Approximation of Some Markov-Modulated Poisson Processes
ORSA Journal on Computing · 1991 · Volume 3 · Issue 1
Abstract
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 MMPP s, 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.
Keywords
communications, probability, stochastic model: applications, packetized voice process, Markov-modulated Poisson process, aggregation algorithm, square-wave power spectral density
Enable JavaScript for citation tools and additional paper interactions.