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
收藏
页码：692 / 695
页数：4
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