COVARIANCE STRUCTURE OF INTERRUPTED MARKOV MODULATED POISSON PROCESS

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概要

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• We consider the covariance structure of an interrupted Markov modulated Poisson process. In this process, periods of on-time and off-time alternate; the on-time interval has a phase-type distribution and the off-time interval has a general one. The off-time period represents the time during which no customers arrive. The on-time period on the other hand, represents the time during which customers do arrive. Here, the arrival rate depends on the phase condition of the on-time interval distribution. We derive the Laplace-Stieltjes transform for the inter-arrival time distribution. Using the results, we study the correlation structures of succeeding inter-arrival times. When the on-time length distribution is hyperexponential, the covariance of succeeding inter-arrival lengths is positive, whereas becomes negative for Erlangian on-time lengths.

• 社団法人日本オペレーションズ・リサーチ学会の論文

著者

• Machihara Fumiaki

  Ntt Laboratories

関連論文

• COVARIANCE STRUCTURE OF INTERRUPTED MARKOV MODULATED POISSON PROCESS
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