Optimality of the fastest available server policy

We give sufficient conditions under which a policy that assigns customers to the Fastest Available Server, labeled FAS, is optimal among nonidling policies in queueing models with multiple independent Markov-modulated Poisson arrival processes and heterogeneous parallel exponential servers with server-dependent service rates. The criteria are to minimize the long-run average cost per unit time and the expected present value of the costs. We obtain results for loss and delay queueing models with finite- or infinite-capacity buffers under a first-come-first-served priority scheme. We analyze the robustness of the cost structure assumptions that are invoked in the proof of FAS optimality.