Optimal Round-Robin Routing to Parallel Servers in Heavy Traffic

We study a system with heterogeneous parallel servers. Upon arrival, a job is routed to the queue of one of the servers. We establish the diffusion limit for the round-robin (RR) policy, and show that with properly chosen parameters, it achieves the optimal performance asymptotically over all blind routing policies. Analysis of the diffusion limit yields a number of insights into the performance of the optimal RR policies.