A discrete-time Geo/G/1 retrial queue with the server subject to starting failures

A discrete-time Geo/G/1 retrial queue with the server subject to starting failures

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Article ID: iaor20062932
Country: Netherlands
Volume: 141
Issue: 1
Start Page Number: 85
End Page Number: 107
Publication Date: Jan 2006
Journal: Annals of Operations Research
Authors: ,
Keywords: GI/G/1 queues
Abstract:

This paper studies a discrete-time Geo/G/1 retrial queue where the server is subject to starting failures. We analyse the Markov chain underlying the regarded queueing system and present some performance measures of the system in steady-state. Then, we give two stochastic decomposition laws and find a measure of the proximity between the system size distributions of our model and the corresponding model without retrials. We also develop a procedure for calculating the distributions of the orbit and system size as well as the marginal distributions of the orbit size when the server is idle, busy or down. Besides, we prove that the M/G/1 retrial queue with starting failures can be approximated by its discrete-time counterpart. Finally, some numerical examples show the influence of the parameters on several performance characteristics.

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