Matrix-geometric solution of a multiserver queue with Markovian group arrivals and coxian servers

摘要

A matrix-geometric solution for the M[x]/C2/S queue is presented. Though the basic structure of the underlying Markov chain is of M/G/1 type, the assumption of bounded group arrivals allows, after a suitable aggregation of states is made and the infinitesimal generator of the resulting process becomes of Quasi-Birth-Death process type, a matrix-geometric solution of the stationary probability vector. The solution is basically based on the calculation of a matrix R the unique non-negative solution of a quadratic matrix equation that is obtained by successive iteration. We obtain analytic expressions for the mean number of customers, the mean queue length, and their second moments as well.