Active hyperpaths in transit networks

This paper examines several important computational aspects of a recently proposed passenger assignment model on transit networks. This model uses a new directed graph framework-the F-hypergraph-to capture the dynamics and stochastic routing aspects embedded in urban transit networks with overlapping lines. After a short introduction to directed hypergraphs, it is shown that a transit network may be completely described by a support F-hypergraph. The shortest hyperpath algorithms are then reviewed in relation to the generation of active hyperpaths-hyperpaths with positive flows. Finally, a stochastic routing model, based on a logit distribution function, which obviates the explicit enumeration of paths and hyperpaths is presented. This model may be interpreted as a generalization of Dial’s model on ordinary graphs to directed hypergraphs.