Analysis of an unreliable repeated service queue with delayed repair under randomized vacation policy

• Published in: Communications in statistics. Theory and methods Vol. 48; no. 21; pp. 5336 - 5369
• Main Authors: Kalita, Chandi Ram, Choudhury, Gautam
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.11.2019; Taylor & Francis Ltd
• Subjects: Customer services; Customers; elapsed times; Poisson density functions; Queues; Queuing theory; Randomization; randomized vacation and cost effectiveness; remaining times; Repair; repeated service; Two types of service; Vacations
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2018.1513142

In this article we consider an unreliable M X /G/1 queue with two types of general heterogeneous service and optional repeated service subject to server's break down and delayed repair under randomized vacation policy. We assume that customer arrive to the system according to a compound Poisson process. The server provides two types of general heterogeneous service and a customer can choose either type of service before its service start. After the completion of either type of service, the customer has the further option to repeat the same type of service once again. While the server is working with any types of service or repeated service, it may breakdown at any instant. Further the concept of randomized vacation is also introduced. For this model, we first derive the joint distribution of state of the server and queue size by considering both elapsed and remaining time, which is one of the objective of this article. Next, we derive Laplace Stieltjes transform of busy period distribution. Finally, we obtain some important performance measure and reliability indices of this model.