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Recursive Solution of Queue Length Distribution for Geo/G/1 Queue with Delayed Min(N, D)-Policy

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  • Wei Yingyuan

    (School of Mathematics & Statistics, Hexi University, Zhangye, 734000, China)

  • Tang Yinghui

    (School of Mathematics Science, Sichuan Normal University, Chengdu, 610068, China)

  • Yu Miaomiao

    (School of Science, Sichuan University of Science and Engineering, Zigong, 643000, China)

Abstract

In this paper we consider a discrete-time Geo/G/1 queue with delayed Min(N, D)-policy. Using renewal process theory, total probability decomposition technique and z-transform, we study the transient and equilibrium properties of the queue length from an arbitrary initial state, and obtain both the recursive expressions of the transient state queue length distribution and the steady state queue length distribution at arbitrary time epoch n+. Furthermore, we derive the important relations between equilibrium queue length distributions at different time epochs n–, n and n+. Finally, we give some numerical examples about capacity decision in queueing systems to demonstrate the application of the analytical results reported in this paper.

Suggested Citation

  • Wei Yingyuan & Tang Yinghui & Yu Miaomiao, 2020. "Recursive Solution of Queue Length Distribution for Geo/G/1 Queue with Delayed Min(N, D)-Policy," Journal of Systems Science and Information, De Gruyter, vol. 8(4), pages 367-386, August.
    • Handle: RePEc:bpj:jossai:v:8:y:2020:i:4:p:367-386:n:6
    DOI: 10.21078/JSSI-2020-367-20
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    References listed on IDEAS

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    1. K. R. Balachandran, 1973. "Control Policies for a Single Server System," Management Science, INFORMS, vol. 19(9), pages 1013-1018, May.
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