Finite Buffer Vacation Queue under E-limited with Limit Variation Service and Batch Markovian Arrival Process

摘要

Weconsiderafinite-buffersingleserverqueuewithsingle(multiple)vacation(s)underbatchMarkovianArrivalProcess(BMAP).Theservicedisciplineisvaryingnumberlimitedservice,alsocalledE-limitedwithlimitvariation(ELV)wheretheserverservesuntileitherthesystemisemptiedorarandomlychosenlimitoflcustomershavebeenserved.Queuelengthdistributionsatvariousepochssuchas,pre-arrival,arbitrary,departureetc.havebeenobtained.Severalotherservicedisciplineslike,Bernoullischeduling,non-exhaustiveserviceandE-limitedservicecanbetreatedasspecialcasesoftheELVservice.Suchaqueueingsystemfindsapplicationsinthetokenringortokenbusoflocalareanetwork(LAN)inwhichthevacationwouldcorrespondtothetimethetokenisawaytotheotherstations.