On the queue length distribution in BMAP systems

Batch Markovian Arrival Process – BMAP – is a teletraffic model which combines high ability to imitate complex statistical behaviour of network traces with relative simplicity in analysis and simulation. It is also a generalization of a wide class of Markovian processes, a class which in particular include the Poisson process, the compound Poisson process, the Markov-modulated Poisson process, the phase-type renewal process and others. In this paper we study the main queueing performance characteristic of a finite-buffer queue fed by the BMAP, namely the queue length distribution. In particular, we show a formula for the Laplace transform of the queue length distribution. The main benefit of this formula is that it may be used to obtain both transient and stationary characteristics. To demonstrate this, several numerical results are presented.