Analytical Dynamic Network Loading Problem: Formulation, Solution Algorithms, and Computer Implementations

Abstract

The dynamic network loading problem is considered. This problem is at the heart of analytical approaches to dynamic traffic assignment models. Given path flow rate and link travel time functions, the dynamic network loading problem consists of determining time-dependent network flow conditions, such as link travel times, total number of vehicles on links, and link inflow and outflow rates. The dynamic network loading problem is formulated as a continuous-time system of nonlinear equations expressing link dynamics, flow conservation, flow propagation, and boundary constraints. A discrete-time version of the continuoustime model is developed to design solution algorithms. Two solution algorithms are developed and implemented efficiently. Techniques are described that were designed to reduce memory usage and computation times of these solution algorithms. Computational results with a realworld traffic network emanating from the Amsterdam A10 beltway, containing 300 nodes, 1,500 paths, 1,000 origin-destination pairs, and 2 h of analysis period indicate that the developed computer implementations can solve the network loading problem in 2 min when a small discretization interval of 3.5 s is used.