On the existence of network Macroscopic Safety Diagrams: Theory, simulation and empirical evidence

Recent studies have proposed using well-defined relationships between network productivity and accumulation-otherwise known as Network or Macroscopic Fundamental Diagrams (network MFDs)-to model the dynamics of large-scale urban traffic networks. Network MFDs have been used to develop a variety of network-wide traffic control policies to improve a network's operational efficiency. However, the relationship between a network's MFD and its safety performance has not been well explored. This study proposes the existence of a Macroscopic Safety Diagram (MSD) that relates safety performance (e.g., likelihood of a crash occurring or number of vehicle conflicts observed) with the current network state (i.e., average density) in an urban traffic network. We theoretically posit a relationship between a network's MSD and its MFD based on the average maneuver envelop of vehicles traveling within the network. Based on this model, we show that the density associated with maximum crash propensity is always expected to be larger than the density associated with maximum network productivity. This finding suggests that congested states are not only inefficient, but they might also be associated with more crashes, which can be both more unsafe and lead to decreased network reliability. These theoretical results are validated using surrogate safety assessment metrics in microsimulation and limited field empirical data from a small arterial network in Riyadh, Kingdom of Saudi Arabia. The existence of such MSDs can be used to develop more comprehensive network-wide control policies that can ensure both safe, efficient and reliable network operations.