An $Ω(\log(N)/N)$ Lookahead is Sufficient to Bound Costs in the Overloaded Loss Network

Abstract: I study the simplest model of revenue management with reusable resources: admission control of two customer classes into a loss queue. This model's long-run average collected reward has two natural upper bounds: the deterministic relaxation and the full-information offline problem. With these bounds, we can decompose the costs faced by the online decision maker into (i) the \emph{cost of variability}, given by the difference between the deterministic value and the offline value, and (ii) the \emph{cost of uncertainty}, given by the difference between the offline value and the online value. \cite{Xie2025} established that the sum of these two costs is $Θ(\log N)$, as the number of servers, $N$, goes to infinity. I show that we can entirely attribute this $Θ(\log N)$ rate to the cost of uncertainty, as the cost of variability remains $O(1)$ as $N \rightarrow \infty$. In other words, I show that anticipating future fluctuations is sufficient to bound operating costs -- smoothing out these fluctuations is unnecessary. In fact, I show that an $Ω(\log(N)/N)$ lookahead window is sufficient to bound operating costs.