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arXiv · 1510.02657

Universality of Load Balancing Schemes on Diffusion Scale

D. Mukherjee·S. C. Borst·J. S. H. van Leeuwaarden·P. A. Whiting
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Abstract

We consider a system of $N$ parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a server with the shortest queue among $d$ randomly selected servers otherwise $(1 \leq d \leq N)$. This load balancing scheme subsumes the so-called Join-the-Idle Queue (JIQ) policy $(d = 1)$ and the celebrated Join-the-Shortest Queue (JSQ) policy $(d = N)$ as two crucial special cases. We develop a stochastic coupling construction to obtain the diffusion limit of the queue process in the Halfin-Whitt heavy-traffic regime, and establish that it does not depend on the value of $d$, implying that assigning tasks to idle servers is sufficient for diffusion level optimality.

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D. Mukherjee, S. C. Borst, J. S. H. van Leeuwaarden, P. A. Whiting. 2016-03-03. Universality of Load Balancing Schemes on Diffusion Scale. https://doi.org/10.1017/jpr.2016.68

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