Performance analysis for Bernoulli feedback queues subject to disasters: a system with batch Poisson arrivals under a multiple vacation policy

IF 2.3 2区工程技术 Q3 ENGINEERING, INDUSTRIAL

Quality Technology and Quantitative Management Pub Date : 2022-07-22 DOI:10.1080/16843703.2022.2092954

George C. Mytalas, M. Zazanis

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引用次数: 2

Abstract

ABSTRACT We analyze an M/G/1 system with batch Poisson arrivals and instantaneous Bernoulli feedback, operating under a Multiple Vacation Policy. The system is subject to disasters that occur according to an independent Poisson process and are followed by (random) repair periods with general distribution. The analysis is carried out using the supplementary variable method. The Laplace transform of the time between two consecutive disasters is obtained and the existence of the stationary regime for the system is shown. Besides obtaining the stationary distribution for the number of customers in the system, we use the information regarding the rates of occurrence of various events provided by the supplementary variable solution to obtain a great variety of additional results. These include the Laplace transform of the busy period distribution and the probability that a customer completes service. We indicate areas of application of our model to real-life systems, in particular in Vehicle ad hoc Networks (VANETs), and we use the analytic results obtained to optimize such a system under a Quality of Service constraint. Finally, we analyze a variant of the system subject to disasters even when the server is not busy.

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灾难条件下伯努利反馈队列的性能分析:多假期策略下的批泊松到达系统

摘要我们分析了一个M/G/1系统，该系统具有批Poisson到达和瞬时Bernoulli反馈，在多重休假策略下运行。系统受到根据独立泊松过程发生的灾害的影响，随后是具有一般分布的（随机）修复期。分析采用补充变量法。得到了两次连续灾害之间时间的拉普拉斯变换，证明了系统平稳状态的存在性。除了获得系统中客户数量的平稳分布外，我们还使用补充变量解提供的关于各种事件发生率的信息来获得各种各样的额外结果。其中包括繁忙时段分布的拉普拉斯变换和客户完成服务的概率。我们指出了我们的模型在实际系统中的应用领域，特别是在车辆自组织网络（VANET）中，并使用获得的分析结果在服务质量约束下优化这样的系统。最后，我们分析了即使服务器不忙也会发生灾难的系统变体。

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

Quality Technology and Quantitative Management ENGINEERING, INDUSTRIAL-OPERATIONS RESEARCH & MANAGEMENT SCIENCE

CiteScore

5.10

自引率

21.40%

发文量

审稿时长

>12 weeks

期刊介绍： Quality Technology and Quantitative Management is an international refereed journal publishing original work in quality, reliability, queuing service systems, applied statistics (including methodology, data analysis, simulation), and their applications in business and industrial management. The journal publishes both theoretical and applied research articles using statistical methods or presenting new results, which solve or have the potential to solve real-world management problems.