服务台不可靠的重试排队系统均衡分析  

Equilibrium analysis in the retrial queue with an unreliable server

作　　者：张钰 王金亭 ZHANG Yu;WANG Jinting(School of Economics and Management,University of Science and Technology Beijing,Beijing 100083,China;School of Management Science and Engineering,Central University of Finance and Economics,Beijing 100081,China)

机构地区：[1]北京科技大学经济管理学院,北京100083 [2]中央财经大学管理科学与工程学院,北京100081

出　　处：《运筹学学报》2022年第2期1-15,共15页Operations Research Transactions

基　　金：国家自然科学基金(Nos.71901024,71871008);中国博士后科学基金(No.2019M650494);中央高校基本科研业务费(Nos.FRF-TP-19-004A1,FRF-IDRY-19-017);中央财经大学新兴交叉学科建设项目(No.21XXJC010)。

摘　　要：本文研究服务台不可靠的M/M/1常数率重试排队系统中顾客的均衡进队策略,其中服务台在正常工作和空闲状态下以不同的速率发生故障。在该系统中,服务台前没有等待空间,如果到达的顾客发现服务台处于空闲状态,该顾客可占用服务台开始服务。否则,如果服务台处于忙碌状态,顾客可以选择留下信息,使得服务台在空闲时可以按顺序在重试空间中寻找之前留下信息的顾客进行服务。当服务台发生故障时,正在被服务的顾客会发生丢失,且系统拒绝新的顾客进入系统。根据系统提供给顾客的不同程度的信息,研究队长可见和不可见两种信息情形下系统的稳态指标,以及顾客基于收入-支出函数的均衡进队策略,并建立单位时间内服务商的收益和社会福利函数。比较发现,披露队长信息不一定能提高服务商收益和社会福利。This paper studies customers’equilibrium joining strategy in an M/M/1 constant retrial queue with an unreliable server,where the server may break down under the busy and idle states.In this system,there is no waiting space in front of the server.If a customer finds the server idle upon arrival,he occupies the server immediately.Otherwise,if the server is found busy,the customer can choose to leave a message so that the server can search for customers in the retrial orbit who have left messages before in order to serve them when it is free.Once the server breaks down,the customer being served will be squeezed out of the system and new customers are not allowed to join again.According to the different information provided for customers,this paper investigates the system characteristics at steady state and customers’equilibrium joining strategies based on a reward-cost function.Further,the server’s revenue and social welfare functions are established.Through comparisons,it is found revealing the queue length may not bring a greater revenue for the server or a larger social welfare.

关 键 词：重试排队 故障 均衡进队策略 服务商收益 社会福利 

分 类 号：O226[理学—运筹学与控制论]