With the rise in demand for local deliveries and e-commerce, robotic deliveries are being considered as efficient and sustainable solutions. However, the deployment of such systems can be highly complex due to numerous factors involving stochastic demand, stochastic charging and maintenance needs, complex routing, etc. We propose a model that uses continuous approximation methods for evaluating service trade-offs that consider the unique characteristics of large-scale sidewalk delivery robot systems used to serve online food deliveries. The model captures both the initial cost and the operation cost of the delivery system and evaluates the impact of constraints and operation strategies on the deployment. By minimizing the system cost, variables related to the system design can be determined. First, the minimization problem is formulated based on a homogeneous area, and the optimal system cost can be derived as a closed-form expression. By evaluating the expression, relationships between variables and the system cost can be directly obtained. We then apply the model in neighborhoods in New York City to evaluate the cost of deploying the sidewalk delivery robot system in a real-world scenario. The results shed light on the potential of deploying such a system in the future.

翻译：随着本地配送和电子商务需求的增长，机器人配送正被视为高效且可持续的解决方案。然而，由于随机需求、随机充电与维护需求、复杂路径规划等多种因素的耦合，此类系统的部署可能高度复杂。我们提出了一种基于连续近似方法的模型，用于评估服务权衡，该模型充分考虑了服务于在线食品配送的大规模人行道配送机器人系统的独特特征。该模型同时刻画了配送系统的初始成本与运营成本，并评估了约束条件及运营策略对部署的影响。通过最小化系统成本，可确定与系统设计相关的变量。首先，基于均质区域构建最小化问题，最优系统成本可推导为闭式表达式。通过对该表达式进行评估，可直接获得变量与系统成本之间的关系。随后，我们将该模型应用于纽约市的多个社区，以评估在实际场景中部署人行道配送机器人系统的成本。研究结果揭示了未来部署此类系统的潜力。