-基于排队论的银行业务窗口设置优化

433Vol．43No．3JOURNALOFSHANDONGUNIVERSITYENGINEERINGSCIENCE20136Jun．20132013-03-202013-05-2809∶38http//．cnki．net/kcms/detail/37．1391．T．20130524．1002．001．html1100105561170211*1967－、、[e-mail]1672-3961201303-0023-07DOI10.6040/j．issn．1672-3961.9.2013.004蔡文婧1，葛连升21．2501002．250100为解决目前办理银行业务顾客等候时间过长的问题，构建了基于排队论的银行业务窗口设置优化模型。将银行前台的业务办理过程视为随机服务系统，在充分认识该系统基本特征的基础上，详细设计了优化银行窗口设置的步骤，并运用排队论，从两个侧重目标分别具体分析了银行窗口设置的优化方法，结合实例给出了合理确定银行窗口数量的一种新思路。排队论;银行业务窗口;优化方法;顾客损失率;服务强度O226AOptimizationofbankcountersettingbasedonqueuingtheoryCAIWen-jing1GELian-sheng21．SchoolofEconomicsShandongUniversityJinan250100China2．NetworkandInformationCenterShandongUniversityJinan250100ChinaAbstractInordertoreducethewaitingtimeofcustomersinthecurrentbankingsystemaqueuingtheorybasedopti-mizationmodelofbankingqueuingsystemwasdeveloped．Theprocessofconductingserviceatthebankcounterswasregardedasrandomservicesystem．Adetaileddesignofbankcounters’optimizationwasgivenbasedonthebasicfea-turesofthissystem．Additionallyaconcreteanalysisofthesystemoptimizationusingqueuingtheoryaccordingtotworespectiveaimswaspresentedandthenanewwaytodecidetheappropriatenumberofbankcounterswasillustratedwithanexample．Keywordsqueuingtheorybankcountersstepsofoptimizationlossrateofclientsserviceintensity0。、、、、。、。。1。、。。。。2-4AgentAgent2443。Agent5-6。。KUTCSKncKn/c7。DAVIDLPc8-10。、。、3。111-12。。1.1。1。。2。。。。。1.21.2.1。。λ。1λ。1.2.2。。。1.2.3c。。μ1μ。3M/M/c/∞λμc。。3251.3。1.3.1。。。1.3.2ρ=λμ。cρc=λcμ。ρc＞1c。ρc=1。ρcρc＜1。22.1。μλ。1μμ。ρc=λcμρc＜1ρ=λμ。NttNtt≥012-14λn=λμn=nμcμ{{n=012…n=123…cn=c+1…。pn=λn－1·λn－2·…·λ0μn·μn－1·…·μ1p0=1nλ()μnp0=1nρnp0n=012…c－11cn－ccλ()μnp0=1cn－ccρnp0n=cc+1{…。1∑∞n=0pn=1ρc＜1∑∞n=0pn=∑c－1n=0pn+∑∞n=cpn=∑c－1n=01nρn+∑∞n=c1cn－ccρ()np0=∑c－1n=0ρnn+1cρc11－ρ()cp0=1。p0=∑c－1n=0ρnn+cρccc－ρ[]－1。1Lq=∑∞n=cn－cpn。pnLq=∑∞n=cn－c1cn－ccλ()μnp[]0=ρc·cρcc·p01－ρc2·c=ccρcc+1p01－ρc2c。2214-16。WqWq=Lqλ=ccρc+1cp01－ρc2c·λ。32643。2.2。1。χ2λμ。2。λ、μ。λμ。1h。λμ。。T。TT。T、。T、T。2.3。2.3.1Wq=ccρc+1cp01－ρc2c·λ＜T。λ、μcWqc。Wqc＜Tccc0。cc0。λc0。c0。2.3.2ρc=λcμ。70%～80%。70%≤ρc≤80%5λ4μ≤c≤10λ7μc。。3。3.75minμ16/h。90λ=90/h。10min20%30%20min40min。5～10min。T=6min。ρc=λcμ=9016c＜1c＞5.6256。ρ=λμ=3279016=458。c6Wqcc=6ρc=λcμ=906×16=1516p06=∑c－1n=0ρnn+cρccc－ρ[]－1=∑5n=045()8nn+6×45()8666－45()8－1=0.00118Wq6=ccρcc+1p01－ρc2c·λ=66×15()167×0.001181－15()[]162×6×90=0.13844＞0.1。c=7ρc=λcμ=907×16=4556p07=∑c－1n=0ρnn+cρccc－ρ[]－1=∑6n=045()8nn+7×45()8777－45()8－1=0.00274Wq7=ccρcc+1p01－ρc2c·λ=77×45()568×0.002741－45()[]562×7×90=0.02242＜0.1。cc≥7。ρc=λcμ=458c∈0.70.8。c7.03125≤c≤8.03571。78。778。78。7。。。Wqc≤Tcc5λ4μ10λ7[]μ。c。4。。1、117-18、28433。。2。119、。20-22。23-26、。1．J．2009365514-518．YANGMishaYIKunnan．OptimizationofbankcountersbasedonthequeuingprocessJ．JournalofZhejiangUniversityScienceEdition2009365514-518．2．AgentJ．200528111817-1822．YANGGongpingZENGGuangzhou．LUZhaoxia．StudyonthequeuingmechanismofmobileagentsystemJ．ChineseJournalofComputers200528111817-1822．3．agentJ．20082512277-280．LIChengjieYANGGongpingYINYilong．AgentbasedsimulationofbankqueuingsystemJ．ComputerSimulation20082512277-280．4．AgentJ．201141468-72．ZHANGQicongYANGGongping．StudyonanagentbasedsimulationofbankingqueuingsystemJ．JournalofShandongUniversityEngineeringScience201141468-72．5KarnikNeeranTripathiAnand．AgentserverarchitecturefortheAjantamobile-agentsystemC//Proceedingsofthe1998InternationalConferenceonParallelandDistributedProcessingTechniquesandApplicationsPDPTA'98．Lasvegass．n．199866-73．6WALSHTPACIOREKNWONGD．SecurityandreliabilityinconcordiaC//ProceedingsoftheThirty-FirstAnnualHa-waiiInternationalConferenceonSystemSciences．KonaHawaiis．n．199844-53．7KUTSCCHRISTOPHERST．OnmanagingoperatingcapacitytoreducecongestioninservicesystemsJ．EuropeanJour-nalofOperationalResearch199692383-98．8DAVIDLPCHRISTOSGC．ModelinganalysisandoptimalcontrolofaclassofhybridsystemsJ．DiscreteEventDy-namicSystemsTheoryandApplications199872175-201．9．J．20014352-57．SONGWeibinSUQin．queuingmodelinvirtualservicesupportSystemJ．JournalofManagementSciencesinChina20014352-57．10．M．2007257-275．11．M．20061-6．12GUOPFPAULZ．Theeffectsoftheavailabilityofwaiting-timeinformationonabankingqueueJ．EuropeanJournalofOperationalResearch20091985199-209．13IVOAANTONISESTELLAK．SynchronizedreneginginqueuingsystemswithvacationsJ．QueuingSyst20096231-33．14．J．2010559-61．SUNHonghuaZENGChao．OptimizeresearchofhospitalbasedonqueuemodelJ．JournalofChineseModernEducationEquipment2010559-61．15．J．201234286-88．CHENLei．ModelingandoptimizationofbankservicewindowresearchingJ．LogisticsEngineeringandManagement329201234286-88．16．J．2011780-81．GAOSibo．ResearchonbankqueuingsystemandoptimizationofservicewindowJ．NorthernEconomy2011780-81．17．J．2011731-35．WANGJianHUBiqin．SimulationresearchonqueuetheoryforberthservicesystemofportJ．LogisticsTechnology2011731-35．18．J．2005233-36．ZHANGMingqiangSHANGJianpingWANGNuo．ApplicationofcomputersimulationinportplanningJ．WaterTans-portationEngineering2005233-36．19．WitnessJ．200823196-98．WANGJianqingSHAOYanjun．SimulationofqueuesystembasedonWITNESSJ．MechanicalManagementandDevel-opment200823196-98．20．M．2007．21．J．20069133-37．GUOYaohuangZHONGXiaopen