In this article, we introduce the online service with delay problem. In this problem, there are n points in a metric space that issue service requests over time, and there is a server that serves these requests. The goal is to minimize the sum of distance traveled by the server and the total delay (or a penalty function thereof) in serving the requests. This problem models the fundamental tradeoff between batching requests to improve locality and reducing delay to improve response time, which has many applications in operations management, operating systems, logistics, supply chain management, and scheduling. Our main result is to show a poly-logarithmic competitive ratio for the online service with delay problem. This result is obtained by an algorithm that we call the preemptive service algorithm . The salient feature of this algorithm is a process called preemptive service, which uses a novel combination of (recursive) time forwarding and spatial exploration on a metric space. We also generalize our results to k > 1 servers and obtain stronger results for special metrics such as uniform and star metrics that correspond to (weighted) paging problems.

中文翻译：

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延迟在线服务

在这篇文章中，我们介绍了在线服务延迟问题。在这个问题中，有n随着时间的推移发出服务请求的度量空间中的点，并且有一个服务器为这些请求提供服务。目标是最小化服务器行进的距离和服务请求的总延迟（或其惩罚函数）之和。这个问题模拟了批处理请求以提高局部性和减少延迟以提高响应时间之间的基本权衡，这在运营管理、操作系统、物流、供应链管理和调度中有许多应用。我们的主要结果是显示具有延迟问题的在线服务的多对数竞争比。这个结果是通过我们称之为的算法获得的抢占式服务算法. 该算法的显着特点是一个称为抢占式服务的过程，它在度量空间上使用（递归）时间转发和空间探索的新颖组合。我们还将我们的结果推广到ķ> 1 个服务器，并针对与（加权）分页问题相对应的统一和星型指标等特殊指标获得更强的结果。