On transience of $M/G/\infty$ queues
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910522288373760 |
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| author | Popov, Serguei |
| author_facet | Popov, Serguei |
| contents | We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also that here (unlike e.g. irreducible Markov chains) it is possible for recurrent and transient states to coexist. We also prove a lower bound on the growth speed in the transient case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On transience of $M/G/\infty$ queues Popov, Serguei Probability 60K25, 60G55 We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also that here (unlike e.g. irreducible Markov chains) it is possible for recurrent and transient states to coexist. We also prove a lower bound on the growth speed in the transient case. |
| title | On transience of $M/G/\infty$ queues |
| topic | Probability 60K25, 60G55 |
| url | https://arxiv.org/abs/2406.03517 |