The boundary between random and non-random passenger arrivals: robust empirical evidence and economic implications

In this paper, we investigate the influence of train headways on passenger platform wait times using automated data from the London Underground metro system. For high frequency services, the literature suggests that passenger arrivals are random and that under perfectly random conditions with all other factors held constant, wait times are equivalent to half of the headway between trains. We test this hypothesis using large-scale smart card and vehicle location data, which enables the extraction of access times from total passenger journey times as well as the precise measurement of train headways. Using a semi para-metric regression modelling framework, we generate non-linear estimates of the relationship between access times and headway while conditioning for other service supply and demand factors. Marginal platform wait times are then derived numerically via an exposure-response model framework which accounts for potential confounding between the walking and waiting components of access times, thus enabling quantification of the unbiased impact of headways on wait times. For three lines in central London, we observe that marginal wait times transition from greater than half of the headway to approximately one third of the headway astrain frequencies decrease. The transition occurs in the range between 2-3 minute headways, lower than earlier estimates in the literature. A series of numerical simulations illustrate the importance of waiting time sensitivity in the optimisation of public transport services. In comparison with the standard wait time assumption, our exercise reveals that the degree of density economies is milder than what the literature suggests, and this may neutralise some of the economic justifications of high public transport subsidie