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

Authors:
S. A. Dudin
Affiliations:
Belarusian State University, Minsk, Russia
Venue:
Problems of Information Transmission
Year:
2009

Citing 4
Cited 1

Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory

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Mathematical and Computer Modelling: An International Journal

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MACOM'10 Proceedings of the Third international conference on Multiple access communications

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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.