Steady-State Solution On A Simple Single Origin-Destination Road Network Based On LWR Model And User-Equilibrium Conditions

The dissertation studies a steady-state solution to the dynamic traffic flow model on a road network,which satisfies the user-equilibrium conditions but may have shock structures on road sections.For a simple road network with just one Origin(O)and one Destination(D),it discusses the method for solving the problem in detail.The main contents are briefly introduced in the following.For a composite roads unit,which is defined as a set of roads connected by an upstream and a downstream junctions,the user-equilibrium conditions are discussed in detail.Accordingly,without shocks we derive the user-equilibrium curves and the fundamental diagram on the roads unit,which respectively help determine the densities on all roads and the total flow,given the average density that is over the area of the unit.Many properties of the fundamental diagram are indicated with strictly mathematical proofs.For the aforementioned one OD road network,we indicate that shock structures have to be introduced to guarantee the existence of solution if and only if total number of vehicles falls into a specific interval,when the flow is limited by road conditions outside in the downstream,or when the flow has already reached the capacity at the bottleneck junction.As a consequence,we are able to completely establish the correlation between the total number of vehicles and the steady-state solution.Moreover,the solution is uniquely determined by introducing priority coefficients for vehicles in higher density region of the shock to enter the downstream road sections.The argument implies that,without shocks the steady-state solution assumed in the classical Transportation Assignment Theory does not exist unless there are no any bottleneck junctions on the road network.A numerical scheme of the LWR(Lighthill-Whitham-Richards)model is designed for evolution of traffic flow into the discussed steady-state solution.Based upon the monotone scheme of the model and the Riemann solver at the junction,the main task for the designing is to determine the percentages of traffic flow at upstream road sections for their entering the downstream road sections,according to the analytical properties of the steady-state solution,i.e.,the user-equilibrium conditions and the information about the priority coefficients.According to the coefficients,we can determine the boundary conditions for traffic flow entering the downstream road sections through the junction.The convergence is observed for numeral simulation on simple one OD road networks with a 1 × 2 and a 2 × 1 junctions and with two 2 × 2junctions,respectively.This research work significantly improves a remarkable shortcoming in classical Transportation Assignment Theory,which assumes that the density is constant in road sections.Therefore,it will surely promote new studies in the related research fields.Moreover,it will provide with key theoretical support and robust modeling and simulation scheme for implementation of equilibrium flow assignments under the background of the smart transportation system.