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We consider a system of $N$ parallel queues with identical exponentialservice 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, ifthere is any, and to a server with the shortest queue among $d$ randomlyselected servers otherwise $(1 \leq d \leq N)$. This load balancing schemesubsumes the so-called Join-the-Idle Queue (JIQ) policy $(d = 1)$ and thecelebrated Join-the-Shortest Queue (JSQ) policy $(d = N)$ as two crucialspecial cases. We develop a stochastic coupling construction to obtain thediffusion 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 thatassigning tasks to idle servers is sufficient for diffusion level optimality.

Universality of Load Balancing Schemes on Diffusion Scale