Connecting networkwide travel time reliability and the network fundamental diagram of traffic flow

The existence of the network fundamental diagram (NFD) has been established at the urban network scale. It relates three traffic descriptors: speed, density, and flow. However, its deterministic nature does not convey the underlying variability within the network. In contrast, travel time reliability as a network performance descriptor is of growing concern to both the traveling public and traffic managers and policy makers. The objectives of this paper were to extend travel time reliability modeling from the link-path level to the network level and to connect overall network variability to NFD. Robust relationships between travel time variability and network density and flow rate were analytically derived, investigated, and validated with both simulated and real-world trajectory data. The distance-weighted standard deviation of travel time rate, as a measure of travel time variability, was found to increase monotonically with network density. A maximum network flow rate existed beyond which network travel time reliability deteriorated at a much faster pace. The results also suggest that these relationships are inherent network properties (signature) that are independent of demand level. The effects of en route information on the proposed relationships were also studied. The results showed that en route information reduced network travel time variability. The findings provide a strong connection between NFD and travel time variability, and this connection can be used further for modeling of network travel time reliability and assessment of measures intended to improve reliability of travel in a network.