The Continuous Dynamic Network Loading Problem: A Mathematical Formulation and Solution Method

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The continuous dynamic network problem aims to find, on a congested network, temporal network flows, arc travel times, and path travel times given time-dependent path flow rates for a given time period. This problem may be considered as a subproblem of a temporal (dynamic) traffic assignment problem. This paper studies this problem and formulates it as a system of functional equations. For computational purposes, the authors develop a polynomial approximation which is almost equivalent to the original formulation on a set of finite discrete points. The approximation formulation is a finite dimensional system of equations which is solved as an optimization problem. The paper includes several numerical examples to illustrate the approach developed.

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