Optimal Admission Control for Many-Server Systems with QED-Driven Revenues

摘要

We consider Markovian many-server systems with admission control operating ina QED regime, where the relative utilization approaches unity while the numberof servers grows large, providing natural Economies-of-Scale. In order todetermine the optimal admission control policy, we adopt a revenue maximizationframework, and suppose that the revenue rate attains a maximum when nocustomers are waiting and no servers are idling. When the revenue functionscales properly with the system size, we show that a nondegenerate optimizationproblem arises in the limit. Detailed analysis demonstrates that the revenue ismaximized by nontrivial policies that bar customers from entering when thequeue length exceeds a certain threshold of the order of the typicalsquare-root level variation in the system occupancy. We identify a fundamentalequation characterizing the optimal threshold, which we extensively leverage toprovide broadly applicable upper/lower bounds for the optimal threshold,establish its monotonicity, and examine its asymptotic behavior, all forgeneral revenue structures. For linear and exponential revenue structures, wepresent explicit expressions for the optimal threshold.