Moderate Deviation Principle for Join-The-Shortest-Queue-d Systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915183210790912 |
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| author | Wang, Zhenhua Wu, Ruoyu |
| author_facet | Wang, Zhenhua Wu, Ruoyu |
| contents | The Join-the-Shortest-Queue-d routing policy is considered for a large system with $n$ servers. Moderate deviation principles (MDP) for the occupancy process and the empirical queue length process are established as $n\to \infty$. Each MDP is formulated in terms of a large deviation principle with an appropriate speed function in a suitable infinite-dimensional path space. Proofs rely on certain variational representations for exponential functionals of Poisson random measures. As a case study, the convergence of rate functions for systems with finite buffer size $K$ to the rate function without buffer is analyzed, as $K \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moderate Deviation Principle for Join-The-Shortest-Queue-d Systems Wang, Zhenhua Wu, Ruoyu Probability 60F10 The Join-the-Shortest-Queue-d routing policy is considered for a large system with $n$ servers. Moderate deviation principles (MDP) for the occupancy process and the empirical queue length process are established as $n\to \infty$. Each MDP is formulated in terms of a large deviation principle with an appropriate speed function in a suitable infinite-dimensional path space. Proofs rely on certain variational representations for exponential functionals of Poisson random measures. As a case study, the convergence of rate functions for systems with finite buffer size $K$ to the rate function without buffer is analyzed, as $K \to \infty$. |
| title | Moderate Deviation Principle for Join-The-Shortest-Queue-d Systems |
| topic | Probability 60F10 |
| url | https://arxiv.org/abs/2503.03695 |