带有负顾客和启动时间的排队系统最优策略分析  

Analysis of Optimal Strategies in a Queueing System with Negative Customers and Setup Times

作　　者：何柳青 田瑞玲[1] HE Liuqing;TIAN Ruiling(School of Science,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《应用数学》2024年第1期226-237,共12页Mathematica Applicata

基　　金：国家自然科学基金(71971189)。

摘　　要：本文考虑带有负顾客和启动时间的排队系统的均衡策略和社会最优问题.负顾客到达时,会使得服务台故障,并且迫使正在接受服务的顾客离开系统.当系统中最后一名顾客的服务完成后,服务台立即关闭.当有新顾客到达时,服务台经历一段随机的启动时间,进而服务顾客.基于线性“收益-成本”结构,本文得到了顾客在几乎不可视和完全不可视两种情形下顾客的均衡进入概率.利用遗传算法得到顾客的最优进入概率.最后,通过数值例子展现了最优进入概率和最优社会福利关于系统参数的敏感性变化,并比较了两种信息水平下的最优社会福利.This paper considers the queueing system with negative customer and setup time,and analyses the equilibrium joining strategies and maximization of social welfare.When a negative customer arrives,it causes the server to breakdown and forces the customer who is being served to leave the system.When the last service in the system is completed,the server will be closed immediately.When a new customer arrives,the server goes through a random setup time and then serves the customer.Based on the linear reward-cost structure,this paper obtains the equilibrium joining strategies under the almost unobservable and fully unobservable cases.The optimal joining probability is obtained by the genetic algorithm.Finally,the sensitivity of optimal joining probability and optimal social welfare to some system parameters is discussed by numerical experiments,and the optimal social welfare under two information levels is compared.

关 键 词：排队系统 负顾客 纳什均衡 社会福利 进入概率 

分 类 号：O226[理学—运筹学与控制论]