The science of cities aims to model urban phenomena as aggregate properties that are functions of a system’s variables. Following this line of research, this study seeks to combine two well-known approaches in network and transportation science: (i) The macroscopic fundamental diagram (MFD), which examines the characteristics of urban traffic flow at the network level, including the relationship between flow, density, and speed. (ii) Percolation theory, which investigates the topological and dynamical aspects of complex networks, including traffic networks. Combining these two approaches, we find that the maximum number of congested clusters and the maximum MFD flow occur at the same moment, precluding network percolation (i.e. traffic collapse). These insights describe the transition of the average network flow from the uncongested phase to the congested phase in parallel with the percolation transition from sporadic congested links to a large, congested cluster of links. These results can help to better understand network resilience and the mechanisms behind the propagation of traffic congestion and the resulting traffic collapse.

The macroscopic fundamental diagram (MFD) measures network-level traffic performance of urban road networks. Large-scale networks are normally partitioned into homogeneous regions in relation to road network topology and traffic dynamics. Existing partitioning algorithms rely on unbiased data. Unfortunately, widely available stationary traffic sensors introduce a spatial bias and may fail to identify meaningful regions for MFD estimations. Thus, it is crucial to revisit and develop stationary-sensor-based partitioning algorithm. This paper proposes an alternative two-step partitioning algorithm for MFD estimations based on information collected solely from stationary sensors. In a first step, possible partitioning outcomes are generated in the road networks using random walks. In a second step, the regions’ MFDs are estimated under every possible partitioning outcome. Based on previous work, an indicator is proposed to evaluate the traffic heterogeneity in regions. The proposed partitioning approach is tested with an abstract grid network and empirical data from Zurich. In addition, the results are compared with an algorithm that disregards stationary detectors’ biases. The results demonstrate that the proposed approach performs well for obtaining the quasi-optimal network partitions yielding the lowest heterogeneity among all possible partition outcomes. The presented approach not only complements existing literature, but also offers practice-oriented solutions for transport authorities to estimate the MFDs with their available data.