Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process
This paper introduces a simplified solution to determine the asymptotic results for the renewal density. It also offers the asymptotic results for the first and second moments of the number of renewals for the discrete-time bulk-renewal process. The methodology adopted makes this study distinguishab...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Belgrade
2019-01-01
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| Series: | Yugoslav Journal of Operations Research |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-0243/2019/0354-02431800031K.pdf |
| _version_ | 1819168527872950272 |
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| author | Kim James J. Chaudhry Mohan L. Mansur Abdalla |
| author_facet | Kim James J. Chaudhry Mohan L. Mansur Abdalla |
| author_sort | Kim James J. |
| collection | DOAJ |
| description | This paper introduces a simplified solution to determine the asymptotic results for the renewal density. It also offers the asymptotic results for the first and second moments of the number of renewals for the discrete-time bulk-renewal process. The methodology adopted makes this study distinguishable compared to those previously published where the constant term in the second moment is generated. In similar studies published in the literature, the constant term is either missing or not clear how it was obtained. The problem was partially solved in the study by Chaudhry and Fisher where they provided a asymptotic results for the non-bulk renewal density and for both the first and second moments using the generating functions. The objective of this work is to extend their results to the bulk-renewal process in discrete-time, including some numerical results, give an elegant derivation of the asymptotic results and derive continuous-time results as a limit of the discrete-time results. |
| first_indexed | 2024-12-22T19:05:02Z |
| format | Article |
| id | doaj.art-1e23df7de0a445b59db9816be8eda99e |
| institution | Directory Open Access Journal |
| issn | 0354-0243 1820-743X |
| language | English |
| last_indexed | 2024-12-22T19:05:02Z |
| publishDate | 2019-01-01 |
| publisher | University of Belgrade |
| record_format | Article |
| series | Yugoslav Journal of Operations Research |
| spelling | doaj.art-1e23df7de0a445b59db9816be8eda99e2022-12-21T18:15:50ZengUniversity of BelgradeYugoslav Journal of Operations Research0354-02431820-743X2019-01-0129113514410.2298/YJOR180418031K0354-02431800031KAsymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal processKim James J.0Chaudhry Mohan L.1Mansur Abdalla2Royal Canadian Air Force (RCAF), Ottawa ON., CanadaRoyal Military College of Canada, Kingston ON., CanadaAbu Dhabi Mens College, Higher Colleges of Technology, Abu Dhabi, United Arab EmiratesThis paper introduces a simplified solution to determine the asymptotic results for the renewal density. It also offers the asymptotic results for the first and second moments of the number of renewals for the discrete-time bulk-renewal process. The methodology adopted makes this study distinguishable compared to those previously published where the constant term in the second moment is generated. In similar studies published in the literature, the constant term is either missing or not clear how it was obtained. The problem was partially solved in the study by Chaudhry and Fisher where they provided a asymptotic results for the non-bulk renewal density and for both the first and second moments using the generating functions. The objective of this work is to extend their results to the bulk-renewal process in discrete-time, including some numerical results, give an elegant derivation of the asymptotic results and derive continuous-time results as a limit of the discrete-time results.http://www.doiserbia.nb.rs/img/doi/0354-0243/2019/0354-02431800031K.pdfrenewal theorydiscrete-timebulk-renewal processgenerating functionasymptotic results |
| spellingShingle | Kim James J. Chaudhry Mohan L. Mansur Abdalla Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process Yugoslav Journal of Operations Research renewal theory discrete-time bulk-renewal process generating function asymptotic results |
| title | Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process |
| title_full | Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process |
| title_fullStr | Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process |
| title_full_unstemmed | Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process |
| title_short | Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process |
| title_sort | asymptotic results for the first and second moments and numerical computations in discrete time bulk renewal process |
| topic | renewal theory discrete-time bulk-renewal process generating function asymptotic results |
| url | http://www.doiserbia.nb.rs/img/doi/0354-0243/2019/0354-02431800031K.pdf |
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