The degradation of road network performance due to incidents is a major concern to traffic operators. The development of urban traffic incident management systems requires a comprehensive understanding of traffic dynamics during incidents. Recently, the concept of the macroscopic fundamental diagram (MFD) contributed to such an understanding and has been used in a wide range of applications. However, the MFD is merely reproducible under recurring traffic patterns. Motivated by a few studies which argue the existence of the MFD with a clockwise hysteresis loop during incidents, we tackle this limitation of the MFD and propose a framework to study the characteristics of the MFD under non-recurring congestion. More specifically, we introduce a criticality score (CS) which represents network redundancy and postulate that links with a higher level of CS impose a larger hysteresis loop on the MFD. We design an experiment in a microscopic traffic simulation to study the relation of closed links and the resulting MFDs. The results confirm our postulation and we observe that links with similar CS have a comparable impact on the shape of the MFD. The main contribution of this paper is the possibility to develop a framework for incident detection in urban networks under limited sensor coverage. However, the findings of the study may strongly rely on the assumptions, for instance, the network structure, the OD pairs, and drivers route choice during incidents. Thus, future studies are required to study other network topologies as well as more realistic driver route choice during incidents.

The well-known Lighthill-Whitham-Richards (LWR) theory is the fundamental pillar for most macroscopic traffic models. In the past, many methods were developed to numerically derive solutions for LWR problems. Examples for such numerical solution schemes are the cell transmission model, the link transmission model, and the variational theory (VT) of traffic flow. So far, the latter framework found applications in the fields of traffic modelling, macroscopic fundamental diagram estimation, multi-modal traffic analyses, and data fusion. However, these studies apply VT only at the link or corridor level. To the best of our knowledge, there is no methodology yet to apply VT at the network level. We address this gap by developing a VT-based framework applicable to networks. Our model allows us to account for source terms (e.g. inflows and outflows at intersections) and the propagation of spillbacks between adjacent corridors consistent with kinematic wave theory. We show that the trajectories extracted from a microscopic simulation fit the predicted traffic states from our model for a simple intersection with both source terms and spillbacks. We also use this simple example to illustrate the accuracy of the proposed model. Additionally, we apply our model to the Sioux Falls network and again compare the results to those from a microscopic simulation. Our results indicate a close fit of traffic states, but with substantially lower computational cost. The developed methodology is useful for network-wide traffic state estimations in real-time, or other applications within a model-based optimization framework.

The growing popularity of mobility-on-demand fleets increases the importance to understand the impact of mobility-on-demand fleets on transportation networks and how to regulate them. For this purpose, transportation network simulations are required to contain corresponding routing methods. We study the trade-off between computational efficiency and routing accuracy of different approaches to routing fleets in a dynamic network simulation with endogenous edge travel times: a computationally cheap but less accurate Network Fundamental Diagram (NFD) based method and a more typical Dynamic Traffic Assignment (DTA) based method. The NFD-based approach models network dynamics with a network travel time factor that is determined by the current average network speed and scales free-flow travel times. We analyze the different computational costs of the approaches in a case study for 10,000 origin-destination (OD) pairs in a network of the city of Munich, Germany that reveals speedup factors in the range of 100. The trade-off for this is less accurate travel time estimations for individual OD pairs. Results indicate that the NFD-based approach overestimates the DTA-based travel times, especially when the network is congested. Adjusting the network travel time factor based on pre-processed DTA results, the NFD-based routing approach represents a computationally very efficient methodology that also captures traffic dynamics in an aggregated way.