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TopBackground
The first feature of the system studied in this chapter is the unreliability of the server. Queueing systems prone to failure are commonly encountered in the real world. The earliest reference on queueing systems with server breakdown that came to our attention is that of White and Christie (1958). Since then, queueing systems with unreliable servers have been extensively studied by many researchers; see Tadj, Choudhury, and Rekab (2012) for a comprehensive survey on the subject.
The next feature of the system of interest to us 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, Wu, and Zhang (2010).
Key Terms in this Chapter
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.
Server Vacation: Term used when the server is not serving the customers and is performing some secondary job.
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.
Optimal Management Policy: Refers to the selection of a best element from some set of available alternatives.
Queue: A line of waiting persons, jobs, or objects.