Stability analysis for distributed perimeter controlled traffic networks

Perimeter control has shown great promise in mitigating congestion and managing heterogeneity in urban traffic networks. A highly heterogeneous traffic network can be partitioned into a great number of homogeneous regions, and distributed perimeter control structures are potentially useful due to fewer communication requirements. Disturbance propagation analysis is crucial in multi-region perimeter control, as a network instability issue arises when the disturbance is magnified while propagating through the regions. This paper establishes sufficient network stability conditions under which the disturbance is attenuated through propagation under a distributed control structure for a tree network. It is shown that these conditions have the same information structure as the distributed controller. Moreover, the number of these conditions grows linearly with the number of regions. Finally, the proposed conditions are verified via simulation.