On the Rate of Convergence of the Power-of-Two-Choices to its Mean-Field Limit

This paper studies the rate of convergence of the power-of-two-choices, a celebrated randomized load balancing algorithm for many-server queueing systems, to its mean field limit. The convergence to the mean-field limit has been proved in the literature, but the rate of convergence remained to be an open problem. This paper establishes that the sequence of stationary distributions, indexed by M, the number of servers in the system, converges in mean-square to its mean-field limit with rate O ( (log M)3(log log M)2 M ) .