Abstract
We consider in this paper the stability of retrial queues with a versatile retrial policy. We obtain sufficient conditions for the stability by the strong coupling convergence to a stationary ergodic regime for various models of retrial queues including a model with two types of customers, a model with breakdowns of the server, a model with negative customers, and a model with batch arrivals. For all the models considered we assume that the service times are general stationary ergodic and interarrival and retrial times are i.i.d. sequences exponentially distributed. For the model with unreliable server we also assume that the repair times are stationary and ergodic and the occurrences of breakdowns follow a Poisson process.
Highlights
We investigate in this paper the problem of stability condition for some retrial queueing models
The first model is a retrial queue with a versatile retrial policy which incorporates simultaneously the classical linear retrial policy and the constant one and is described as follows
The second model is a retrial queue with two types of arriving customers, known as “impatient” and “persistent.” If an impatient customer finds the server busy, it leaves the system
Summary
We investigate in this paper the problem of stability condition for some retrial queueing models. Aıssani 3 with the versatile retrial policy and we derive a sufficient stability condition under general assumption of stationary and ergodic service times, exponentially distributed interarrival and retrial times.
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