Exact waiting time and queue size distributions for equilibrium M/G/1 queues with Pareto service

被引：12

作者：

Ramsay, Colin M. ^{[1
]}

机构：

[1] Univ Nebraska, Dept Finance, Lincoln, NE 68588 USA

来源：

QUEUEING SYSTEMS | 2007年 / 57卷 / 04期

关键词：

Laplace transform; Kummer function; generalized exponential integral; steady-state queue; Pollaczek-Khinchin formula; power-tail; heavy-tail; heavy traffic;

D O I：

10.1007/s11134-007-9052-7

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper solves the problem of finding exact formulas for the waiting time cdf and queue length distribution of first-in-first-out M/G/1 queues in equilibrium with Pareto service. The formulas derived are new and are obtained by directly inverting the relevant Pollaczek-Khinchin formula and involve single integrals of non-oscillating real valued functions along the positive real line. Tables of waiting time and queue length probabilities are provided for certain parameter values under heavy traffic conditions.

引用

页码：147 / 155

页数：9

共 50 条

[1] Exact waiting time and queue size distributions for equilibrium M/G/1 queues with Pareto service
Colin M. Ramsay
Queueing Systems, 2007, 57 : 147 - 155
[2] Optimal Service Time Distribution for an M/G/1 Waiting Queue
Lefebvre, Mario
Yaghoubi, Roozbeh
AXIOMS, 2024, 13 (09)
[3] CHARACTERIZATIONS OF EQUILIBRIUM QUEUE LENGTH DISTRIBUTIONS IN M/GI/1 QUEUES
REGO, V
COMPUTERS & OPERATIONS RESEARCH, 1988, 15 (01) : 7 - 17
[4] Waiting time distributions in an M/G/1 retrial queue with two classes of customers
Kim, Bara
Kim, Jeongsim
ANNALS OF OPERATIONS RESEARCH, 2017, 252 (01) : 121 - 134
[5] Waiting time distributions in an M/G/1 retrial queue with two classes of customers
Bara Kim
Jeongsim Kim
Annals of Operations Research, 2017, 252 : 121 - 134
[6] EQUILIBRIUM QUEUE SIZE DISTRIBUTIONS FOR SEMI-REVERSIBLE QUEUES
FAKINOS, D
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1990, 36 (02) : 331 - 337
[7] ALGORITHMS FOR WAITING-TIME DISTRIBUTIONS UNDER VARIOUS QUEUE DISCIPLINES IN M/G/1 QUEUE WITH A SERVICE-TIME DISTRIBUTION OF PHASE TYPE
NEUTS, MF
ADVANCES IN APPLIED PROBABILITY, 1976, 8 (02) : 252 - 252
[8] WAITING TIME CONVEXITY IN THE M/G/1 QUEUE
JAGERMAN, DL
AT&T TECHNICAL JOURNAL, 1985, 64 (01): : 33 - 41
[9] A new approach to the queue length and waiting time of BMAP/G/1 queues
Lee, HW
Park, NI
Jeon, J
COMPUTERS & OPERATIONS RESEARCH, 2003, 30 (13) : 2021 - 2045
[10] 2-SIDED INEQUALITIES FOR WAITING TIME AND QUEUE SIZE DISTRIBUTIONS IN GI/G/1
DALEY, DJ
MORAN, PAP
THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1968, 13 (02): : 338 - &

← 1 2 3 4 5 →