Analysis of multivariate Markov modulated Poisson processes

Ushio Sumita, Yasushi Masuda

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2 Citations (Scopus)

Abstract

A multivariate Markov modulated Poisson process M(t) = [M1(t),...,MK(t)] governed by a Markov chain {J(t):t ≥ 0} on N = {0, 1,...,N} is introduced where jumps of Mk(t) occur according to a Poisson process with intensity λ(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.

Original languageEnglish
Pages (from-to)37-45
Number of pages9
JournalOperations Research Letters
Volume12
Issue number1
DOIs
Publication statusPublished - 1992 Jul
Externally publishedYes

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Keywords

  • asymptotic analysis
  • covariance functions
  • multivariate Markov modulated Poisson processes
  • probability generating function
  • time-dependent joint distribution

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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