An M[X]/G/1 retrial queue with server breakdowns and constant rate of repeated attempts

An M[X]/G/1 retrial queue with server breakdowns and constant rate of repeated attempts

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Article ID: iaor2009700
Country: Netherlands
Volume: 157
Issue: 1
Start Page Number: 225
End Page Number: 243
Publication Date: Jan 2008
Journal: Annals of Operations Research
Authors: , ,
Keywords: markov processes
Abstract:

We consider an M[X]/G/1 retrial queue subject to breakdowns where the retrial time is exponential and independent of the number of customers applying for service. If a coming batch of customers finds the server idle, one of the arriving customers begins his service immediately and the rest joins a retrial group (called orbit) to repeat his request later; otherwise, if the server is busy or down, all customers of the coming batch enter the orbit. It is assumed that the server has a constant failure rate and arbitrary repair time distribution. We study the ergodicity of the embedded Markov chain, its stationary distribution and the joint distribution of the server state and the orbit size in steady-state.

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