Consider a set of k(¸≥2) heterogeneous and exponential servers which operate in parallel. Customers arrive into a single infinite capacity buffer according to a Poisson process, and are routed to available servers in accordance with some routing policy. The authors show that for arrival rates in some positive interval (0,λ0], every routing policy which minimizes the long-run expected holding cost is contained in the set of routing policies that minimize the expected flow time for a system with fixed initial population and no new arrivals.
