Rank-based stochastic differential inclusions and diffusion limits for a load balancing model

Rami Atar; Tomoyuki Ichiba

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arXiv · 2409.15121

Rank-based stochastic differential inclusions and diffusion limits for a load balancing model

Rami Atar·Tomoyuki Ichiba

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Abstract

In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of rank-based Brownian particles on the half-line. This paper extends these results from the case of exponential service time to an invariance principle, where service times have finite second moment. The main tool is a new notion of rank-based stochastic differential inclusion, which may be of interest in its own right.

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Rami Atar, Tomoyuki Ichiba. 2024-09-23. Rank-based stochastic differential inclusions and diffusion limits for a load balancing model. https://arxiv.org/abs/2409.15121

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