Introducing pattern graph rewriting in novel spatial aggregation procedures for a class of traffic assignment models

Abstract

In this study two novel spatial aggregation methods are presented compatible with a class of traffic assignment models. Both methods are formalized using a category theoretical approach. While this type of formalization is new to the field of transport, it is well known in other fields that require tools to allow for reasoning on complex structures. The method presented stems from a method originally developed to deal with quantum physical processes. The first benefit of adopting this formalization technique is that it provides an intuitive graphical representation while having a rigorous mathematical underpinning. Secondly, it bears close resemblances to regular expressions and functional programming techniques giving insights in how to potentially construct solvers (i.e. algorithms). The aggregation methods proposed in this paper are compatible with traffic assignment procedures utilising a path travel time function consisting out of two components, namely (i) a flow invariant component representing free flow travel time, and (ii) a flow dependent component representing queuing delays. By exploiting the fact that, in practice, most large scale networks only have a small portion of the network exhibiting queuing delays, this method aims at decomposing the network into a constant free flowing part to compute once and a, much smaller, demand varying delay part that requires recomputation across demand scenarios. It is demonstrated that under certain conditions this procedure is lossless. On top of the decomposition method, a path set reduction method is proposed. This method reduces the path set to the minimal path set which further decreases computational cost. A large scale case study is presented to demonstrate the proposed methods can reduce computation times to less than 5% of the original without loss of accuracy.