This article is cited in 12 papers

Communication Network Theory

The $MAP/M/N$ retrial queueing system with time-phased batch arrivals

S. A. Dudin

Belarusian State University, Minsk

Abstract: We consider a retrial queueing system with batch arrival of customers. Unlike standard batch arrival, where a whole batch enters the system simultaneously, we assume that customers of a batch (session) arrive one by one in exponentially distributed time intervals. Service time is exponentially distributed. The batch arrival flow is MAP. The number of customers in a session is geometrically distributed. The number of sessions that can enter the system simultaneously is a control parameter. We analyze the joint probability distribution of the number of sessions and customers in the system using the techniques of multidimensional asymptotically quasi-Toeplitz Markov chains.

UDC: 621.391.71+519.2

Received: 12.11.2008
Revised: 25.04.2009

 English version: Problems of Information Transmission, 2009, 45:3, 270–281

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