Understanding traffic statics and dynamics in urban networks is very critical and also helpful in developing signal control strategies and solving network traffic problems. In this paper, a link queue approach is used to study the traffic statics and dynamics in both a double-ring network and a homogeneous grid network with signals. Traffic stationary states in the signalized double-ring network are analytically solved, and two types of stationary states are found: periodical states and gridlock states, both of which are closely related to the retaining ratios, cycle lengths, and initial densities. Stability properties of these stationary states are analyzed in the signalized double-ring network. It is found that the gridlock states are asymptotically stable when the retaining ratios are greater than 0.5, while they are unstable when the retaining ratios are smaller than or equal to 0.5. Macroscopic fundamental diagrams are derived based on the stationary states in the signalized double-ring network with different retaining ratios and cycle lengths. Simulation results in a 6 by 6 grid network show that the signalized grid network is consistent with the signalized double-ring network when the retaining ratios are deterministic.
↧