Rapid, efficient analysis of the λ(n)/Ck/r/N queue, with application to decomposition of closed queuing networks

In this paper, we exploit advances in computational linear algebra and computing power to solve for the stationary probability vector of the related continuous time Markov chain (CTMC) of a λ(n)/Ck/r/N queue. The insights gained from studying the transition rate matrix of this chain are used to develop a list of candidate solution methods, each of which is used to calculate stationary probabilities for a set of 46 representative large-dimension problems. Based on this computational experience, a preferred solution approach for this type of CTMC is proposed. The effectiveness of the solution approach is demonstrated by using Marie's method to decompose four queuing networks containing stations with multiple k-phase Coxian servers.