Estimation of metro network passenger delay from individual trajectories

Smart card data enables the estimation of passenger delays throughout the public transit network. However, this delay is measured per passenger trajectory and not per network component. The implication is that it is currently not possible to identify the contribution of individual system components – stations and track segments – to overall passenger delay and thus prioritize investments and disruption management measures accordingly. To this end, we propose a novel method for attributing passenger delays to individual transit network elements from individual passenger trajectories. We decompose the delay along a passenger trajectory into its corresponding track segment delay, initial waiting time and transfer delay. Using these delay components, we construct a solvable system of equations, using which the delays on each network component can be computed. The estimation method is demonstrated on one year of data from the Washington DC metro network. Our approach produces promising results by compressing millions of individual trajectories into 3D networks, leading to a dimensionality reduction of 94%. Moreover, the mean slack variable value (that can be interpreted as proxies for estimation errors) is smaller than five seconds per passenger, and has the desired positive sign for almost 90% of all travelers. Applications using the estimation results include revealing network-wide recurrent delay patterns, modeling delay propagation and detecting disruptions.