具有伯努利休假的可修重试排队系统进队策略分析

doi:10.15960/j.cnki.issn.1007-6093.2026.01.009

摘要/Abstract

摘要： 本文研究具有伯努利休假和服务台不可靠的M/M/1常数重试排队模型, 其中服务台在正常工作和空闲状态下以不同的速率发生故障。系统没有等待空间, 如果到达的顾客发现服务台处于空闲状态则立即开始服务。如果服务台处于繁忙、休假和故障状态, 顾客则根据系统提供的不同程度信息决定是否加入轨道。在每次完成服务后, 服务台开始进行休假或保持可用。服务台发生故障时系统拒绝新的顾客进入系统。根据系统提供的不同程度信息, 研究在几乎不可视和完全不可视情况下稳态指标, 以及基于收入-支出费用结构研究两种情况下顾客的均衡策略。最后, 通过数值算例比较发现, 披露服务台状态信息不会使社会收益增加。

关键词: 重试排队, 故障, 伯努利休假, 均衡策略, 社会收益

Abstract: This paper studies the M/M/1 constant retrial queueing model with Bernoulli vacations and server unreliability, where the server breaks down at different rates in normal and idle states. The system has no waiting space and service starts immediately if the arriving customer finds the server is idle. Otherwise, if the system is busy, on vacation, and in a breakdown state, the customer decides whether or not to join the orbit based on the different levels of information provided by the system. After each completed service, the system starts to go on vacation or remains available. The system rejects new customers from entering the system in the event of server breakdown. Based on the different levels of information provided by the system, we study the steady-state indicators in the almost unobservable case and fully unobservable case, as well as the equilibrium strategies of customers in both cases based on the reward-cost structure. Finally, we use numerical examples to show that revealing server status information does not increase the social benefit.

Key words: retrial queues, breakdowns, Bernoulli vacations, equilibrium strategy, social benefit

中图分类号:

O226

韩云娜, 田瑞玲. 具有伯努利休假的可修重试排队系统进队策略分析[J]. 运筹学学报（中英文）, 2026, 30(1): 137-155.

HAN Yunna, TIAN Ruiling. Strategic analysis in repairable retrial queueing systems with Bernoulli vacations[J]. Operations Research Transactions, 2026, 30(1): 137-155.

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