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arXiv · 2505.04754

Multiserver-job Response Time under Multilevel Scaling

Isaac Grosof·Hayriye Ayhan
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Abstract

We study the multiserver-job setting in the load-focused multilevel scaling limit, where system load approaches capacity much faster than the growth of the number of servers $n$. We consider the ``1 and $n$'' system, where each job requires either one server or all $n$. Within the multilevel scaling limit, we examine three regimes: load dominated by $n$-server jobs, 1-server jobs, or balanced. In each regime, we characterize the asymptotic growth rate of the boundary of the stability region and the scaled mean queue length. We demonstrate that mean queue length peaks near balanced load via theory, numerics, and simulation.

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Isaac Grosof, Hayriye Ayhan. 2025-05-07. Multiserver-job Response Time under Multilevel Scaling. https://doi.org/10.1017/s0269964826100266

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