Batch Markovian Arrival Processes (BMAP) (PREPRINT)

This article describes the batch Markovian arrival process BMAP, a point process that is characterized by Markov-modulated batch arrivals of random size. The BMAP is a generalization of many well-known processes including the Markovian arrival process MAP, the Poisson process, and the Markov-modulated Poisson process. It provides a common framework for modeling arrival processes in a variety of applications. We formally define the continuous- and discrete-time BMAP, review a few basic results for each, and show how these processes generalize many common point processes. Additionally, we provide suggestions for further reading on the subject.