We give sufficient conditions under which a policy that assigns customers to the Fastest Available Server, labelled FAS, is optimal in queueing models with multiple independent Poisson arrival processes and heterogeneous parallel exponential servers. The criterion is to minimize the long-run average cost per unit time. We obtain results for loss models and for queueing systems with a finite-capacity or infinite-capacity buffer under a head-of-the-line priority scheme. The results depend on cost assumptions, so we analyze the robustness of the cost structure and present counter-examples to illustrate when FAS is not optimal.
Millhiser, W. P., Sinha, C., & Sobel, M. J. (2016). Optimality of the fastest available server policy. Queueing Systems, 84(3–4), 237–263. https://doi.org/10.1007/s11134-016-9502-1