带有止步、中途退出和负顾客的多服务台优先权人工客服排队系统  

A Multi-Server Priority Agent Service Queueing System with Balking,Reneging and Negative Customers

作　　者：陈燕婷 陈嘉颖 CHEN Yanting;CHEN Jiaying(Business School,University of Shanghai for Science and Technology,Shanghai 200093;School of Mathematics,Hunan University,Changsha 410082)

机构地区：[1]上海理工大学管理学院,上海200093 [2]湖南大学数学学院,长沙410082

出　　处：《系统科学与数学》2022年第12期3253-3272,共20页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金青年项目(71701066);上海理工大学管理学院2021年度科研启动项目(KYQD202101)资助课题。

摘　　要：当前以聊天为基础的智能客服大量取代了传统的电话客服,但由于大多智能客服的回复较单一,所以人们往往倾向于选择转接人工客服进行问题咨询.进行人工客服咨询时,经常会出现排队人数多、网络中断等现象.于是以此为背景研究了带有止步、中途退出和负顾客的多服务台优先权排队系统.首先,以人工客服为例,在经典的强占优先权策略下建立了包含顾客在排队过程中出现止步和中途退出行为的排队系统,同时将网络中断模拟为排队系统中的负顾客.其次,通过矩阵分析法推导出了两类顾客的稳态分布并计算了相关的性能指标.进一步利用数值实例说明了止步、中途退出和负顾客3种因素对系统性能指标的综合影响是不可忽视的.最后,分析了个人及系统收益并给出了系统优化控制建议.Nowadays,chatting-based intelligent customer service has largely replaced the traditional call centers.However,due to the simple replies from the most intelligent customer service,customers tend to transfer to an agent for problem consultation.When conducting agent service consultation,quite often,there are many customers in the system together with network interruption.Based on this system,we study a multi-server priority queueing system with balking,reneging,and negative customers.Firstly,taking the agent service as an example,we develop a queueing model which includes the balking and reneging behaviors under the classic preemptive priority rule,and model the network interruption as negative customers.Secondly,we derive the steady-state distribution of two types of customers through the matrix analytical method and compute the corresponding performance measures.Furthermore,the numerical examples show that the comprehensive impacts of balking,reneging,and negative customers on the system performance are profound.Finally,we analyze the individual and system utilities,and provide suggestions for system optimal control.

关 键 词：顾客行为 优先权 负顾客 人工客服 拟生灭过程 

分 类 号：O226[理学—运筹学与控制论] F274[理学—数学]