Approximation of Some Markov-Modulated Poisson Processes

The Markov-modulated Poisson process (MMPP) is a doubly stochastic Poisson process in which the arrival rate varies according to a finite state irreducible Markov process. In many applications of MMPPs, the point process is constructed by superpositions or similar constructions, which lead to modulating Markov processes with a large state space. Since this limits the feasibility of numerical computations, it is important to approximate an MMPP represented by a large Markov process by one with fewer states. In particular, we focus attention on approximating a simple but useful special case of the MMPP, the Birth and Death Modulated Poisson process. At the validation stage, the quality of the approximation is examined in relation to the MMPP/G/1 queue. The aggregation algorithm is the main contribution of this paper; it has applications in analyzing the performance of a statistical multiplexer for which the input is the superposition of packetized voice processes.

INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.