A Three-stage Algorithm for Coordinate Controlling of Multi-intersection Signal

It is understandable that the traffic light plans at one intersection interact with the adjacent intersections in traffic networks. It cannot be negligible to consider that inflow vehicles are not from adjacent intersections and that outflow vehicles are the connection links of two adjacent intersections. In this study, signal adaptive control is formulated a convex model for multi-intersection traffic network and a three-stage algorithm to solve the model. Before modeling, to simplify the optimization model, the "T" model of the intersections are switched into the + model. In the model, first, the arrival rates of connection lanes, which are utilized to connect the outside traffic network, should be adaptively estimated. Then, the difference between the number of inflow vehicles not from adjacent intersections and the number of outflow vehicles from the adjacent intersections is adaptively predicted. Next, the phases of adjacent intersections are matched. The changeable probability of the vehicles in the connection links is computed for transition probability equation. Focusing on the estimated arrival rates, phases are matched and the transition probability of the vehicles is calculated. A three-stage algorithm is proposed. The first stage adaptively estimates the arrival rates of the entry lanes, which are connected to the outside traffic network, by nonlinear methods or machine learning models (Li et al., 2020a). The difference between the number of inflow vehicles does not come from the adjacent intersections on the entrance lanes and that the number of outflow vehicles comes from the adjacent intersections is also adaptively computed in the first stage by an automatic update iterated algorithm. The second stage adaptively matches the phases of the adjacent intersections by matching components in the model and adaptively determines the transition probabilities of the intersections in the traffic network by an automatic update fraction. In the last stage, some classical algorithms for the convex model are utilized to solve the model. Finally, some methods are employed to compare the proposed model and algorithm. In the first three experiments, that model and algorithm can optimize the signa plans for multi-intersection in the intersection traffic network, and the model and algorithm are effective. The real data is tested in the fourth experiment. The results show that the model and algorithm are also adaptive to real case in theory. In the last experiment, five other methods are employed to compare to the proposed method. The queueing lengths of each proposed intersection are smaller than those with the other approaches, and the optimal values of the proposed model is also smaller than those with the other methods. The results of the numerical experiments indicate that the model and the algorithm are effective and that the optimization model and the three-state algorithm could be more reasonable for the plans of multi-intersections than the state of the arts.