基于排队系统的队长管理分析

Management analysis of queue leader based on queueing system

现实生活中经常遇到带有不耐烦顾客的排队情况,顾客等待有限时间后不能进入服务则选择离开系统.考虑具有泊松到达、指数服务时间和不耐烦顾客的单服务台排队系统,且假设不耐烦时间服从指数分布.当这些不耐烦的顾客到达排队系统时会面临两种不同的选择:进入系统或离开系统.与普通顾客的排队系统不一样的是当不耐烦的顾客进入系统后可能在没有接受服务后离开.研究顾客的个人效用和系统的整体效用是如何随着排队队长变化的.最后证明系统只需要提供有限的排队空间,当顾客数量超过这个有限空间数,即将到达的顾客就不能进入系统.这样有限的排队位置就会减少资源的浪费.

Queueing systems with impatient customer often run into our real life,in which impatient customers would leave the system if they did not get service after some waiting time.This paper considered a single-server queueing system with impatient customers,exogenous Poisson arrival,exponential service time and impatient customers.Any impatient customer must do two different decisions when arriving the queueing system:to join or not.Be different from the queueing system without impatient customers,a joining customer might leave the system without service.This paper studied how both customers’personal utility and system’s total utility changed in the number of the queue length.Finally,this paper proved that the system manager only needed to provide a finite waiting room because that customers chose not to join the system when the queue length was more than the finite number.Based on that,the finite waiting room may induce the manager to avoid wasting resources.