A Bayesian modelling framework for individual passenger’s probabilistic route choices: A case study on the London underground

This study applies Bayesian inference in an attempt to trace probabilistic route choices made by public-transport users, particularly on an underground rail network. Within the scope of this paper, a journey of any passenger travelling from an origin (O) to a destination (D) is investigated on a station basis, where an automatic fare collection system holds a wealth of individuals’ travel data from their smart cards being used. Thus, a sufficiently large sample of the smartcard users’ journey times can be obtained by calculating the time-stamped O-D records. Nonetheless, transit routes that the passengers actually chose were not recorded, and hence unobservable. Based on the journey time data, a mixture model is formulated for estimating posterior probabilities that a passenger was likely to have chosen any route from all possible alternatives, that is, the probabilistic route choices, between a given pair of O-D stations. The estimated results are fundamentally dependent upon observational data of the passengers’ journey times being modelled by mixture distributions. Accordingly, proportions of the passenger traffic flowing on the different transit routes are calculated as well, in view of the O-D travel demand. The inferences of traffic proportions are validated by comparing them to survey findings, which in turn affords corroborative evidence supporting the estimated results of the individuals’ probabilistic route choices. This approach is illustrated with a case study on one pair of O-D stations inside the central zone of the London Underground network, by taking advantage of the Oyster smartcard data. Both Gaussian and lognormal mixture models are tested on the selected O-D example and the outcome demonstrates a good performance of the proposed method. In addition, limitations and potential practical applications of the modelling framework are also discussed.