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)
DOI: 10.4018/978-1-5225-7766-9.ch002


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. The authors 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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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).

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