On the single server retrial queue subject to breakdowns
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 Aissani  and Kulkarni and Choi . 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.
Unable to display preview. Download preview PDF.
- A. Aissani, On the M/G/1/1 queueing system with repeated orders and unreliable server, J. Technology 6 (1988) 98-123 (in French).Google Scholar
- V.V. Anisimov and K.L. Atadzhanov, The diffusion approximation of systems with repeated calls, Theory Probab. Math. Statist. 44 (1992) 1-5.Google Scholar
- J.R. Artalejo, New results in retrial queueing systems with breakdown of the servers, Statistica Neerlandica 48 (1994) 23-36.Google Scholar
- J.R. Artalejo, Accessible bibliography on retrial queues, to appear in Math. Comput. Modell. (1998).Google Scholar
- J.R. Artalejo and G.I. Falin, Stochastic decomposition for retrial queues, Top 2 (1994) 329-342.Google Scholar
- G.I. Falin and J.G.C. Templeton, Retrial Queues (Chapman and Hall, London, 1997).Google Scholar
- D.P. Gaver, A waiting line with interrupted service, including priorities, J. Roy. Statist. Soc. Ser. B 24 (1962) 73-90.Google Scholar
- V.G. Kulkarni and H.M. Liang, Retrial queues revisited, in: Frontiers in Queueing, ed. J.H. Dshalalow (CRC Press, Boca Raton, FL, 1997) pp. 19-34.Google Scholar