Optimal traffic control at smart intersections: Automated network fundamental diagram

Recent advances in artificial intelligence and wireless communication technologies have created great potential to reduce congestion in urban networks. In this research, we develop a stochastic analytical model for optimal control of communicant autonomous vehicles (CAVs) at smart intersections. We present the automated network fundamental diagram (ANFD) as a macro-level modeling tool for urban networks with smart intersections. In the proposed cooperative control strategy, we make use of the headway between the CAV platoons in each direction for consecutive passage of the platoons in the crossing direction through non-signalized intersections with no delay. For this to happen, the arrival and departure of platoons in crossing directions need to be synchronized. To improve system robustness (synchronization success probability), we allow a marginal gap between arrival and departure of the consecutive platoons in crossing directions to make up for operational error in the synchronization process. We then develop a stochastic traffic model for the smart intersections. Our results show that the effects of increasing the platoon size and the marginal gap length on the network capacity are not always positive. In fact, the capacity can be maximized by optimizing these cooperative control variables. We analytically solve the traffic optimization problem for the platoon size and marginal gap length and derive a closed-form solution for a normal distribution of the operational error. The performance of the network with smart intersections is presented by a stochastic ANFD, derived analytically and verified numerically using the results of a simulation model. The simulation results show that optimizing the control variables increases the capacity by 138% when the error standard deviation is 0.1 s.