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

Abstract

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.

Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation

“…Bouchentouf et al [26] have investigated finite capacity Markovian queues with different WV. Liu et al [27] have presented the Markovian queue with preemptive priority and WV interruption. Yang [28] has established the retrial queue with WVs together with the starting fail server.…”

Maximum Entropy Solution for M^X/G/1 Priority Reiterate G-queue Under Working Breakdown and Working Vacation

“…As a result, a working malfunction service is a more suitable repair policy to waiting framework that are unreliable. For further study go through the references Yang et al (2002), Ke et al (2009), Dimitriou and Langaris (2010), Choudhury and Tadj (2011), Choudhury and Ke (2012), Dimitriou (2013) and recent references include Vijayalakshmi et al (2021), Seenivasan and Abinaya (2022), Liu et al (2023).…”