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

Jewgeni H. Dshalalow and Jean-Baptiste Bacot

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 26, 1-10

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.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:849718

DOI: 10.1155/S0161171201005221

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