Decentralized algorithms for stochastic and dynamic vehicle routing with general demand distribution

We present decentralized algorithms for a class of stochastic and dynamic vehicle routing problems, known as the multiple-vehicle dynamic traveling repairperson problem (m-DTRP), in which demands arrive randomly over time and their locations have an arbitrary distribution, and the objective is to minimize the average waiting time between the appearance of a demand and the time it is visited by a vehicle. The best previously known control algorithms rely on centralized, a-priori task assignment, and are therefore of limited applicability in scenarios involving large ad-hoc networks of autonomous vehicles. By combining results from geometric probability and locational optimization, we provide a policy that solves, providing a constant-factor approximation to the optimal achievable performance, the decentralized version of the m-DTRP; such policy (i) does not rely on centralized and a priori task assignment, (ii) is spatially distributed, scalable to large networks, and adaptive to network changes. Simulation results are presented and discussed.