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

TL;DR

This paper demonstrates that a logarithmic lookahead window in a loss network model is sufficient to effectively bound operating costs, emphasizing the importance of anticipating future fluctuations over smoothing them.

Contribution

It shows that the cost of variability remains bounded while the cost of uncertainty dominates, and that a logarithmic lookahead suffices to control costs in the model.

Findings

Cost of variability remains O(1) as N increases

Cost of uncertainty accounts for the $ heta( ext{log} N)$ growth

A $ ext{Omega}( ext{log} N / N)$ lookahead window bounds costs

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.