Exact time-dependent solutions for the M/D/1 queue

被引：2

作者：

Baek, Jung Woo ^{[1
]}

Lee, Ho Woo ^{[2
]}

Ahn, Soohan ^{[3
]}

Bae, Yun Han ^{[4
]}

机构：

[1] Chosun Univ, Dept Ind Engn, Gwangju, South Korea

[2] Sungkyunkwan Univ, Dept Syst Management Engn, Suwon, South Korea

[3] Univ Seoul, Dept Stat, Seoul, South Korea

[4] Sangmyung Univ, Dept Math Educ, Seoul, South Korea

来源：

OPERATIONS RESEARCH LETTERS | 2016年 / 44卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

M/D/1; queue; Time-dependent queue length probability; Time-dependent waiting time distribution; Closed-form solution; TRANSIENT SOLUTION; BUSY PERIOD; FORMULA;

D O I：

10.1016/j.orl.2016.08.003

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Time-dependent solutions to queuing models are very useful for evaluating the performance of real-world systems. However, because of their mathematical complexity, few available results exist. In this paper, we derive the time-dependent performance measures for an M/D/1 queue starting with a positive number of initial customers. Using the limiting property of an Erlang distribution, we obtain closed-form time dependent formulas for the queue length and the waiting time. Furthermore, the time-dependent queue length probability in a busy period is derived. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：692 / 695

页数：4

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