The Piecewise Constant/Linear Solution for Dynamic User Equilibrium

The aim of this work is to increase the precision of the solution of dynamic user equilibrium assuming that the computation takes a reasonable time so that the solution is useful in practice. The proposed method replaces the classical grid-based solution by a near continuous-time solution based on piecewise linear/constant functions that removes a lot of disadvantage of discretization. The testing shows that the precision of the solution can be easily driven by a few approximation parameters that can be changed during computation. Using the proposed method, the near continuous time solution of the dynamic user equilibrium for a real size network can be computed in reasonable computation time.