Optimal two-threshold policies in an M/G/1 queue with two vacation types

Z.G. Zhang, R.G. Vickson, M.J.A. Eenige, van

Research output: Contribution to journalArticleAcademicpeer-review

25 Citations (Scopus)

Abstract

This paper treats two-threshold policies for an M/G/1 queue with two types of generally distributed random vacations: type 1 (long) and type 2 (short) vacations. Upon returning from a vacation, the server observes the queue length. If this is less than the lower threshold, the server takes a type 1 vacation; if it is between the two thresholds, the server takes a type 2 vacation; and if it is at or above the upper threshold, the server resumes serving the queue exhaustively. There is a shutdown cost for starting a series of vacations, a linear customer waiting cost, and type-dependent vacation reward rates. Renewal theory or the PASTA property is used to develop expressions for the average queue length and the average system cost for generally distributed vacations. A search procedure, which is provably finite for exponentially distributed vacations, is developed for determining the optimal threshold values.
Original languageEnglish
Pages (from-to)63-80
JournalPerformance Evaluation
Volume29
Issue number1
DOIs
Publication statusPublished - 1997

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M/G/1 Queue
Vacation
Servers
Server
Costs
Queue Length
Policy
Renewal Theory
Threshold Value
Reward
Queue
Customers

Cite this

Zhang, Z.G. ; Vickson, R.G. ; Eenige, van, M.J.A. / Optimal two-threshold policies in an M/G/1 queue with two vacation types. In: Performance Evaluation. 1997 ; Vol. 29, No. 1. pp. 63-80.
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Optimal two-threshold policies in an M/G/1 queue with two vacation types. / Zhang, Z.G.; Vickson, R.G.; Eenige, van, M.J.A.

In: Performance Evaluation, Vol. 29, No. 1, 1997, p. 63-80.

Research output: Contribution to journalArticleAcademicpeer-review

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