Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals

IF 0.7 3区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Queueing Systems Pub Date : 2023-10-07 DOI:10.1007/s11134-023-09891-x

Somya Mehra, Peter G. Taylor

引用次数: 1

Abstract

Abstract In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution.

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具有非齐次多元批泊松到达的无限服务器队列开放网络

摘要本文考虑了具有非齐次泊松过程的多元批到达的无限服务器队列开放网络的占用分布和一般服务时间分布。导出了网络暂态占用分布的概率生成函数，并证明了每批期望占用时间有限是遍历性的充分必要条件。此外，我们还恢复了瞬态概率质量函数的递归关系，该函数是通过将批大小与多项分布复合得到的分布来表示的。

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

Queueing Systems 数学-计算机：跨学科应用

CiteScore

2.30

自引率

33.30%

发文量

146

审稿时长

>12 weeks

期刊介绍： Queueing Systems: Theory and Applications (QUESTA) is a well-established journal focusing on the theory of resource sharing in a wide sense, particularly within a network context. The journal is primarily interested in probabilistic and statistical problems in this setting. QUESTA welcomes both papers addressing these issues in the context of some application and papers developing mathematical methods for their analysis. Among the latter, one would particularly quote Markov chains and processes, stationary processes, random graphs, point processes, stochastic geometry, and related fields. The prospective areas of application include, but are not restricted to production, storage and logistics, traffic and transportation, computer and communication systems.