BMAP/G/1/N queue with vacations and limited service discipline

We consider a finite buffer single server queue with batch Markovian arrival process (BMAP), where server serves a limited number of customer before going for vacation(s). Single as well as multiple vacation policies are analyzed along with two possible rejection strategies: partial batch rejection and total batch rejection. We obtain queue length distributions at various epochs and some important performance measures. The Laplace–Stieltjes transforms of the actual waiting time of the first customer and an arbitrary customer in an accepted batch have also been obtained.