Optimal repairable M\(^{x}\)/G/1 queue with multi-optional services and Bernoulli vacation
type: Item
instance of: scholarly article
title: Optimal repairable M\(^{x}\)/G/1 queue with multi-optional services and Bernoulli vacation
zbMATH Open document ID: 1176.90124
DOI: 10.1504/IJOR.2010.029520
author: Madhu Jain
author: Shweta Upadhyaya
published in: International Journal of Operational Research
publication date: 2009-12-07T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 5643188
zbMATH Keywords: bulk queues
zbMATH Keywords: essential services
zbMATH Keywords: generating function
zbMATH Keywords: \(N\)-policy
zbMATH Keywords: optional phase services
zbMATH Keywords: queue size
zbMATH Keywords: supplementary variables
zbMATH Keywords: unreliable servers
zbMATH Keywords: modified Bernoulli vacation schedule
zbMATH Keywords: batch arrival queueing
MaRDI profile type: Publication
full work available at URL: ijor.2010.029520
OpenAlex ID: W2133200786
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description: scientific article; zbMATH DE number 5643188