Equilibrium strategies in a tandem queue under various levels of information

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We analyze from an economical point of view a tandem network with two nodes. We look at different situations, that is, when customers upon their arrival are no informed, partially informed or totally informed about the state of the system. For each case, we look for the strategy that optimizes the individual net benefit. In addition, for the totally unobservable case, we also study the strategy what would be socially optimal, i.e. maximizing the overall welfare.

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Published 01 October 2011
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EquilibriumstrategiesinatandemqueueundervariouslevelsofinformationBernardoDAuriaSpyridoulaKantaAbstractWeanalyzefromaneconomicalpointofviewatandemnetworkwithtwonodes.Welookatdifferentsituations,thatis,whencustomersupontheirarrivalarenoinformed,partiallyinformedortotallyinformedaboutthestateofthesystem.Foreachcase,welookforthestrategythatoptimizestheindividualnetbenefit.Inaddition,forthetotallyunobservablecase,wealsostudythestrategythatwouldbesociallyoptimal,i.e.maximizingtheoverallwelfare.1IntroductionInthelastdecadesthereisatendencyofstudyingqueueingmodelsfromaneconomicviewpoint.Moreconcretelyareward/coststructureisintroducedandtheobjectiveistheoptimizationofthesystem.Eachcustomercantakehisowndecision.Ofcoursethecustomersactindividuallyandindependentlyonefromtheothersinordertomaximizetheirwelfare.Inevitably,eachcustomer’sdecisionaffectsandisaffectedbythedecisionsoftheothercustomersandtheadministratorofthesystem.Theresultisanequilibriumschemewherenoonehasincentivetodeviatefromthis.Suchkindofsituationscanbeconsideredasagamebetweenthecustomersorbetweenthecustomersandthemanagerofthesystem.Forthatreasongame-theoreticideasareappliedwhenaqueueingsystemisanalyzedunderaneconomicframework.Thenotionsofsupplyanddemandlieattheheartoftheeconomicanalysis.Asitisstraight-forward,thepriceisusedastherationingdeviceinmosteconomicmodels.Acloselyrelatedformofrationingthatcanbedistinguishedisthewaitingline.Therefore,whenaneconomicframeworkisconsidered,conceptsoftheeconomictheoryshouldbeintroducedsothataqueueingsystemcanbestudied.AccordingtoMartinandSmith(1999),exceptfortheprice,thewaitinglistandthewaitinglinearethemostrelatedtothepriceformsofrationing.Theindividualsjoinandremaininaqueuetogainaccesstothegoodorserviceconcerned.Aboutfiftyyearsago,adiscussionbeganregardingthequestionifanentrancefeeimposedtothearrivingcustomersataservicestationisarationalmeasure.Thesituationissimilarwhenahighwayisconsideredandtheimpositionofatolltocontrolthetrafficisdiscussed.Arationalconsumerissearchingforlowwaitingtimeononehandandontheotherhandishiswillingnessofpayingthecorrespondingprice.Alonglineindicatesanunderpricedexperience.Bychargingeachindividual,thedemandcanberationeduntilthequeueiswinnoweddowntosomethingreasonable.Hence,pricingaqueuecanregulatethedemand.Asstatedbefore,aspecificcharacteristicofaqueueingsystemisthewaitingtimeofthecustomers.Thewaitingtimeplaysasignificantroleinthedecisionoftheconsumersanditformspartoftheproductquality(ZimmermanandEnell,1993).Therefore,thewaitingtimecanbeconsideredasaninseparablepartofagoodorservice.Greaterwaitingtimesimplylargercostsonbehalfoftheconsumersadditionallytothepriceoftheproductorservice.Rationalconsumers2