Continuous Dynamic Network Loading Models

The dynamic network equilibrium models have a renewed interest in Europe, Japan and North America. This is due to the design and implementation of Advanced Transport Telematic (ATT) systems require of network models which may evaluate dynamically such actions. The main modeling approaches for the dynamic network equilibrium are: Aggregated macroscopic models in which traffic flows are regarded in an aggregated way as a fluid and microscopic approaches in which it is tried to understand the behavior of the system by modeling the individual vehicles. See Barceló (1998) for a overview of some currently used microscopic traffic simulators. Daganzo (1995) considers that a basic theory of macroscopic traffic models for networks in the context of dynamic assignment would have to include a the least realistic models of: 1. Traffic behavior when the vehicle paths are known. This sub model is known as the dynamic network loading problem (DNLP) and consists of finding temporal arc volumes, arc travel times and path travel times given time-dependent path flow rates for a given time period. 2. Path choice when the time-varying arc times are known. 3. Equilibrium to reconcile the predictions items 1 and 2. The macroscopic models for DNLP can be classified according to several criterion (see Wu (1998)). In this paper we consider two categories defined by whether arc exit functions are used or not: 1. Travel time function models (Astarita (1996), Ran and Boyce (1996), Wu (1998), Xu (1999)). These approaches assume that the travel time from the beginning to the end of an arc of the network can be expressed as an increasing function of the flow on