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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00387 |
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| _version_ | 1866908857032245248 |
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| author | Hurtado-Lange, Daniela Grosof, Izzy |
| author_facet | Hurtado-Lange, Daniela Grosof, Izzy |
| contents | In parallel-server systems with a single stream of arrivals (a.k.a. load balancing), Join-the-Shortest-Queue (JSQ) is a popular routing algorithm. There is extensive literature studying this system in various asymptotic regimes, but all assume constant parameters (arrival and service rates). We study the JSQ system with Markov-modulated parameters and heterogeneous servers. Our main contributions are: (i) We compute the heavy-traffic distribution of the scaled vector of queue lengths; (ii) We utilize a novel hybrid methodology that combines the Transform Method for queue-lengths analysis and the Poisson equation; (iii) We provide sufficient conditions to ensure state space collapse, showing provable balancing power of JSQ for heterogeneous servers. Unlike other studies involving Markov-modulated queues, these conditions don't depend on the mixing time of the modulating chain and are valid for a countably infinite state space. We numerically demonstrate the strength of our results under moderate traffic intensities and showcase their independence from the corresponding mixing times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00387 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Markov Modulated JSQ in Heavy Traffic Via the Poisson Equation Hurtado-Lange, Daniela Grosof, Izzy Probability In parallel-server systems with a single stream of arrivals (a.k.a. load balancing), Join-the-Shortest-Queue (JSQ) is a popular routing algorithm. There is extensive literature studying this system in various asymptotic regimes, but all assume constant parameters (arrival and service rates). We study the JSQ system with Markov-modulated parameters and heterogeneous servers. Our main contributions are: (i) We compute the heavy-traffic distribution of the scaled vector of queue lengths; (ii) We utilize a novel hybrid methodology that combines the Transform Method for queue-lengths analysis and the Poisson equation; (iii) We provide sufficient conditions to ensure state space collapse, showing provable balancing power of JSQ for heterogeneous servers. Unlike other studies involving Markov-modulated queues, these conditions don't depend on the mixing time of the modulating chain and are valid for a countably infinite state space. We numerically demonstrate the strength of our results under moderate traffic intensities and showcase their independence from the corresponding mixing times. |
| title | Markov Modulated JSQ in Heavy Traffic Via the Poisson Equation |
| topic | Probability |
| url | https://arxiv.org/abs/2603.00387 |