State Dependence in M / G /1 Server-Vacation Models

Carl M. Harris and William G. Marchal
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Carl M. Harris: George Mason University, Fairfax, Virginia
William G. Marchal: University of Toledo, Toledo, Ohio

Operations Research, 1988, vol. 36, issue 4, 560-565

Abstract: This paper examines a generalization of the exhaustive and one-at-a-time-discipline M / G /1 server vacation models. This alternative model is viewed as a state-dependent (nonvacation) M / G /1 queue in which the original service times are extended to include a (possibly zero length) state-dependent vacation after each service. Such a vacation policy permits greater flexibility in modeling real problems, and does, in fact, subsume most prior M / G /1 approaches. This device reveals a fundamental decomposition somewhat like that previously established for the classical vacation disciplines. In addition, necessary and sufficient conditions for system ergodicity are established for the state-dependent vacation policy, and some comments are offered on computations.

Keywords: queues: server-vacation queues; queues; cyclic: single-server decomposition; queues; nonstationary: state-dependent (search for similar items in EconPapers)
Date: 1988
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