Busy periods of discrete-time queues using the Lagrange implicit function theorem

被引：1

作者：

Brown, Geoffrey W. ^{[1
]}

Balakrishnan, Narayanaswamy ^{[1
]}

机构：

[1] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

来源：

OPERATIONS RESEARCH LETTERS | 2021年 / 49卷 / 05期

基金：

欧盟地平线“2020”;

关键词：

Lagrange implicit function theorem; Discrete-time queues; Busy periods; Computational methods;

D O I：

10.1016/j.orl.2021.06.014

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：

In this paper, we study the busy-period distribution for discrete-time queues assuming a Bernoulli arrival process, with arbitrary service-time and batch-arrival distributions. We derive explicit analytic formulas for these distributions using the Lagrange Implicit Function Theorem applied to probability generating functions. The convenient coefficient operator notation used in these formulas leads to a computationally efficient method for obtaining the distributions in their entirety from these analytic formulas. (C) 2021 Elsevier B.V. All rights reserved.

引用

页码：650 / 654

页数：5

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