Stability of a retrial queueing network with different classes of customers and restricted resource pooling

Bara Kim

doi:10.3934/jimo.2011.7.753

Article Contents

2011, Volume 7, Issue 3: 753-765. Doi: 10.3934/jimo.2011.7.753

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Stability of a retrial queueing network with different classes of customers and restricted resource pooling

Bara Kim^1,

1.
Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 136-713

Received: August 31, 2010

Revised: April 30, 2011

Published: June 2011

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Abstract

We consider a retrial queueing network with different classes of customers and several servers. Each customer class is associated with a set of servers who can serve the class of customers. Customers of each class exogenously arrive according to a Poisson process. If an exogenously arriving customer finds upon his arrival any idle server who can serve the customer class, then he begins to receive a service by one of the available servers. Otherwise he joins the retrial group, and then tries his luck again after exponential time, the mean of which is determined by his customer class. Service times of each server are assumed to have general distribution. The retrial queueing network can be represented by a Markov process, with the number of customers of each class, and the customer class and the remaining service time of each busy server. Using the fluid limit technique, we find a necessary and sufficient condition for the positive Harris recurrence of the representing Markov process. This work is the first that applies the fluid limit technique to a model with retrial phenomena.

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Mathematics Subject Classification: Primary: 60K25; Secondary: 60J25.

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