E-限量服务单重休假排队系统中顾客的止步行为研究

Customer Balking Behavior in Queueing System with E-Limited Service Rule and Single Vacation

文章研究E-限量服务单重休假马尔可夫排队系统中顾客的止步行为策略.在该系统中,一个服务期内最多可连续服务Φ个顾客,因此其兼具限量服务系统与空竭服务系统的特点.对于顾客来说,基于顾客到达时系统信息可视与系统信息不可视两个信息水平,通过建立线性成本-收益模型并求解,分别得到了两类情形下顾客的均衡止步策略,以及系统信息不可视情形下顾客的社会最优止步策略.在信息可视系统中,顾客的均衡止步阈值存在且唯一.在信息不可视系统中,顾客的均衡进入率始终高于社会最优进入率.而且,无论是顾客的均衡止步阈值亦或是顾客的均衡/社会最优进入率,均与Φ值正向相关.

This paper studies customer balking behavior in Markovian queues with E-limited service rule and single vacation.In this system,there are no more thanΦcustomers can be served in a service period,so this service policy combines the features of both a limited service system and an exhaustive service system.In view of whether the system information is observable to customers,we consider two types of information levels:The observable case and the unobservable case.By establishing the linear cost-reward model and solving it,we get customers'equilibrium balking strategies and their socially optimal balking strategy in the unobservable case.In the observable case,customers'equilibrium balking threshold exists and is unique.In the unobservable case,customers'equilibrium joining rate is always higher than their socially optimal joining rate.Moreover,both the customers'equilibrium balking thresholds and their equilibrium/socially optimal joining rate are positively correlated with the value ofΦ.