Heavy Traffic Diffusion Limit for a Closed Queueing Network with Single-Server and Infinite-Server Stations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910050023374848 |
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| author | Alwan, Amir A. Ata, Barış |
| author_facet | Alwan, Amir A. Ata, Barış |
| contents | This paper studies the limiting behavior of a closed queueing network with multiple single-server and infinite-server stations. Under a heavy traffic asymptotic regime$\unicode{x2014}$where the number of jobs and single-server service rates grow large while infinite-server rates remain fixed$\unicode{x2014}$we prove a weak convergence result for the queue length and idleness process vector, providing an approximation for the original system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heavy Traffic Diffusion Limit for a Closed Queueing Network with Single-Server and Infinite-Server Stations Alwan, Amir A. Ata, Barış Probability This paper studies the limiting behavior of a closed queueing network with multiple single-server and infinite-server stations. Under a heavy traffic asymptotic regime$\unicode{x2014}$where the number of jobs and single-server service rates grow large while infinite-server rates remain fixed$\unicode{x2014}$we prove a weak convergence result for the queue length and idleness process vector, providing an approximation for the original system. |
| title | Heavy Traffic Diffusion Limit for a Closed Queueing Network with Single-Server and Infinite-Server Stations |
| topic | Probability |
| url | https://arxiv.org/abs/2509.13748 |