An M/G/1 retrial queue with balking and retrials during service

Xiaoyong Wu · Percy H. Brill · Myron Hlynka · Jinting Wang

37 citations0/0 files storedInternational Journal of Operational Research

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Advanced Queuing Theory Analysis Customer Service Quality and Loyalty Age of Information Optimization

Abstract

We consider an M/G/1 retrial queue with general retrial times. Customers may balk or renege at particular times. The server is subject to breakdown (with repairs). While the server is being repaired, the customer in service can either remain in the service position or leave and return, while maintaining its rights to the server. We find a stability condition for this system. In the steady state, the joint distribution of the server state and queue length is obtained, leading to useful measures of the system, such as the probability of an empty system, the mean number of customers in the retrial queue and the expected retrial time.

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References

1997Retrial Queues 1999Accessible bibliography on retrial queues 1999A classified bibliography of research on retrial queues: Progress in 1990–1999 2001Reliability Analysis of the Retrial Queue with Server Breakdowns and Repairs 1999Stochastic analysis of a single server retrial queue with general retrial times 1990Single line queue with repeated demands 2002The M/G/1 retrial queue with Bernoulli schedules and general retrial times 2004A Discrete-Time Geo /G/1 Retrial Queue with General Retrial Times

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2016Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers 2009AN M / G /1 RETRIAL QUEUE WITH UNRELIABLE SERVER FOR STREAMING MULTIMEDIA APPLICATIONS 2019Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)2014Optimization of an M/M/1/N feedback queue with retention of reneged customers 2017Analysis of M/G/1 retrial queues with second optional service and customer balking under two types of Bernoulli vacation schedule

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