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

  • Yingyuan Wei EMAIL logo , Yinghui Tang and Miaomiao Yu
Published/Copyright: September 3, 2020
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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.


Supported by the National Natural Science Foundation of China (71571127)


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Received: 2018-12-20
Accepted: 2019-03-29
Published Online: 2020-09-03
Published in Print: 2020-08-26

© 2020 Walter De Gruyter GmbH, Berlin/Boston

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