Day-to-day and within-day network dynamics encapsulating hyperbolic traffic behavior

In most historical studies, link cost function applied in solving the dynamic traffic assignment problem is assumed as a separable function of link flaw itself. Further developments of a non-linear theory for the network dynamics in the presence of hyperbolic traffic behavior are presented in this paper. By dividing a time period of interest into several minute intervals, both day-to-day and within-day evolutions of system variables are embedded in the proposed formulation simultaneously. In particular, dynamic traffic flow model, the Lighthill-Whitham-Richards model, is introduced into whole system dynamics and the corresponding path cost operator is also derived. Based on this methodology, the network traffic dynamics simulator (NTDS) is developed and the simulation results of a real road network at Hsinchu Science-based Industrial Park (HSIP) are also presented. We numerically show that the steady state of proposed dynamic system satisfies the Wardrop's user equilibrium.