具有两类顾客和轨道搜索的重试排队系统的均衡策略分析

Equilibrium Strategies Analysis of a Retrial Queueing System with Two Classes of Customers and Orbital Search

文章考虑一个具有两类顾客和轨道搜索的M/M/1重试排队系统.到达系统的顾客如果服务受到阻碍,优先顾客可以排队等待,且在服务台前的等待空间有限;而普通顾客可以选择加入具有无穷容量的重试轨道,等待稍后重试.如果服务台在服务完一位顾客后发现系统中不存在优先顾客,但轨道中存在普通顾客,则服务台会以概率p保持空闲状态,等待顾客的到来;或者以概率1-p从轨道队列的队首开始搜索普通顾客.文章首先利用拟生灭过程的遍历条件推导出系统的稳态条件,并基于生成函数方法得到一些重要的系统性能指标.然后根据线性“收益-成本”结构,在完全不可见和部分可见情形下研究普通顾客的均衡策略.最后通过数值实例探究系统参数对均衡策略的影响.

In this paper,we consider an M/M/1 retrial queueing system with two classes of customers and orbital search.If the service of arriving customers is obstructed,priority customers can wait in line and have limited waiting space in front of the server;The ordinary customers can join an infinite-capacity retrial orbit and retry later.If the server finds that there is no priority customer in the system after serving a customer,but there are ordinary customers in orbit,the server will keep idle with probability p and wait for customers to arrive or start searching for customers from the head of the orbit with probability 1-p.We first derive the stability condition of the system using the ergodic condition of the quasi-birth-and-death(QBD)process and obtain some important system performance measures based on the generating function approach.Then,depending on a linear reward-cost structure,we study ordinary customers'equilibrium joining strategies in the fully unobservable and partially observable cases.Finally,the effects of the system parameters on the equilibrium strategies are explored through numerical examples.