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Multivariate distributions in open Markovian systems

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Trabajos de estadistica y de investigacion operativa

Abstract

In an open Markov process, individuals arriving according to a stochastic pattern, are distributed into a system with a finite number of interconnecting states, within and from which movement is made at regular instants of time. The multivariate distributions describing the system variates (number of individuals in different states), the output variates (number of individuals leaving the system) and the total population in the system, at any time, are obtained. An alternative method for evaluating these distributions, which employs a generalization of the inversion formula, is also described.

It is established that the necessary and sufficient condition that the system variates (or output variates) be independently distributed (as Poisson) is that the input variate be Poisson distributed. Some other properties of the system are obtained, with particular results for the one-state system noted. The limiting form of the joint distributions is discussed when the mean input becomes large. An example is given to illustrate the theory developed in the paper.

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Authors and Affiliations

  1. The University of New South Wales, New South Wales, Australia

    P. J. Staff & M. K. Vagholkar

Authors
  1. P. J. Staff
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  2. M. K. Vagholkar
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Staff, P.J., Vagholkar, M.K. Multivariate distributions in open Markovian systems. Trab. Estad. Invest. Oper. 25, 119–140 (1974). https://doi.org/10.1007/BF03030156

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  • DOI: https://doi.org/10.1007/BF03030156

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