带有N策略,启动时间和服务台故障的M/M/1排队的均衡策略  

Equilibrium Strategies in an M/M/1 Queue with the N-Policy,Setup Time and Server Breakdown

作　　者：蒋毓灵 刘力维[1] JIANG Yuling;LIU Liwei(School of Science,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学理学院,江苏南京210094

出　　处：《应用数学》2021年第2期408-418,共11页Mathematica Applicata

基　　金：国家自然科学基金(61773014)。

摘　　要：本文考虑带有N策略,启动时间和服务台故障的M/M/1排队的顾客的策略行为.当系统为空时服务台关闭,并且只有当系统中的顾客数达到一个给定的阈值时才会被激活,启动时间服从指数分布.服务台在工作时可能会故障,一旦发生故障,它立即被维修,维修的时间服从指数分布.我们得到了不同状态的均衡到达率并且给出了均衡社会收益函数.最后对均衡到达率和均衡社会收益进行了数值研究.In this article,we consider customers’strategic behavior in an M/M/1 queue with the N-policy,setup time and server breakdown.The server is closed whenever the system becomes empty,and is activated when the number of customers in the system reaches a threshold.The setup times follow an exponential distribution.The server may break down when busy.Once broken down,it will be repaired immediately and the repair times are exponentially distributed.We obtain the equilibrium arrival rates in different states and give the expression of equilibrium social welfare.Finally,the equilibrium arrival rates and equilibrium social welfare are investigated numerically.

关 键 词：排队 均衡策略 N策略 启动时间 服务台故障 

分 类 号：O226[理学—运筹学与控制论]