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

This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will on...

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Bibliographic Details
Published inComputation Vol. 11; no. 5; p. 89
Main Authors Liu, Tzu-Hsin, Hsu, He-Yao, Ke, Jau-Chuan, Chang, Fu-Min
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 27.04.2023
Subjects
Cost analysis
Customer services
Distribution (Probability theory)
Equilibrium
imperfect coverage
Mathematical optimization
Optimization
Preempting
preemptive priority queue
Probability
Queuing theory
Random variables
Servers
unreliable server
vacation interruption
Vacations
working vacation
Taiwan
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Summary:This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization.
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ISSN:2079-3197
2079-3197
DOI:10.3390/computation11050089