On the single server retrial queue subject to breakdowns. (English) Zbl 0918.90073

Summary: This paper deals with a single server retrial queueing system subject to active and independent breakdowns. The objective is to extend the results given independently by the first author [J. Technology 6, 98-123 (1988)] and V. G. Kulkarni and B. D. Choi [Queuing Syst. 7, No. 2, 191-208 (1990; Zbl 0727.60110)]. To this end, we introduce the concept of fundamental server period and an auxiliary queueing system with breakdowns and option for leaving the system. Then, we concentrate our attention on the limiting distribution of the system state. We obtain simplified expressions for the partial generating functions of the server state and the number of customers in the retrial group, a recursive scheme for computing the limiting probabilities and closed-form formulae for the second-order partial moments. Some stochastic decomposition results are also investigated.


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


Zbl 0727.60110
Full Text: DOI