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，吞吐量指需求对资源的预期利用率。我们提出了一种集中不等式生成器，针对容量固定、需求独立但未必同分布且不超过单位规模的场景，给出了可行可用性与吞吐量组合的下界。研究表明，可用性与吞吐量不可能同时表现较差。这些界限类似于独立随机变量和的尾不等式，但适用于需求分布的整个支撑集。该分析提供了支持Chawla、Devanur与Lykouris（2023）单位需求刻画的可解析处理界限，并推广至不超过单位需求的情形。我们的界限还为改进多单位先知不等式（Hajiaghayi、Kleinberg与Sandholm，2007）提供了一种方法。这些结果在交易费用机制设计（针对区块链）中具有应用价值，其中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）。