Scheduling Automated Traffic on a Network of Roads

The authors consider the problem of scheduling automated traffic in a city. Such automatic scheduling can improve efficiency of the system by decreasing delays, increasing capacity, and easing congestion. The algorithms described in this paper can be thought of as which belongs to a layer in the corresponding control–communication–computational system, which is responsible for generating timed trajectories for individual vehicles [S. Graham, G. Baliga, and P. Kumar, “Issues in the convergence of control with communication and computing: Proliferation, architecture, design, services, and middleware,” in Proceedings of CDC ’04, Nassau, Bahamas, December 2004]. Each vehicle has a specified route from its origin to its destination, and the task of the scheduler is to provide timed trajectories for all vehicles, which follow the respective vehicles' routes and further ensure that no collisions or deadlock will result. The authors' approach reduces the problem to a discrete-time graph-scheduling problem, by defining an appropriate graph to model the road network. Their main result is a sufficient condition on the graph of the road network and on the initial distribution of vehicles, under which there exists a scheduling algorithm that is guaranteed to clear the system in finite time. The nature of this result allows the design of provably correct scheduling algorithms that require only a small portion of future routes of all vehicles to be known, and are consequently able to work in real time. The authors also address the optimization of performance with respect to delay, by focusing on the “one-step move” problem. Finding an optimal solution for the one-step problem would provide a greedy solution of the original network-wide scheduling problem, but is itself NP-hard. They present a polynomial time heuristic algorithm and evaluate its performance through simulations.