Sensitivity analysis of an M/G/1 retrial queueing system with disaster under working vacations and working breakdowns

P. Rajadurai

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Advanced Queuing Theory Analysis Reliability and Maintenance Optimization Age of Information Optimization

Abstract

This paper deals with the new type of retrial queueing system with working vacations and working breakdowns. The system may become defective by disasters at any point of time when the regular busy server is in operation. The occurrence of disasters forces all customers to leave the system and causes the main server to fail. At a failure instant, the main server is sent to the repair and the repair period immediately begins. As soon as the orbit becomes empty at regular service completion instant or disaster occurs in the regular busy server, the server goes for a working vacation and working breakdown (called lower speed service period). During this period, the server works at a lower service rate to arriving customers. Using the supplementary variable technique, we analyze the steady state probability generating function of system size. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.

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References

2008Retrial Queueing Systems 2002M/M/1 queues with working vacations (M/M/1/WV)2010Accessible bibliography on retrial queues: Progress in 2000–2009 2005M/G/1 queue with multiple working vacations 1999Stochastic analysis of a single server retrial queue with general retrial times 2015Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns 2012A queue with working breakdowns 2013The M/G/1 queue with disasters and working breakdowns

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2019Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)2020Bernoulli vacation model for M X /G/ 1 unreliable server retrial queue with bernoulli feedback, balking and optional service 2020On retrial queue with customer balking and feedback subject to server breakdowns

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