On the M/G/1 retrial queue with batch arrivals and impatience phenomenon

Queueing systems in which arriving customers who find all servers and waiting positions occupied may retry for service after a period of time are called retrial queues or queues with repeated orders [3]. These models arise in the analysis of different communication systems [1]. In this work, we consider an M/G/1 retrial queue with batch arrivals and impatient customers. By using the method of supplementary variables, we find the partial generating functions of the steady state joint distribution of the server state and the number of customers in retrial group. The obtained results permit us to obtain some performance measures (the mean number of customers in retrial group, the mean number of customers in the system, …). To complete the analysis of the considered model, we find the steady state distribution of the embedded Markov chain. As mentioned in literature [2], for the M/G/1 retrial queue with single arrivals, we have that the steady state distribution of the number of customers in the system is identical to the one of the embedded Markov chain, but for the case of batch arrivals and also of impatient customers, this is not so.

Keywords: retrial queue, embedded Markov chain, batch arrival, impatient customer, steady state distribution

[1] J.R. Artalejo and A. Gomez-Corral. Retrial Queueing Systems. A Computational Approach. Springer, 2008.
[2] G.I. Falin and J.G.C. Templeton. Retrial Queues. Chapman and Hall, 1997.
[3] T.Yang and J.G.C. Templeton. A survey on retrial queues. Queueing Systems 2, 201-233, 1987.

Joint work with K. Nawel Arrar (Department of Mathematics, University of Annaba, Algeria).