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On a switch-over policy for controlling the workload in a queueing system with two constant service rates and fixed switch-over costs

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Summary

This paper considers a single-server system where jobs arrive in accordance with a Poisson process. Each job involves an amount of work which is known upon arrival and is sampled from an exponential distribution. The server has available two constant service rates 1 and 2 where rate 2 is faster than rate 1. The total work remaining to be processed in the system (= workload) is controlled by a switch-over policy which switches from rate 1 to rate 2 only when the workload exceeds the levely 1 and switches from rate 2 to rate 1 only when the workload falls to the levely 2 where 0⩽y 2⩽y 1. The costs of this system consist of a linear holding cost, a service-cost rate and fixed switch-over costs. The purpose of this paper is to derive an explicit expression for the average cost of this policy.

Zusammenfassung

Es wird ein einzelner Bedienungskanal betrachtet, bei dem die Belastungen gemäß einem Poisson-Prozeß eintreffen und unabhängig voneinander dieselbe Exponentialverteilung besitzen. Der Bedienungskanal verfügt über zwei verschiedene konstante Bedienungsraten. Wenn die Gesamtbelastung über einen vorgegebenen Werty 1 steigt, so wird von der kleineren auf die größere Bedienungsrate umgeschaltet. Auf die kleinere Bedienungsrate wird zurückgeschaltet, wenn die Gesamtbelastung unter den vorgegebenen Werty 1 fällt, wobei 0⩽y 2⩽y 1 sei. Jedes Umschalten von einer Bedienungsrate auf die andere verursache fixe Kosten. Außerdem entstehen Kosten pro Zeiteinheit für die Bedienung und die Gesamtbelastung.

Die Bedienungskostenrate hängt von der jeweiligen verwendeten Bedienungsrate ab während die durch die Belastung bedingte Kostenrateproportional zur Gesamtbelastung ist. Der Zweck der Arbeit ist die Angabe eines expliziten Ausdrucks für die entstehenden durchschnittlichen Gesamtkosten.

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Authors and Affiliations

  1. Department of Operations Research, Mathematisch Centrum, Amsterdam 2e Boerhavestraat 49, 1005, Amsterdam

    H. C. Tijms

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  1. H. C. Tijms
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This paper is registered as Mathematical Centre Report BW 45/75

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Tijms, H.C. On a switch-over policy for controlling the workload in a queueing system with two constant service rates and fixed switch-over costs. Zeitschrift für Operations Research 21, 19–32 (1977). https://doi.org/10.1007/BF01918455

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  • DOI: https://doi.org/10.1007/BF01918455

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