Modelling traffic flows and estimating road travel times in transportation network under dynamic disturbances

Traffic congestion is a common phenomenon in road transportation networks, especially during peak hours. More accurate prediction of dynamic traffic flows is very important for traffic control and management. However, disturbances caused by the time-varying origin-destination matrix, dynamic route choices, and disruptions make the modelling of traffic flows difficult. Therefore, this study focuses on modelling the dynamic evolution processes of traffic flows under disturbances and estimating dynamic travel times for arbitrary moment. A revised Lighthill–Whitham–Richards (RLWR) model with non-equilibrium states is presented to describe the dynamic traffic states on individual roads, and the ripple-spreading model (RSM) is integrated to investigate the interactions among several shockwaves from multiple roads. We propose a hybrid RLWR–RSM to model the congestion and congestion-recovery propagations in an entire transportation network. After predicting the dynamic traffic flows by the RLWR–RSM, the road travel times for arbitrary moment were estimated. Theoretical analyses indicated that (1) the RLWR–RSM inherits the advantages of macroscopic traffic flow models and integrates the characteristics of both low- and high-order continuum models, and (2) the RLWR–RSM considers multiple disturbances. From numerical experiments with various inputs, the variation in travel times under disturbances was investigated, and this further demonstrated that (1) the modelled dynamic traffic flows have four basic properties, and (2) the experimental results validate the theoretical analyses. In addition, the RLWR–RSM can explain several distinct traffic phenomena. Finally, the estimated travel times can provide decision supports for vehicle navigation.