Series expansion techniques for fast evaluation of acyclic finite-capacity queueing networks

An efficient numerical evaluation technique is presented for families of finite Markov chains indexed by a parameter e, that possess a monotonicity property for the chain at e = 0. The monotonicity allows for retrieving the series expansion of the steady state solution in e = 0 in O(NM) operations, where N is the size of the state space and M is the number of terms in the series expansion. We then apply the method to a layered queueing network with four queues, three queues in tandem and one queue for the servers operating this tandem queue.