带有N-策略和负顾客的可修重试排队系统均衡策略研究  

Research on Equilibrium Strategies of Repairable and Retrial Queue with N-Policy and Negative Customers

作　　者：赵欣宜 刘力维[1] ZHAO Xinyi;LIU Liwei(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学数学与统计学院,江苏南京210094

出　　处：《应用数学》2024年第3期589-600,共12页Mathematica Applicata

基　　金：国家自然科学基金(61773014)。

摘　　要：本文研究带有N-策略和负顾客的M/M/1可修常数重试排队系统中正顾客的策略行为.当系统中的正顾客数达到规定阈值N时,处于空闲状态的服务台才会重新启动提供服务.系统中没有等待空间,若正顾客在服务台处于空闲状态时抵达,则他会立即接受服务;若正顾客在服务台处于忙期时抵达,则他会进入重试轨道,或者选择离开系统.当服务台再次为空时,它会遵循先到先服务的规则从重试轨道中选择正顾客进行服务.负顾客在到达系统时会抵消正在被服务的正顾客,并且导致服务台发生故障.若服务台发生故障,它会立刻被送去修理,修理时间服从指数分布.我们首先推导出系统的稳态概率和正顾客的平均逗留时间,求得了不同状态下正顾客的均衡到达率和单位时间社会收益.最后,对正顾客的社会最优到达率和最优社会收益进行了数值分析.In this paper,we research positive customers’strategic behavior in a repairable and constant retrial M/M/1 queue with N-policy and negative customers.The idle server restarts and provides service when the number of positive customers in the system reaches the specified threshold N.There is no waiting space in the system.If positive customers arrive when the server is idle,they will accept the service immediately;If positive customers arrive when the server is busy,they will choose to join the retrial orbit or leave the system.When the server becomes empty again,it will look for a positive customer from the retrial orbit to provide service following an FCFS principle.When negative customers arrive at the system,they will delete the positive customer who is served and cause the server’s breakdown.Once the server breaks down,it will be sent to repair immediately and the maintenance time follows the exponential distribution.Firstly,we derive the steady-state probabilities of this system and the mean sojourn time of positive customers.Then we acquire the equilibrium arrival rates of positive customers in various situations and social benefit per unit time.Finally,the numerical analyses of the socially optimal arrival rates of positive customers and the optimal social benefit are carried out.

关 键 词：排队系统 均衡策略 负顾客 N-策略 重试 可修 

分 类 号：O226[理学—运筹学与控制论]