinity]^K network 
# with R different arrival processes 
# 
# initial conditions for the queue are empty and idle
#
# this version is designed to work with Maple V release 5
#              
# last update 1/26/01
#
# Inputs:
# A = Markov chain transition matrix for the arrival process
#     [vector of matrices of dimension R]
# vA = number of absorbing states in Map representation
#     [vector of numbers of dimension R]
# lambda = arrival rate vector
#     [vector of vectors of dimension R]
# R = number of distinct Ph arrival processes
# B = Markov chain transition matrix for the service process
#     [vector of matrices of dimension K]
# mu = service rate vector
#     [vector of vectors of dimension K]
# Pr = Markov routing probabilities
#

	local r, deq, initial, temp;
	if R = 1 then
	   RETURN(MapPhInfNetSymbolic(A, vA, lambda, B, mu, K, Pr));
	else
	   deq := vector(R);
	   temp := MapPhInfNetSymbolic(A[1], vA[1], lambda[1], B, mu, K, Pr[1]);
	   deq[1] := temp;
	   for r from 2 to R do
	      temp := MapPhInfNetSymbolic(A[r], vA[r], lambda[r], B, mu, K, Pr[r]);
	      deq[r] := temp;
	   od;
	   RETURN(deq);
	fi;

	end;