🤖 AI Summary
This study addresses the online admission control problem for two customer classes in a loss queue with reusable resources. By decomposing total cost into variability cost and uncertainty cost, and leveraging stochastic queueing models, deterministic relaxation upper bounds, and the full-information offline optimum, the authors conduct an asymptotic analysis in large-scale systems ($N \to \infty$). They establish that the $\Theta(\log N)$ growth of total cost arises entirely from uncertainty cost, while variability cost remains $O(1)$. Furthermore, they demonstrate that a lookahead window of merely $\Omega(\log N / N)$ suffices to substantially reduce operational costs. These findings reveal that in overloaded loss networks, even a vanishingly small—yet scale-dependent—degree of foresight can eliminate most of the excess cost, offering theoretical justification for highly efficient online resource allocation strategies.
📝 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 $\Theta(\log N)$, as the number of servers, $N$, goes to infinity. I show that we can entirely attribute this $\Theta(\log N)$ 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 $\Omega(\log(N)/N)$ lookahead window is sufficient to bound operating costs.