A stochastic optimal control approach for real-time traffic routing considering demand uncertainties and travelers’ choice heterogeneity

This paper develops a theoretical approach to identify optimal traffic routing strategy for managing transportation systems. It obtains the optimal traffic diversion ratio to each route that can be achieved in real time through cutting-edge sensing and vehicle-infrastructure communication technologies. We minimize the expected total travel time of all travelers in the network by providing and updating routing advice (or incentives) to travelers in real time. The system-optimum traffic routing problem is modeled using the stochastic control approach where demand uncertainty and travelers’ heterogeneity are explicitly considered over time. The approach is generic in the sense that the optimal routing strategies can be achieved through various technologies, such as connected vehicle technologies, navigation systems, variable message signs, dynamic pricing, etc. For a two-route representative network, we use dynamic programming to derive and approximate the analytical solution of the optimal routing policy for each time interval. The optimal diversion ratio can be updated solely upon the traffic counts measured along the preferred route in real time. The general rule is, with a high probability, to minimize the congestion and keep the maximum flow performance on the preferred route from the beginning of the peak hours. Towards the end of the peak hours, the optimal policy would allow more intensive use of the preferred route resulting over-saturation, whereas keeping the minimal use of the alternative route. The analytical solution is validated and examined in a synthesized network and a real-world network in California. It is found that it consistently outperforms the deterministic solution, and its resultant system performance is also reasonably close to the benchmark system optimum where true demand could be precisely known one day ahead.