基于Q图的M(t)/M/C服务台配置优化  

Staffing Level for Dynamic M(t)/M/C:A Q-Chart Method

作　　者：高琦 宫丽芳 武艳华 戴洪帅 GAO Qi;GONG Lifang;WU Yanhua;DAI Hongshuai(School of Statistics,Shandong University of Finance and Economics,Jinan 250000,China)

机构地区：[1]山东财经大学统计学院,济南250000

出　　处：《西南大学学报（自然科学版）》2022年第4期206-212,共7页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11901347);山东自然科学基金项目(ZR2019MA035,ZR2020MA036).

摘　　要：排队问题随处可见,如何科学有效地对排队拥堵状况进行监控,合理配置资源具有重要的理论和现实价值.与平稳模型相比,动态排队模型由于其时变特征,适用性更广.本文根据逐段平稳和M/M/C模型的相关理论,构建了基于Q图的动态M(t)/M/C模型.该模型利用Q控制图对过程中的到达率λ进行实时监测,根据变点对到达过程进行分段,进而优化服务台的配置问题.随机模拟结果表明,该模型具有优良的检测效果,能够使有限的服务台资源得到有效利用.最后,本文基于收费站数据,进行了实证分析,结果表明该模型可以实时监测到达率的变化情况,从而达到合理安排人工收费车道的目的.Queueing problems can be seen everywhere.How to effectively monitor queueing congestion and rationally allocate resources have important theoretical and practical values.The study of dynamic queues with time-varying arrival rates has become popular in queueing theory.In this work,we applied the Q-chart to study the staffing level for dynamic queueing system M(t)/M/C.This chart was applied to monitor the arrival rateλin the process in real time.According to the change points,the process was segmentized to optimize the configuration of service station.Stochastic simulation results show that the method has advantage in improving the utilization rate of the service station.An empirical analysis was conducted in this study.

关 键 词：Q图 M(t)/M/C模型 逐段平稳 

分 类 号：C931.1[经济管理—管理学] O226[理学—运筹学与控制论]