On Erlang Queue with Multiple Arrivals and its Time-changed Variant
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915104586465280 |
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| author | Pote, R. B. Kataria, K. K. |
| author_facet | Pote, R. B. Kataria, K. K. |
| contents | We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an infinitesimal time interval. We call it the Erlang queue with multiple arrivals. Some of its distributional properties are obtained that includes the state-phase probabilities, the mean queue length and the distribution of busy period etc. Also, we study a time-changed variant of it by subordinating it with an independent inverse stable subordinator where we obtain its state probabilities and the mean queue length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Erlang Queue with Multiple Arrivals and its Time-changed Variant Pote, R. B. Kataria, K. K. Probability Primary: 60K15, 60K20, Secondary: 60K25, 26A33 We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an infinitesimal time interval. We call it the Erlang queue with multiple arrivals. Some of its distributional properties are obtained that includes the state-phase probabilities, the mean queue length and the distribution of busy period etc. Also, we study a time-changed variant of it by subordinating it with an independent inverse stable subordinator where we obtain its state probabilities and the mean queue length. |
| title | On Erlang Queue with Multiple Arrivals and its Time-changed Variant |
| topic | Probability Primary: 60K15, 60K20, Secondary: 60K25, 26A33 |
| url | https://arxiv.org/abs/2501.08789 |