1IntroductionPollingsystemstriggeredextensiveresearcheffortsthatcontinuedoverthelasttwodecades.Duringthisperiodnumerousresearchersfromallareas,mainlyengineering,findthatpollingsystemsarepowerfultoolsinmodelingawidevarietyofapplications.Therangeofapplicationsinwhichpollingmodelcanbeusedisverybroad.Ontheba-sisofthecyclicpolling,inthispaperanewmodel,theasymmetriccyclicpollingmodelwithlimited(k=1)serviceindiscretetimeinloopLANofATMnetworks,issetup,andithasthefollowingcharacteristics:
