A novel relationship model between signal timing, queue length and travel speed

This paper aims to determine the relationship between signal timing, queue length and travel speed. To this end, based on the kinematics theory and the spatio-temporal features of the vehicle trajectories, the operation process of traffic flow is first abstracted into two stages: traveling freely on the road section and queuing at the intersection. The problem solved is then transformed into determining the correlation between signal timing, queue length and average vehicle delay. Second, since vehicles move and stop dynamically, it is difficult to directly construct the model of delay and the other two parameters. To cope with this problem, the paper proposes an innovative concept — equivalent queue length, which enables vehicles to move continuously under the premise of ensuring the same number of vehicles before and after the equivalence. After this series of conversions, the relationship between average vehicle delay and equivalent queue length is obtained. Third, the calculation models of average travel speed are established according to timing parameters and queue length under different road network structures. Finally, multi-perspective case studies are provided to demonstrate the impressive performance of the proposed models. It is also found that the multi-dimensional optimization control of relationship model can significantly improve the service level of the road. The findings can provide support for the optimization of signal control and speed guidance.