Customer Joining Behavior and Regulation Strategy in Visible Multi-Server Queues with Synchronous Vacations of Partial Servers  

作　　者：SUN Wei WANG Hao XIE Xumeng LI Shiyong 

机构地区：[1]School of Economics and Management,Yanshan University,Qinhuangdao 066004,China

出　　处：《Journal of Systems Science & Complexity》2024年第3期1209-1232,共24页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.71971188;the Humanities and Social Science Fund of Ministry of Education of China under Grant No.22YJCZH086;the Hebei Natural Science Foundation under Grant Nos.G2023203008 and G2022203003。

摘　　要：This paper studies customer joining behavior and system regulation strategy in nonexhaustive visible M/M/m queues with synchronous vacations of a part of the servers.Once this part of the servers are idle,they take multiple vacations simultaneously(vacation period).Until there are customers waiting in the queue,they are reactivated and all servers are busy or idle(busy period).The authors call this part of the servers as“partial servers”.In view of the fully visible queue and the almost visible queue,the authors obtain customers’equilibrium joining threshold strategies and their socially optimal joining threshold strategies,respectively,and observe that customer joining behavior in equilibrium generally makes the system overcrowded,which makes the equilibrium social welfare lower than the optimal social welfare.After regulation,interestingly,for optimizing social welfare,the system manager hopes not only customers arriving in vacation period pay attention to the number of partial servers,but also customers arriving in busy period should care about it rather than ignore.Moreover,arranging more servers for vacation does not necessarily lead to the decrease of social welfare on condition that the number of partial servers is close to m.As for the information advantage of the fully visible case,it is not obvious for increasing social welfare and even unfavorable to servers’profit unless the number of partial servers is big enough.Furthermore,given the different composition of social welfare,there exists the optimal number of partial servers and the optimal arrival rate of customers for maximizing social welfare.

关 键 词：Customer behavior non-exhaustive service partial servers regulation strategy synchronous vacations visible queue 

分 类 号：O226[理学—运筹学与控制论]