Calculating equilibrium probabilities for &lgr;(n)/Ck/1/N queues

Abstract

Equilibrium state distributions are determined for queues with load-dependent Poisson arrivals and service time distributions representable by Cox's generalized method of stages. The solution is obtained by identifying a birth-death process that has the same equilibrium state distribution as the original queue. Special cases of two-stage (C2) and Erlang-k (Ek) service processes permit particularly efficient algorithms for calculating the load - dependent service rates of the birth-death process corresponding to the original queue. Knowing the parameters of the birth-death process, the equilibrium state probabilities can be calculated straight-forwardly. This technique is particularly useful when subsystems are reduced to flow-equivalent servers representing the complementary network.