Low-rank approximation of path-based traffic network models

Traffic network models have been widely used in transportation planning and management. However, the use of path sets in certain models introduces practical issues to the applications of those models in real world, due to the large number of paths in a network that usually cannot be explicitly enumerated. To reduce the size of the path set and thus make such network models more applicable in practice, we propose a novel method to generate a small hypothetical path set tailored for network flow models in a way analogous to low-rank matrix approximation. The generated hypothetical path set are no longer based on the topological structure of the network, but on traffic flows in the network, making it possible to represent the information of the original path set in the context of network modeling with a much smaller set. The hypothetical path set is created through fitting a surrogate traffic assignment model, which could be employed as a replacement of the original model in a variety of transportation network design problems. In addition, the reduced hypothetical path set itself, even though does not fully preserve the physical information of the original path set, may also be directly used in network modeling. As an example we show an efficient way to estimate origin-destination travel demands with the reduced hypothetical path set. Proposed methods are examined on four toy networks and one real-world network. Numerical experiments show the proposed methods could well approximate the original network models, and meanwhile bring nontrivial improvement in run time efficiency and large-scale data calibration of path-based network models.