Abstract
We consider a finite-buffer single server queue with single (multiple) vacation(s) under batch Markovian Arrival Process (BMAP). The service discipline is varying number limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of l customers have been served. Queue length distributions at various epochs such as, pre-arrival, arbitrary, departure etc. have been obtained. Several other service disciplines like, Bernoulli scheduling, non-exhaustive service and E-limited service can be treated as special cases of the ELV service. Such a queueing system finds applications in the token ring or token bus of local area network (LAN) in which the vacation would correspond to the time the token is away to the other stations.
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