Online Service with Delay

TL;DR

This paper introduces the online service with delay problem, balancing request batching and response delay, and presents a poly-logarithmic competitive algorithm with potential applications in logistics and scheduling.

Contribution

It proposes a novel preemptive service algorithm with recursive time forwarding and spatial exploration, achieving a poly-logarithmic competitive ratio for the problem.

Findings

Achieves poly-logarithmic competitive ratio

Introduces preemptive service algorithm with recursive techniques

Generalizes results to multiple servers

Abstract

In this paper, 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 a server that serves these requests. The goal is to minimize the sum of distance traveled by the server and the total delay in serving the requests. This problem models the fundamental tradeoff between batching requests to improve locality and reducing delay to improve response time, that 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 hope this technique will be useful for related problems such as reordering buffer management, online TSP, vehicle routing, etc. We also generalize our results to $k > 1$ servers.