A mixed integer programming formulation and scalable solution algorithms for traffic control coordination across multiple intersections based on vehicle space-time trajectories

Thanks to the development of mobile computing, novel traffic data sources are emerging as the promising building blocks for more effective traffic control strategies. It is expected that the vehicle space-time trajectories will become ubiquitously available in foreseeable future. Real-time trajectory data will provide full-spectrum pattern of traffic dynamics among multiple intersections. In this paper, we present a new traffic control representation for multiple intersections. A new multi-intersection phase (MI-phase) is proposed to represent safe vehicle movements across a few tightly connected intersections. All the intersections are also viewed as one integral “super intersection” within which vehicles move according to their planned paths. Through scheduling the sequence and durations of MI-phases over time, the vehicles will be crossing intersections with minimal delays. This approach can provide more flexibilities for traffic control coordination than the traditional Cycle-Split-Offset approach. A linear integer programming formulation is presented for joint optimization of vehicle space-time trajectories and traffic control. We also design a scalable optimization frame for real-world traffic control optimization, referred to as “Lagrangian decomposition with subproblem approximation” approaches. In this new framework, we construct the dynamic network loading based lower bound estimator (DNL-LBE) in which the relaxed constraints and sensitivity to the Lagrangian multiplier prices are explicitly considered while vehicular flows are being loaded. By doing so, the complex controlled dynamic network loading process can be represented through Lagrangian multipliers interfacing with the MI-phase optimization module (then solved by Dynamic Programming). This approach can facilitate price-based search heuristics to find high quality solutions for both vehicular space-time trajectories and traffic control plans without increasing the overall computing complexity. The efficiency of the proposed optimization framework is further improved through multiple advanced computing techniques. In the end, one demonstrative and one real-world example are provided to show the performance of the new approach.