AN M/G/1 RETRIAL QUEUE WITH GENERAL RETRIAL TIMES, WORKING VACATIONS AND VACATION INTERRUPTION

Shan Gao · Jinting Wang · Wei Wayne Li

45 citations0/0 files storedAsia Pacific Journal of Operational Research

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

We consider an M/G/1 retrial queue with general retrial times, and introduce working vacations and vacation interruption policy into the retrial queue. During the working vacation period, customers can be served at a lower rate. If there are customers in the system at a service completion instant, the vacation will be interrupted and the server will come back to the normal working level. Using supplementary variable method, we obtain the stationary probability distribution and some performance measures. Furthermore, we carry out the waiting time distribution and prove the conditional stochastic decomposition for the queue length in orbit. Finally, some numerical examples are presented.

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References

1986Queueing systems with vacations ? A survey 1990A survey of retrial queues 1999A classified bibliography of research on retrial queues: Progress in 1990–1999 2010Accessible bibliography on retrial queues: Progress in 2000–2009 2010Recent Developments in Vacation Queueing Models : A Short Survey 1999Stochastic analysis of a single server retrial queue with general retrial times 2002Standard and retrial queueing systems: a comparative analysis 1990Single line queue with repeated demands

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2017A survey on queues in machining system: Progress from 2010 to 2017 2019Performance Analysis of Preemptive Priority Retrial Queueing System with Disaster under Working Breakdown Services 2019Admission control for finite capacity queueing model with general retrial times and state-dependent rates 2016Analysis of an unreliable retrial G-queue with working vacations and vacation interruption under Bernoulli schedule 2018An M/G/1 retrial queue with balking customers and Bernoulli working vacation interruption

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