Calculating joint queue length moments with RECAL

RECAL is a new algorithm for solving closed, product form queueing networks. For networks with many chains, each chain having only a relatively few jobs, RECAL is one of the most, if not the most, computationally efficient algorithms currently available. It had been noted earlier that RECAL can be interpreted as recurrence relations between joint mean values of queue lengths. The purpose of this paper is to exploit this fact and show that RECAL yields joint mean queue lengths almost as a by-product of calculating the partition function. The explicit details of calculating higher order, joint mean queue lengths are given, and the computational complexity of the algorithm is described.