We consider the problem of scheduling automated traffic in a city. Each car has a specified route from its origin to its destination, and the task of the scheduler is to provide timed trajectories for all cars, which follow the respective cars' routes and further ensure that no collisions or deadlock will result Our approach reduces the problem to a discrete-time graph scheduling problem, by defining an appropriate graph to model the road network. Our main result is a sufficient condition on the graph of the road network and on the initial distribution of cars, 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 cars to be known, and are consequently able to work in real time. We 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. We present a polynomial time heuristic algorithm and evaluate its performance through simulations.