On the blocking probability in batch Markovian arrival queues

In this paper we investigate the blocking probability in a finite–buffer queue whose arrival process is given by the batch Markovian arrival process (BMAP). BMAP generalizes a wide set of Markovian processes and is especially useful as a precise model of aggregated IP traffic. We first give a detailed description of the BMAP, next we prove a formula for the transform of the blocking probability and show how time-dependent and stationary characteristics can be obtained by means of this formula. Then we discuss the computational complexity and other computational issues. Finally, we present a set of numerical results for two different BMAP parameterizations. In particular, we show sample transient and stationary blocking probabilities and the impact of the auto-correlated structure of the arrival process on the blocking probability.