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On functionals of a marked Poisson process observed by a renewal process

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  • Jewgeni H. Dshalalow
  • Jean-Baptiste Bacot

Abstract

We study the functionals of a Poisson marked process Π observed by a renewal process. A sequence of observations continues until Π crosses some fixed level at one of the observation epochs (the first passage time). In various stochastic models applications (such as queueing with N -policy combined with multiple vacations), it is necessary to operate with the value of Π prior to the first passage time, or prior to the first passage time plus some random time. We obtain a time-dependent solution to this problem in a closed form, in terms of its Laplace transform. Many results are directly applicable to the time-dependent analysis of queues and other stochastic models via semi-regenerative techniques.

Suggested Citation

  • Jewgeni H. Dshalalow & Jean-Baptiste Bacot, 2001. "On functionals of a marked Poisson process observed by a renewal process," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 26, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:849718
    DOI: 10.1155/S0161171201005221
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    Cited by:

    1. Jewgeni H. Dshalalow & Ryan T. White, 2021. "Current Trends in Random Walks on Random Lattices," Mathematics, MDPI, vol. 9(10), pages 1-38, May.

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