An $Ω(\log(N)/N)$ Lookahead is Sufficient to Bound Costs in the Overloaded Loss Network
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912841568616448 |
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| author | Bray, Robert L. |
| author_facet | Bray, Robert L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14538 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An $Ω(\log(N)/N)$ Lookahead is Sufficient to Bound Costs in the Overloaded Loss Network Bray, Robert L. Theoretical Economics Probability 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. |
| title | An $Ω(\log(N)/N)$ Lookahead is Sufficient to Bound Costs in the Overloaded Loss Network |
| topic | Theoretical Economics Probability |
| url | https://arxiv.org/abs/2601.14538 |