This paper studies the fundamental limits of availability and throughput for independent and heterogeneous demands of a limited resource. Availability is the probability that the demands are below the capacity of the resource. Throughput is the expected fraction of the resource that is utilized by the demands. We offer a concentration inequality generator that gives lower bounds on feasible availability and throughput pairs with a given capacity and independent but not necessarily identical distributions of up-to-unit demands. We show that availability and throughput cannot both be poor. These bounds are analogous to tail inequalities on sums of independent random variables, but hold throughout the support of the demand distribution. This analysis gives analytically tractable bounds supporting the unit-demand characterization of Chawla, Devanur, and Lykouris (2023) and generalizes to up-to-unit demands. Our bounds also provide an approach towards improved multi-unit prophet inequalities (Hajiaghayi, Kleinberg, and Sandholm, 2007). They have applications to transaction fee mechanism design (for blockchains) where high availability limits the probability of profitable user-miner coalitions (Chung and Shi, 2023).

翻译：本文研究了有限资源在独立且异质需求下的可用性与吞吐量的基本极限。可用性指需求低于资源容量的概率，吞吐量则指资源被需求利用的预期比例。我们提出一种集中不等式生成器，能够在给定容量以及独立但未必同分布的至多单位需求分布下，为可行的可用性与吞吐量对提供下界。我们证明可用性与吞吐量不可能同时处于低水平。这些界限类似于独立随机变量和的尾部不等式，但在需求分布的整个支撑集上均成立。该分析给出了解析可处理的界限，支持了Chawla、Devanur与Lykouris（2023）提出的单位需求刻画，并推广至至多单位需求情形。我们的界限还为改进多单位先知不等式（Hajiaghayi、Kleinberg与Sandholm，2007）提供了新途径。这些结论可应用于（区块链）交易费用机制设计，其中高可用性限制了用户-矿工联盟获利的概率（Chung与Shi，2023）。