Asymptotic optimality of the generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si4.svg"><mml:mrow><mml:mi>c</mml:mi><mml:mi>μ</mml:mi></mml:mrow></mml:math> rule under model uncertainty

We consider a critically-loaded multiclass queueing control problem with model uncertainty. The consists of I types customers and single server. At any time instant, decision-maker (DM) allocates the server’s effort to customers. DM’s goal is minimize convex holding cost that accounts for ambiguity respect model, i.e., arrival service rates. For this, we an adversary player whose role choose worst-case scenario. Specifically, assume DM has reference probability in mind function formulated by supremum over equivalent admissible measures measure two components, first expected cost, second one penalty deviating from model. term general divergence measure. show although under critically-load condition might be violated, generalized cμ rule asymptotically optimal this problem.