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

Wei Yingyuan (), Tang Yinghui () and Yu Miaomiao ()
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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

Journal of Systems Science and Information, 2020, vol. 8, issue 4, 367-386

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.

Keywords: delayed Min(N; D)-policy discrete-time queue; total probability decomposition technique; z-transform; queue length distribution; system capacity optimum design (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/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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