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.
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页码：147 / 155
页数：9
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