Tempered Erlang Queue with Multiple Arrivals
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912610763407360 |
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| author | Dhillon, Manisha Kataria, Kuldeep Kumar |
| author_facet | Dhillon, Manisha Kataria, Kuldeep Kumar |
| contents | In this paper, we introduce and study a time-changed variant of the Erlang queue with multiple arrivals where the time-changing component used is the first hitting time of a tempered stable subordinator. The system of fractional difference-differential equations that governs its state probabilities is derived which is solved to obtain their explicit expressions. An equivalent representation in terms of phases and the mean queue length is obtained. For a particular case, the distribution of inter-arrival times, inter-phase times, sojourn times, busy period and that of conditional waiting times are derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tempered Erlang Queue with Multiple Arrivals Dhillon, Manisha Kataria, Kuldeep Kumar Probability Primary: 60K15, 60K25, Secondary: 60K20, 26A33 In this paper, we introduce and study a time-changed variant of the Erlang queue with multiple arrivals where the time-changing component used is the first hitting time of a tempered stable subordinator. The system of fractional difference-differential equations that governs its state probabilities is derived which is solved to obtain their explicit expressions. An equivalent representation in terms of phases and the mean queue length is obtained. For a particular case, the distribution of inter-arrival times, inter-phase times, sojourn times, busy period and that of conditional waiting times are derived. |
| title | Tempered Erlang Queue with Multiple Arrivals |
| topic | Probability Primary: 60K15, 60K25, Secondary: 60K20, 26A33 |
| url | https://arxiv.org/abs/2505.21804 |