Abstract
Markovian arrival process (MAP) is a generalization of the Markov process where arrivals are governed by an underlying m-state Markov chain. MAP includes phase-type renewal processes and Markov-modulated Poisson process (MMPP). A version that includes batch arrivals is called batch Markovian arrival process (BMAP). The process was developed in response to the limitations of the Poisson process in dealing with different measured features of Internet traffic and other types of traffic. These limitations include the inability of the Poisson model to handle self-similarity and long-range dependence (LRD). This chapter discusses the different types of MAPs including the MMPP, the Markov-modulated Bernoulli process (MMBP), and the MMPP queueing system.
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