Drone delivery systems: job assignment and dimensioning

This article studies how to dimension and control at the system level a fleet of autonomous aerial vehicles delivering goods from depots to customers. Customer requests (jobs) arrive according to a space-time stochastic process. We compute a lower bound for the infrastructure expenditure required to achieve a certain expected delivery time. It is shown that job assignment policies can exhibit a tipping point behavior: One vehicle makes the difference between almost optimal delivery time and instability. This phenomenon calls for careful dimensioning of the system. We thus demonstrate the trade-off between financial costs and service quality. We propose a policy that assigns each incoming job to the vehicle that will do the job faster than other ones, seeking to minimize the overall workload in the system in the long term. This policy is scalable with the number of depots and vehicles, performs optimal in low load, and works well up to high loads. Simulations suggest that it stabilizes the system for any load if the number of vehicles per depot is sufficient.