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的独立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，吞吐量指资源被需求使用的期望比例。我们提出了一种集中不等式生成器，针对给定容量及独立但不必同分布的单位上限需求，给出了可行的可用性-吞吐量配对的下界。我们证明可用性与吞吐量无法同时处于低水平。这些界类似于独立随机变量和的尾部不等式，但适用于需求分布的整个支撑集。该分析提供了解析可处理的界，支持了Chawla、Devanur与Lykouris（2023）的单位需求刻画，并推广至单位上限需求。我们的界还为改进多单位先知不等式（Hajiaghayi、Kleinberg与Sandholm，2007）提供了方法。其在交易费用机制设计（区块链领域）中具有应用价值：高可用性限制了有利可图的用户-矿工联盟的概率（Chung与Shi，2023）。