A continuous space and time representation of dynamic road traffic flows consistent with hydrodynamic traffic theory

We present an approach to solving the dynamic network loading problem (DNLP). The approach views the roadway in terms of the underlying densities, segmenting the roadway into blocks of constant density. Using hydrodynamic theory, we describe how these blocks can be used to provide a solution method to the DNLP with a continuous representation of space and time which is readily implementable. This solution method provides an exact solution with piece-wise linear link travel times. We present a pseudocode description of the algorithm and discuss a sample computer implementation.