Optimal Distributed Policies for Choosing among Multiple Servers'

We analyze a system consisting of multiple identical deterministic servers. Customers arrive in several streams; each customer has to decide which server to join by looking only at previous decisions of customers of the same stream. For three variations of this problem, we prove that Round Robin is the policy minimizing the total expected delay over all customers of an individual stream. We also consider the problem of optimizing the total expected delay over all streams; we investigate the performance of Round Robin and we argue that it is not optimal for this problem. Most of our results also apply under more general service time distributions.