Optimal repairable Mx/G/1 queue with multi-optional services and Bernoulli vacation

Madhu Jain · Shweta Upadhyaya

22 citations0/0 files storedInternational Journal of Operational Research

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

Abstract

This article deals with the modified Bernoulli vacation schedule for the unreliable server batch arrival queueing system with essential and multi-optional services under N-policy. The server is subject to breakdown while rendering service to the customers. At the completion of service of the customer, the server has the option to take a vacation or to remain idle in the system waiting for the next customer to arrive. The server follows N-policy, i.e. the server will not initiate the service until the queue size reaches or exceeds N. All customers demand for the first 'essential' service whereas only some of them demand for other 'optional' services. After getting first essential service, the customer may demand for the second optional phase service with some probability; if the customer completes its second optional phase service, he may demand for the next optional phase services with some other probabilities and so on. We derive the system size distribution at random points and at departure points and other performance indices by employing generating function and supplementary variable techniques. By taking numerical illustration, the sensitivity analysis is also conducted to determine the effects of the system parameters on various performance measures.

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References

1986Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules 2001Reliability Analysis of the Retrial Queue with Server Breakdowns and Repairs 2000An M/G/1 queue with second optional service 2002A Single Server Poisson Input Queue with a Second Optional Channel 2002An M/G/1 Retrial Queueing System with Two-Phase Service and Preemptive Resume 2005A two-stage batch arrival queueing system with a modified bernoulli schedule vacation under N-policy 2004A single-server retrial queue with general retrial times and Bernoulli schedule 2006A Batch Arrival Queue with a Second Optional Service Channel UnderN-Policy

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2012A two-phase quorum queueing system with Bernoulli vacation schedule, setup, and N-policy for an unreliable server with delaying repair 2014Analysis of M[X]/G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown 2021Particle Swarm Optimization and Maximum Entropy Results for MX/G/1 Retrial G-Queue with Delayed Repair 2015Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation

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