Analysis of multivariate Markov modulated Poisson processes

Authors:
Ushio Sumita;Yasushi Masuda
Affiliations:
Graduate School of International Management, The International University of Japan, Niigata, Japan and William E. Simon Graduate School of Business Administration, University of Rochester, Rochest ...;Graduate School of Management, University of California, Riverside, CA 92521, USA
Venue:
Operations Research Letters
Year:
1992

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Abstract

A multivariate Markov modulated Poisson process M(t) = [M"1(t),...,M"K(t)] governed by a Markov chain {J(t):t = 0} on N = {0, 1,...,N} is introduced where jumps of M"k(t) occur according to a Poisson process with intensity @l(k, i) whenever the Markov chain J(t) is in state i, 1 @? k @? K, 0 @? i @? N. Of interest to the paper is the time-dependent joint distribution of the multivariate process [M(t), J(t)]. In particular, the Laplace transform generating function is explicitly derived and its probabilistic interpretation is given. Asymptotic expansions of the cross moments and covariance functions of M(t) are also discussed.