Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911130613448704 |
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| author | Dai, J. G. Glynn, Peter Xu, Yaosheng |
| author_facet | Dai, J. G. Glynn, Peter Xu, Yaosheng |
| contents | We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an exponential distribution, corresponding to the Brownian approximation of a single station queue. The ``single station'' can be constructed precisely and its parameters have a good intuitive interpretation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01499 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic Dai, J. G. Glynn, Peter Xu, Yaosheng Probability 60K25, 60J27, 60K37 We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an exponential distribution, corresponding to the Brownian approximation of a single station queue. The ``single station'' can be constructed precisely and its parameters have a good intuitive interpretation. |
| title | Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic |
| topic | Probability 60K25, 60J27, 60K37 |
| url | https://arxiv.org/abs/2304.01499 |