Improvements to road networks have to be planned, since drivers switch their routes to take advantage of these improvements. Additionally, transportation networks reach different user equilibria as a consequence of the route changes. Therefore, in transportation planning and engineering, a basic task is to analyze the performance of road network user equilibria, subject to different improvement strategies, for present or future demand levels during peak periods. Existing models of user equilibrium are either based on unrealistic estimation of travel times or are too complicated to calculate. This research is fundamental and provides an alternative model of user equilibrium, which is based on a realistic estimation of travel times that can be efficiently calculated for large-scale networks. The new model enables the development of alternative methods for transportation planning, network design, traffic control, and congestion pricing. These methods are important for improving the safety, mobility, and environmental impacts of a transportation system. This research addresses a problem that is foundational for transportation and involves researchers, and practitioners.
During peak periods, traffic reaches a stationary state in a road network, where the locations and sizes of queues are relatively constant for a sustained period of time. Traditional static user equilibrium during peak periods is formulated based on link performance functions, which fail to capture realistic traffic characteristics on links or through junctions; while the dynamic traffic assignment problems based on realistic traffic flow models are too complicated to analyze and compute. This research fills the gap between network traffic flow theory and traffic assignment in stationary road networks. The research uses network kinematic wave theory to establish existence, stability, and numerical methods of stationary states in a road network, derives physically meaningful formulas for calculating travel times on stationary links in terms of both link flow-rates and congestion levels, explores various formulations of user equilibria and system optima.
