带有N策略的不可靠重试队列的均衡策略分析

Equilibrium Strategies in a Constant Retrial Queue with an Unreliable Server and the N-Policy

本文提出带有N策略和不可靠服务台且拥有恒定重试率的M/M/1排队系统,并研究了关于它的顾客策略行为和社会最优问题.在服务台前没有等待空间,如果顾客到达时发现服务台处于繁忙状态,则他要么选择加入轨道,要么选择离开系统.当服务台服务完一名顾客以后,他会按照恒定重试率和FCFS原则从轨道中选择重试顾客.当系统变空时,服务台会关闭直到轨道中的顾客数达到给定的阈值.假设顾客到达系统时会根据已知的信息和线性收支结构判断是否加入系统,我们得到了服务台处于不同状态下顾客的均衡到达率,并且发现该系统中到达顾客存在拥挤偏好(FTC)情形和拥挤厌恶(ATC)情形,另外还分析顾客均衡到达率的稳定性.因为得到的社会收益函数过于复杂,我们利用PSO算法得到服务台处于不同状态下顾客的社会最优到达率.最后,通过数值例子说明了系统性能指标的敏感性.

In this article,customers’ strategic behavior and the social maximization problem in a constant retrial queue with an unreliable server and the N-policy are considered.There is no waiting space in front of the server.If the customers arrive and find the server is busy,they either choose to join the orbit or leave the system.After a service completion,the server will seek a customer from the orbit at a constant retrial rate on an FCFS principles.When the system becomes empty,the server will close until the number of customers in the orbit reaches a given threshold.Assume that the arriving customers will determine whether to join the system based on known information and a liner reward-cost structure.We obtain the equilibrium arrival rate of customers under different conditions of the server.It is shown that there exist both Follow-the-Crowd(FTC) and Avoid-the-Crowd(ATC) behaviors for the arriving customers,and therefore,the multiple and unique equilibrium arrival rates could exist.Through the Particle Swarm Optimization(PSO) algorithm,we numerically obtain the optimal solution of the social welfare maximization problem under different conditions of the server.Finally,the numerical examples are presented to illustrate the sensitivity of the system performance measures.