An \(M/G/1\) retrial queue with active breakdowns and Bernoulli schedule in the server. (English) Zbl 1118.90035

Atencia, Ivan; Fortes, Inmaculada; Moreno, Pilar; Sánchez, Sixto

Int. J. Inf. Manage. Sci. 17, No. 1, 1-17 (2006).

Summary: This paper analyses a retrial queue with active breakdowns where the customer being served during the failure decides, with probability \(q\in(0,1]\), to join the orbit (impatient customer) and, with complementary probability \(p\), to remain in the server for the repair in order to conclude his remaining service (patient customer). Both service and repair times are assumed to have a general distribution. We consider two variants of the model in accordance with the discipline to access to the server from the orbit. Firstly, all the repeated customers apply at a fixed rate (classical retrial policy). Secondly, repeated customers are discouraged and reduce their retrial rate as more customers join the orbit (constant retrial policy). We find various characteristic quantities of these queueing systems.

MSC:

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

Keywords:

impatient and patient customers; retrial queues; steady-state distribution; stochastic decomposition; unreliable server