Batch Markovian Arrival Processes ( BMAP )

Abstract

Abstract 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.

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