Rank-based stochastic differential inclusions and diffusion limits for a load balancing model
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913513518137344 |
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| author | Atar, Rami Ichiba, Tomoyuki |
| author_facet | Atar, Rami Ichiba, Tomoyuki |
| contents | In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of rank-based Brownian particles on the half-line. This paper extends these results from the case of exponential service time to an invariance principle, where service times have finite second moment. The main tool is a new notion of rank-based stochastic differential inclusion, which may be of interest in its own right. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rank-based stochastic differential inclusions and diffusion limits for a load balancing model Atar, Rami Ichiba, Tomoyuki Probability 60K25, 60J60, 60H10, 34A60 In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of rank-based Brownian particles on the half-line. This paper extends these results from the case of exponential service time to an invariance principle, where service times have finite second moment. The main tool is a new notion of rank-based stochastic differential inclusion, which may be of interest in its own right. |
| title | Rank-based stochastic differential inclusions and diffusion limits for a load balancing model |
| topic | Probability 60K25, 60J60, 60H10, 34A60 |
| url | https://arxiv.org/abs/2409.15121 |