Optimal distributed policies for choosing among multiple servers

The authors 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, it is proved that round robin is the policy minimizing the total expected delay over all customers of an individual stream. The problem of optimizing the total expected delay over all streams is considered. The performance of the round robin policy is investigated and the conclusion is that it is not optimal for this problem. Most of the results also apply under more general service time distributions