  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.
