Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience

IF 0.7 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
A. Bouchentouf, Abdelhak Guendouzi, Meriem Houalef, Shakir Majid
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引用次数: 2

Abstract

In this paper, we analyze an M/M/1 queueing system under both single and multiple working vacation policies, multiphase random environment, waiting server, balking and reneging. When the system is in operative phase j = 1,2,...,K, customers are served one by one. Whenever the system becomes empty, the server waits a random amount of time before taking a vacation, causing the system to move to working vacation phase 0 at which new arrivals are served at a lower rate. Using the probability generating function method, we obtain the distribution for the steady-state probabilities of the system. Then, we derive important performance measures of the queueing system. Finally, some numerical examples are illustrated to show the impact of system parameters on performance measures of the queueing system.
考虑工作假期和客户不耐烦的多阶段随机环境下的单服务器队列分析
本文分析了一个M/M/1排队系统在单休假和多休假政策、多相随机环境、等待服务器、拒绝和违约情况下的排队问题。当系统处于运行相j = 1,2时,…,K,顾客挨个服务。每当系统变为空时,服务器在休假前等待一段随机的时间,导致系统移动到工作休假阶段0,在此阶段,新到达的服务以较低的速率提供。利用概率生成函数法,得到了系统稳态概率的分布。然后,给出了排队系统的重要性能指标。最后,通过数值算例说明了系统参数对排队系统性能指标的影响。
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
Operations Research and Decisions
Operations Research and Decisions OPERATIONS RESEARCH & MANAGEMENT SCIENCE-
CiteScore
1.00
自引率
25.00%
发文量
16
审稿时长
15 weeks
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