An improved truncation technique to analyze a Geo/PH/1 retrial queue with impatient customers

Abstract

This paper considers a discrete-time retrial queue with impatient customers. We establish the global balance equations of the Markov chain describing the system evolution and prove that this queueing system is stable as long as the customers are strict impatient and the mean retrial time is finite. Direct truncation with matrix decomposition is used to approximate the steady-state distribution of the system state and hence derive a set of performance measures. The proposed matrix decomposition scheme is presented in a general form which is applicable to any finite Markov chain of the GI/M/1-type. It represents a generalization of the Gaver–Jacobs–Latouche's algorithm that deals with QBD process. Different sets of numerical results are presented to test the efficiency of this technique compared to the generalized truncation one. Moreover, an emphasis is put on the effect of impatience on the main performance measures.