Optimality of static routing policies in queueing systems with blocking

The authors prove the optimality of static routing policies (using no state information) that can be used to maximize the throughput in systems with arbitrary arrival processes and finite capacities. Using sample path arguments, it is shown that when service times are exponential and capacities are equal, the round-robin policy is optimal among all static policies. When service times are deterministic a simple modified round-robin policy is shown to outperform all dynamic policies, and static policies that have richer state information. In both types of systems the optimal allocation is to divide capacities equally among the queues