具有耐心顾客的在线资源分配中的预先承诺
Upfront Commitment in Online Resource Allocation with Patient Customers
AI总结：
针对在线平台中耐心与不耐心代理的资源分配问题，在对抗性到达模型下提出POLYRA算法，通过多面体约束实现最优或接近最优（至少80%）的竞争比。
摘要：
在许多按需在线平台（如网约车、杂货配送或航运）中，一些到达的代理是耐心的，只要存在服务将在一定延迟内最终提供的预先保证，他们愿意等待一小段时间以获取资源或服务。受此启发，我们提出了一个包含耐心和不耐心代理的设定，他们寻求定期补充的资源或服务。不耐心代理在到达时立即要求资源，而耐心代理愿意在获得接收资源预先承诺的条件下等待一小段时间。我们在对抗性到达模型下使用竞争比的松弛概念研究了这一设定。我们提出了一类基于多面体（Polytope）的资源分配（POLYRA）算法，能够实现最优或接近最优的竞争比。这类POLYRA算法通过参考特定多面体并仅做出保证算法状态在该多面体内保持可行的决策来运作。当代理类型数量为两种或三种时，POLYRA算法可获得最优竞争比。为设计这些多面体，我们构建了任意算法竞争比的上界，该上界通过一个线性规划（LP）来刻画，该规划考虑了一组重叠的最坏情况输入序列。我们设计的POLYRA算法随后通过其多面体的定义模拟该上界LP的最优解，从而获得最优竞争比。当类型超过三种时，我们设计的重叠最坏情况输入序列不必然产生可达到的竞争比，因此我们提出了一类简单且可解释的POLYRA算法，其至少能达到最优竞争比的80%。我们通过数值分析补充了理论研究，展示了我们的算法在对抗性到达之外的效率。
英文摘要：
In many on-demand online platforms such as ride-sharing, grocery delivery, or shipping, some arriving agents are patient and willing to wait a short amount of time for the resource or service as long as there is an upfront guarantee that service will be ultimately provided within a certain delay. Motivated by this, we present a setting with patient and impatient agents who seek a resource or service that replenishes periodically. Impatient agents demand the resource immediately upon arrival while patient agents are willing to wait a short period conditioned on an upfront commitment to receive the resource. We study this setting under adversarial arrival models using a relaxed notion of competitive ratio. We present a class of POLYtope-based Resource Allocation (POLYRA) algorithms that achieve optimal or near-optimal competitive ratios. Such POLYRA algorithms work by consulting a particular polytope and only making decisions that guarantee the algorithm's state remains feasible in this polytope. When the number of agent types is either two or three, POLYRA algorithms can obtain the optimal competitive ratio. To design these polytopes, we construct an upper bound on the competitive ratio of any algorithm, which is characterized via a linear program (LP) that considers a collection of overlapping worst-case input sequences. Our designed POLYRA algorithms then mimic the optimal solution of this upper bound LP via its polytope's definition, obtaining the optimal competitive ratio. When there are more than three types, our overlapping worst-case input sequences do not necessarily result in an attainable competitive ratio, and so we present a class of simple and interpretable POLYRA algorithm which achieves at least 80% of the optimal competitive ratio. We complement our theoretical studies with numerical analysis which shows the efficiency of our algorithms beyond adversarial arrivals
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
