Analysis of theN-policy GI/M/1/K Queueing Systems with Working Breakdowns and Repairs

Dong‐Yuh Yang · Yi-Chun Cho

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

Abstract

In this paper, we present an algorithmic approach to the analysis of the finite-capacity GI/M/1 queue with working breakdowns under N-policy. When there are no customers in the system, the server is turned off. If the number of customers in the system reaches threshold N, then the server is turned on and working. The recently introduced working breakdown involves serving newly arrived customers at a lower service rate in cases where the server breaks down. Service times during busy and breakdown periods are exponentially distributed. When a breakdown occurs, the failed server is not repaired until there are no customers remaining in the system. In this type of queueing system, we compute the steady-state probabilities at arbitrary and pre-arrival epochs using the supplementary variable method. We propose an algorithm for computing the steady-state probabilities at pre-arrival epochs and develop system performance measures. Finally, numerical analysis is used to evaluate the effects of various system parameters on system performance measures.

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References

1963Queueing Systems with a Removable Service Station 2005Optimal design and control of queues 2006On the GI/M/1/N queue with multiple working vacations—analytic analysis and computation 2015Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns 2012A queue with working breakdowns 2016Strategic behavior and social optimization in a constant retrial queue with the N -policy 2013The M/G/1 queue with disasters and working breakdowns 2000A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity

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2023Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

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