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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005221 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567495803797504 |
|---|---|
| author | Jewgeni H. Dshalalow Jean-Baptiste Bacot |
| author_facet | Jewgeni H. Dshalalow Jean-Baptiste Bacot |
| author_sort | Jewgeni H. Dshalalow |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-16c0af89be4b4d9f8277df877dc75828 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-16c0af89be4b4d9f8277df877dc758282025-02-03T01:01:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126742743610.1155/S0161171201005221On functionals of a marked Poisson process observed by a renewal processJewgeni H. Dshalalow0Jean-Baptiste Bacot1Applied Mathematics Program, Florida Institute of Technology, Melbourne 32901, FL, USAOperations Research Program, Florida Institute of Technology, Melbourne 3201, FL, USAWe 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.http://dx.doi.org/10.1155/S0161171201005221 |
| spellingShingle | Jewgeni H. Dshalalow Jean-Baptiste Bacot On functionals of a marked Poisson process observed by a renewal process International Journal of Mathematics and Mathematical Sciences |
| title | On functionals of a marked Poisson process observed by a renewal process |
| title_full | On functionals of a marked Poisson process observed by a renewal process |
| title_fullStr | On functionals of a marked Poisson process observed by a renewal process |
| title_full_unstemmed | On functionals of a marked Poisson process observed by a renewal process |
| title_short | On functionals of a marked Poisson process observed by a renewal process |
| title_sort | on functionals of a marked poisson process observed by a renewal process |
| url | http://dx.doi.org/10.1155/S0161171201005221 |
| work_keys_str_mv | AT jewgenihdshalalow onfunctionalsofamarkedpoissonprocessobservedbyarenewalprocess AT jeanbaptistebacot onfunctionalsofamarkedpoissonprocessobservedbyarenewalprocess |