Robust dynamic routing of aircraft under uncertainty

Much of the delay in the US National Airspace System (NAS) arises from convective weather. One major objective of our research is to take a less conservative route, where we take a risk of higher delay to attain a better expected delay, instead of avoiding the bad weather zone completely. We address the single aircraft problem using a Markov decision process model and a stochastic dynamic programming algorithm, where the evolution of the weather is modeled as a stationary Markov chain. Our solution provides a dynamic routing strategy for an aircraft that minimizes the expected delay. A significant improvement in delay is obtained by using our methods over the traditional methods. In addition, we propose an algorithm for dynamic routing where the solution is robust with respect to the estimation errors of the storm probabilities. To the Bellman equations, which are derived in solving the dynamic routing strategy of an aircraft, we add a further requirements: we assume that the transition probabilities are unknown, but bounded within a convex set. The uncertainty described in our approach is based on likelihood functions.