The design of online algorithms for matching markets and revenue management settings is usually bound by the stochastic prior that the demand process is formed by a fixed-length sequence of queries with unknown types, each drawn independently. This assumption of {\em serial independence} implies that the demand of each type, i.e., the number of queries of a given type, has low variance and is approximately Poisson-distributed. This paper explores more general stochastic models for online edge-weighted matching that depart from the serial independence assumption. We propose two new models, \Indep and \Correl, that capture different forms of serial correlations by combining a nonparametric distribution for the demand with standard assumptions on the arrival patterns -- adversarial or random order. The \Indep model has arbitrary marginal distributions for the demands but assumes cross-sectional independence for the customer types, whereas the \Correl model captures common shocks across customer types. We demonstrate that fluid relaxations, which rely solely on expected demand information, have arbitrarily bad performance guarantees. In contrast, we develop new algorithms that essentially achieve optimal constant-factor performance guarantees in each model. Our mathematical analysis includes tighter linear programming relaxations that leverage distribution knowledge, and a new lossless randomized rounding scheme in the case of $\Indep$. In numerical simulations of the $\Indep$ model, we find that tighter relaxations are beneficial under high-variance demand and that our demand-aware rounding scheme can outperform stockout-aware rounding.

翻译：在线匹配市场和收益管理场景的算法设计通常受限于随机先验假设：需求过程由一系列固定长度的未知类型查询序列组成，每个查询独立同分布。这种**序列独立性**假设意味着每种类型的需求（即给定类型查询的数量）具有低方差且近似服从泊松分布。本文探索了更一般的在线边加权匹配随机模型，突破了序列独立性假设。我们提出两种新模型**\Indep**与**\Correl**，通过将需求的非参数分布与到达模式（对抗性顺序或随机顺序）的标准假设相结合，捕捉不同形式的序列相关性。**\Indep**模型允许需求具有任意边际分布，但假设客户类型截面独立；而**\Correl**模型则刻画了客户类型间的共同冲击。我们证明，仅依赖期望需求信息的流体松弛方法会带来任意差的性能保证。与此相对，我们开发的新算法在每种模型中均能实现本质最优的常数因子性能保证。数学分析包括：利用分布知识设计更紧的线性规划松弛，以及针对**\Indep**模型提出的无损随机舍入方案。在**\Indep**模型的数值模拟中，我们发现紧松弛在高方差需求下具有优势，且需求感知舍入方案优于库存感知舍入方案。