A discrete-time batch Markovian arrival process as B-ISDN traffic model

A class of versatile discrete-time Markovian arriaval processes (D-BMAP’s) is introduced. A model for the superposition of video sources, both with uniform and multiple activity levels, belongs to this class. Formulae for the correlation between arrivals in the D-BMAP are derived. Observing the D-BMAP/G/1/N queue at departure epochs results in a finite Markov chain of M/G/1 type. An efficient method allowing the computation of the queue length distribution at departures is proposed. Using matrix analytical methods, the paper derives a solution for the buffer occupancy and for the loss probability which can be expressed in a form suitable for numerical computations. Finally, it shows that the output process of this queue is again a DMAP.