同步多重休假M/M/c不可视排队系统中的顾客行为及定价策略研究  

Customer Behavior and Pricing Strategy in the Unobservable M/M/c Queue with Synchronous Multiple Vacations

作　　者：孙微[1] 谢旭梦 李世勇[1] SUN Wei;XIE Xumeng;LI Shiyong(School of Economics and Management,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学经济管理学院,河北秦皇岛066004

出　　处：《运筹与管理》2023年第10期88-94,共7页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(71971188);教育部人文社会科学基金项目(22YJCZH086);河北省自然科学基金项目(G2022203003,G2023203008);河北省省级科技计划(22550301D)。

摘　　要：本文研究同步多重休假M/M/c排队系统中顾客的止步行为和定价策略。当系统为空时,c个服务员同时进入休假状态,一次休假结束后,若系统仍为空,所有服务员继续进行下一次休假,否则同步返回工作状态。基于系统信息几乎不可视和完全不可视两种情形,首先推导出系统的队长稳态分布和顾客的平均逗留时间等性能指标,接着分别从个人最优和系统整体最优的角度出发建立个人剩余效用函数和单位时间社会收益函数,得到两种情形下顾客的均衡止步策略与社会最优止步策略,然后依此为系统制定定价策略,以实现社会收益的最大化。最后,通过数值实验,分别对两种情形下顾客的均衡到达率,社会最优到达率,最优社会收益与系统定价策略关于服务员数量进行灵敏度分析,观察其变化规律及相互关系,以及信息量对顾客行为的影响。Due to the randomness of both the arrival intervals of customers and the service times of servers,queueing phenomena is inevitable in our daily life.When a customer arrives at a certain queueing system,he/she always estimates his/her personal expected residual utility according to the system information he/she gets first,and then decides whether to join the queue or not.Regardless of the visible queueing phenomena like going to the hospital for treatment,purchasing tickets at the train station and so on,or the invisible queueing phenomena like shopping online,consulting business by telephone and so on,there are always several servers in most queueing scenarios.Thus,the research on the balking behavior of customers in the multi-server queueing systems has important practical significance in improving service efficiency,reducing service cost and improving resource utilization and many other aspects.Considering two information levels:Nearly unobservable case and entirely unobservable case,we study the customers’balking behavior and the pricing strategy in an M/M/c queueing system with synchronous multiple vacations.Once the system is empty,all servers will enter the vacation state synchronously.After a vacation,if there is still no customer in the system,all servers will continue to the next vacation,otherwise they will start to work meanwhile.The nearly unobservable case means that the servers’state is disclosed to the customer but the queue length is not,and the entirely unobservable case means that customers don’t know both the servers’state and the queue length.Based on the two information levels,we deduce the stationary distribution of the queue length and some performance indicators like the mean sojourn time of customers by using the quasi birth and death process theory and the matrix geometric method.Next,we obtain the customers’equilibrium balking strategy and socially optimal balking strategy by formulating the personal expected residual utility and the social welfare per unit time from the view

关 键 词：多服务员排队 同步多重休假 队长不可视 止步行为 定价策略 

分 类 号：O226[理学—运筹学与控制论]