Efficacy of decentralized traffic signal controllers on stabilizing heterogeneous urban grid network

Macroscopic Fundamental Diagrams (MFDs) are valuable for designing and evaluating network-wide traffic management schemes. Since obtaining empirical MFDs can be expensive, analytical methodologies are crucial to estimate variations in MFD shapes under different control strategies and predict their efficacy in mitigating congestion. Analyses of urban grid networks' abstractions can provide an inexpensive methodology to obtain a qualitative understanding of impacts of control policies. However, existing abstractions are valid only for simple intersection layouts with unidirectional and single-lane links and two conflicting movement groups. Naturally, the real intersections are more complex, with multiple incoming and outgoing lanes, heterogeneous incoming links' capacities and several conflicting movement groups. To this end, we consider a grid network with differences in capacities of horizontal and vertical directions, allowing us to investigate the characteristics of control policies that can avoid pernicious gridlock in heterogeneous networks. We develop a new, more comprehensive network abstraction of such grid networks to analyze and compare the impacts of two families of decentralized Traffic Signal Controllers (TSCs) on the network's stability. The obtained theoretical insights are verified using microsimulation results of grid networks with multiple signalized intersections. The analyses suggest that considering both upstream and downstream congestion information in deciding signal plans can encourage more evenly distributed traffic in the network, making them more robust and effective at all congestion levels. The study provides a framework to understand general expectations from decentralized control policies when network inhomogeneity arises due to variations in incoming link capacities and turning directions.