On functionals of a marked Poisson process observed by a renewal process
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 wi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005221 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |