Optimal routing to parallel heterogeneous servers-small arrival rates
Zvi Rosberg, Armand M. Makowski · IEEE Transactions on Automatic Control · 1990
Consider a set of k(>or=2) heterogeneous and exponential servers that 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. It is shown that for arrival rates in some possible interval (0, lambda /sub 0/), ever 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.>