可视情形下具有休假策略的流体排队均衡策略研究  

Study on Fluid Queuing Equilibrium Strategy with Vacation Strategy under Visual Scenarios

作　　者：蔡思佳 叶晴晴 CAI Sijia;YE Qingqing(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210000,China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210000

出　　处：《重庆工商大学学报（自然科学版）》2023年第2期79-84,共6页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(1190107);江苏省自然科学基金(BK20180783)项目资助。

摘　　要：现实生活中,排队系统中离散顾客的输入流越来越接近连续流体,利用纳什均衡理论提出具有多重休假策略的M/M/1流体排队模型,该模型基于个体和管理决策者考虑收益和系统故障不会让系统长期处于工作忙期。当系统中流体容量为空,系统进入休假阶段,休假期结束,若系统内流体容量仍为空,系统进入下一个休假期,流体根据提供的信息水平和预期收益决定是否加入系统;研究系统服务状态和流体长度均已知情形下流体的进队阈值策略和最优社会策略,在此基础上,考虑系统服务状态不可知的情形;研究发现:是否告知流体系统服务状态,两者的预期流体服务时间和社会收益不同,但最优社会策略相同;利用数值实验分析了不同情况下的最优社会收益和不同系统参数对最优社会收益的影响;通过对具有多重休假策略的流体排队模型的均衡策略分析,为个人和政策制定者降低资源损耗和实现最优社会收益提供参考。In real life,the input flow of discrete customers in queuing systems is getting closer to a continuous fluid.This paper proposed an M/M/1 fluid queuing model with multiple vacation strategies using Nash equilibrium theory,which was based on the fact that individuals and management decision-makers do not leave the system in a long working busy period considering the benefits and system failures.When the fluid capacity in the system was empty,the system entered the holiday phase and the holiday period ended.If the fluid capacity in the system was still empty,the system entered the next holiday period and the fluid decided whether to join the system based on the level of information provided and the expected benefits.The queue threshold strategy and the optimal social strategy of the fluid were studied when the system service state and fluid length were known.On this basis,the situation where the system service state was not known was considered.It was found that whether the fluid system service status was informed or not,the expected fluid service time and social benefits in these two situations were different,but the optimal social strategies in these two situations were the same.Numerical experiments were used to analyze the optimal social gain under different scenarios and the effect of different system parameters on the optimal social gain.The equilibrium strategy analysis of a fluid queuing model with multiple vacation strategies provides a reference for individuals and policymakers to reduce resource depletion and achieve optimal social gain.

关 键 词：多重休假 流模型 纳什均衡 社会收益 均衡阈值 

分 类 号：O226[理学—运筹学与控制论]