Analysis of Two Phases Queue With Vacations and Breakdowns Under T-Policy

Analysis of Two Phases Queue With Vacations and Breakdowns Under T-Policy

Khalid Alnowibet (King Saud University, Saudi Arabia) and Lotfi Tadj (Fairleigh Dickinson University, Canada)
Copyright: © 2018 |Pages: 14
DOI: 10.4018/978-1-5225-2255-3.ch136

Abstract

The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. We assume the possibility that the server may take a vacation at the end of a given service completion. The server resumes operation according to T-policy to check if enough customers have arrived while he was away. The actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. A Markov chain approach is used to obtain the steady state system size probabilities and different performance measures. The optimal value of the threshold level is obtained analytically.
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Background

The unreliability of the server is one of the main features of the queueing system studied in this chapter. Queueing systems prone to failure are commonly encountered in the real world. The server breakdown was first analyzed by White and Christie (1958). Since then, queueing systems with unreliable servers have been extensively studied by many researchers; see Tadj et al. (2012) for a comprehensive survey on the subject.

The next feature of the system of interest in this chapter is the Bernoulli vacation schedule. The classical vacation scheme with Bernoulli service discipline was introduced and developed by Keilson and Servi (1986). Various aspects of Bernoulli vacation models have been discussed by a number of authors; see the survey of Ke et al. (2010).

Key Terms in this Chapter

Optimal Management Policy: Refers to the selection of a best element from some set of available alternatives.

Server Vacation: Term used when the server is not serving the customers and is performing some secondary job.

Queueing System: Consists of three major components: (1) the source population and the way customers arrive to the system, (2) the serving systems, and (3) how customers exit the system.

T-Policy: A service discipline specifying that, when the system is empty, the server takes vacations of fixed length T, as long as no customers arrive to the system.

Unreliable Server: A server that can breakdown while providing service, and become unavailable to customers.

Bernoulli Vacation Schedule: Service discipline specifying that, at the end of a service, the server may either take a vacation or serve the next customer.

Queue: A line of waiting persons, jobs, or objects.

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