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

共 50 条

[41] EXACT-SOLUTIONS TO A TIME-DEPENDENT VACUUM TRANSPORT PROBLEM
HOFFMAN, N
[J]. JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, 1985, 34 (05): : 435 - 445
[42] A TIME-DEPENDENT STUDY OF THE KNOCKOUT QUEUE
Fralix, Brian
[J]. PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 2013, 27 (03) : 309 - 317
[43] Time-Dependent Analytical and Computational Study of an M/M/1 Queue with Disaster Failure and Multiple Working Vacations
Jain, Madhu
Singh, Mayank
Meena, Rakesh Kumar
[J]. MATHEMATICAL ANALYSIS AND APPLICATIONS, MAA 2020, 2021, 381 : 293 - 304
[44] EXACT-SOLUTIONS FOR TIME-DEPENDENT PHENOMENA IN QUANTUM-MECHANICS
KLEBER, M
[J]. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1994, 236 (06): : 331 - 393
[45] Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D
Cadilhe, A.
Voter, Arthur F.
[J]. JOURNAL OF CHEMICAL PHYSICS, 2018, 148 (08):
[46] Exact solutions of general time-dependent three-generator systems
Zhu, HY
Shen, JQ
[J]. ACTA PHYSICA SINICA, 2002, 51 (07) : 1448 - 1452
[47] Exact solutions to three-dimensional time-dependent Schrodinger equation
Chand, Fakir
Mishra, S. C.
[J]. PRAMANA-JOURNAL OF PHYSICS, 2007, 68 (06): : 891 - 900
[48] Exact solutions of Feinberg–Horodecki equation for time-dependent anharmonic oscillator
P K Bera
Tapas Sil
[J]. Pramana, 2013, 80 : 31 - 39
[49] Exact solutions to the supply chain equations for arbitrary, time-dependent demands
Warburton, Roger D. H.
Hodgson, J. P. E.
Nielsen, E. H.
[J]. INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS, 2014, 151 : 195 - 205
[50] EXACT-SOLUTIONS TO THE MULTIREGION TIME-DEPENDENT BIOHEAT EQUATION .1. SOLUTION DEVELOPMENT
DURKEE, JW
ANTICH, PP
LEE, CE
[J]. PHYSICS IN MEDICINE AND BIOLOGY, 1990, 35 (07): : 847 - 867

← 1 2 3 4 5 →