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OntheDelayofGeographicalCachingMethods inTwo-TieredHeterogeneousNetworks Abstract Weconsiderahierarchicalnetworkthatconsistsofmobileusers,atwo-tieredcellularnetwork(namelysmallcellsandmacrocells)andcentralrouters,eachofwhichfollowsaPoissonpointprocess(PPP).Inthisscenario,smallcellswithlimited-capacitybackhaulareabletocachecontentunderagivensetofrandomizedcachingpoliciesandstorageconstraints.Moreover,weconsiderthreedifferentcontentpopularitymodels,namelyfixedcontentpopularity,distance-dependentandload-dependent,inordertomodelthespatio-temporalbehaviorofusers’contentrequestpatterns.Wederiveexpressionsfortheaveragedelayofusersassumingperfectknowledgeofcontentpopularitydistributionsandrandomizedcachingpolicies.Althoughthetrendoftheaveragedelayforallthreecontentpopularitymodelsisessentiallyidentical,ourresultsshowthattheoverallperformanceofcached-enabledheterogeneousnetworkscanbesubstantiallyimproved,especiallyundertheloaddependentcontentpopularitymodel. Besides,Becauseofthelimitationofresearchconditions,thetotalnetworkdelay,networkcostandoptimizationofnetworkparametersarenotanalyzed. Keywords:edgecaching,Poissonpointprocess,stochasticgeometry,mobilewirelessnetworks,5G Introduction Itisknownthatcontentcachingin5Gheterogeneouswirelessnetworksimprovesthesystemperformance,andisofhighimportanceinlimited-backhaulscenarios.Mostexistingliteraturefocusesonthecharacterizationofkeyperformancemetricsneglectingthebackhaullimitationsandthespatio-temporalcontentpopularityprofiles.Inthiswork,weanalyzethegainsofcachinginheterogeneousnetworkdeployment,andconsidertheaveragedelayasaperformancemetric. Firstlyweusepassionpointprocess(PPP)methodtobuildthemodel.Thisheterogeneousnetworkconsistsofmobileterminals(users),cache-enabledsmallbasestations(SBSs),macrobasestations(MBSs)andcentralrouters.Inthisnetworksetting,ausermayexperiencedelaysduetodownlinktransmissions,backhaulandcaches. Moreover,inordertocapturethespatio-temporalcontentaccesspatternsofusers,wesupposefixedcontentpopularity,

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