We study the problem of deploying a fleet of mobile robots to service tasks that arrive stochastically over time and at random locations in an environment. This is known as the Dynamic Vehicle Routing Problem (DVRP) and requires robots to allocate incoming tasks among themselves and find an optimal sequence for each robot. State-of-the-art approaches only consider average wait times and focus on high-load scenarios where the arrival rate of tasks approaches the limit of what can be handled by the robots while keeping the queue of unserviced tasks bounded, i.e., stable. To ensure stability, these approaches repeatedly compute minimum distance tours over a set of newly arrived tasks. This paper is aimed at addressing the missing policies for moderate-load scenarios, where quality of service can be improved by prioritizing long-waiting tasks. We introduce a novel DVRP policy based on a cost function that takes the $p$-norm over accumulated wait times and show it guarantees stability even in high-load scenarios. We demonstrate that the proposed policy outperforms the state-of-the-art in both mean and $95^{th}$ percentile wait times in moderate-load scenarios through simulation experiments in the Euclidean plane as well as using real-world data for city scale service requests.

翻译：我们研究部署一组移动机器人为随机到达的任务提供服务的问题，这些任务随时间随机到达环境中的随机位置。这被称为动态车辆路径规划问题（DVRP），要求机器人之间分配新到达的任务，并为每个机器人找到最优的序列。现有方法仅考虑平均等待时间，并侧重于高负载场景，即任务到达率接近机器人可处理的上限，同时使未服务任务队列保持有界（即稳定）。为确保稳定性，这些方法反复计算新到达任务集合的最小距离路径。本文旨在解决中等负载场景下的策略缺失问题，在这种场景下，通过优先处理等待时间较长的任务可以改善服务质量。我们提出一种基于代价函数的新型DVRP策略，该函数采用累积等待时间的$p$-范数，并证明即使在高等负载场景下也能保证稳定性。通过欧几里得平面中的仿真实验以及基于真实城市规模服务请求数据的实验，我们证明了所提策略在中等负载场景下的平均等待时间和第95百分位等待时间均优于现有方法。