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An improved truncation technique to analyze a \(Geo/PH/1\) retrial queue with impatient customers. (English) Zbl 1348.90202

Summary: 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.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)

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