阈值调控可变服务率的平行顾客重试排队系统均衡研究  

Equilibrium Analysis of Retrial Queuing System with Parallel Customers and Variable Service Rate Modulated by Threshold

作　　者：刘昕蕾 徐秀丽[1] LIU Xinlei;XU Xiuli(School of Science,Yanshan University,Qinhuangdao 066004;School of Statistics,University of International Business and Economics,Biejing 100029)

机构地区：[1]燕山大学理学院,秦皇岛066004 [2]对外经济贸易大学统计学院,北京100029

出　　处：《系统科学与数学》2025年第2期485-501,共17页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(62171143);河北省自然科学基金项目(G2024203008)资助课题。

摘　　要：文章针对带有N策略的两类平行顾客的M/M/1重试排队系统进行均衡分析.在该排队系统中,两类顾客平行进入系统,并服从不同参数的负指数分布.当顾客进入系统时,若观察到服务台为空,将立刻开始服务;若观察到服务台处于服务状态,则进入重试空间等待重试.系统开始服务需要一定的条件:重试空间中“等待顾客”的数目需达到一定阈值N.此外,视“等待顾客”的数量,服务台的服务速率会相应变化.在完全可见情形下,基于“收益-成本”理论提出效益函数并对两类平行顾客的行为以及社会收益进行分析.最后,运用数值计算直观地表示出系统参数对顾客行为策略以及平均社会收益的影响.This paper considers the equilibrium strategy of the M/M/1 retrial queue with two types of parallel customers and an-policy.In this queuing system,two kinds of customers enter the system in parallel and respectively follow the negative exponential distribution of different parameters.An arriving customer will be served immediately if the server stays idle;Otherwise,the customer enters the retrial space and waits for retry.There are some necessary conditions for the server to start service:The number of two types of customers in the retrial space reaches a given threshold.Moreover,the service rate dynamically changes according to the number of waiting customers in retrial space.A benefit function is introduced according to revenue-cost theory,and equilibrium analysis is conducted for two types of parallel customers in a fully observable case.The average social benefits of the system are also analyzed.Finally,the numerical examples are used to visualize the changes in customer behavior strategies and the average social benefits as the different system parameters.

关 键 词：重试排队 平行顾客 N策略 均衡策略 社会收益 

分 类 号：O226[理学—运筹学与控制论]