Matrix Analytic Solutions for M/M/S Retrial Queues with Impatient Customers

Abstract

In this paper, we investigate the nonhomogeneity of state space for solving retrial queues through the performance of the M/M/S retrial system with impatient customers and S servers that is modeled under quasi-birth-and-death processes with level-dependent transient rates. We derive the analytic solution of multiserver retrial queues with orbit and develop an efficient method to solve this type of systems effectively. The methods proposed are based on nonhomogeneity of the state space although this queueing model was tackled by many researchers before. Under a weaker assumption in this paper, we study and provide the exact expression based on an eigenvector approach. Constructing an efficient algorithm for the stationary probability distribution by the determination of required eigenvalues with a specific accuracy, we develop streamlined matrices of state-balanced equations with the efficient implementation for computation of the performance measures.