Regularly varying tail of the waiting time distribution in M/G/1 retrial queue

Authors:
Jerim Kim;Jeongsim Kim;Bara Kim
Affiliations:
Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Seoul, Korea 136-701;Department of Mathematics Education, Chungbuk National University, Cheongju, Chungbuk, Korea 361-763;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Seoul, Korea 136-701
Venue:
Queueing Systems: Theory and Applications
Year:
2010

Citing 9
Cited 2

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A survey of retrial queues

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Appendix: A primer on heavy-tailed distributions

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Waiting Time Asymptotics in the Single Server Queue with Service in Random Order

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Tail asymptotics for the queue length in an M/G/1 retrial queue

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Tail asymptotics for the fundamental period in the MAP/G/1 queue

Queueing Systems: Theory and Applications
Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue

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Accessible bibliography on retrial queues

Mathematical and Computer Modelling: An International Journal
Accessible bibliography on retrial queues: Progress in 2000-2009

Mathematical and Computer Modelling: An International Journal

Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue

Queueing Systems: Theory and Applications
Tail asymptotics of the queue size distribution in the M/M/m retrial queue

Journal of Computational and Applied Mathematics

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Abstract

We consider an M/G/1 retrial queue where the service time distribution has a regularly varying tail with index 驴β, β1. The waiting time distribution is shown to have a regularly varying tail with index 1驴β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue with random order service policy.