Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-09-03 DOI:10.1155/2019/6480139

M. Chaudhry, James J. Kim, A. Banik

引用次数: 5

Abstract

A simple solution to determine the distributions of queue-lengths at different observation epochs for the model GIX/Geo/c is presented. In the past, various discrete-time queueing models, particularly the multiserver bulk-arrival queues, have been solved using complicated methods that lead to incomplete results. The purpose of this paper is to use the roots method to solve the model GIX/Geo/c that leads to a result that is analytically elegant and computationally efficient. This method works well even for the case when the inter-batch-arrival times follow heavy-tailed distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue-lengths at different time epochs.

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GIX/Geo/c队列的简单解析和高效计算结果

给出了一种确定模型GIX/Geo/c在不同观测时段的排队长度分布的简单解。在过去，各种离散时间队列模型，特别是多服务器批量到达队列，一直使用复杂的方法来解决，导致结果不完整。本文的目的是使用根法求解模型GIX/Geo/c，从而得到解析优雅且计算效率高的结果。这种方法即使在批间到达时间遵循重尾分布的情况下也能很好地工作。底层特征方程的根构成了不同时间点上所有队列长度分布的基础。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.