Estimation of Platform Waiting Time Distribution Considering Service Reliability Based on Smart Card Data and Performance Reports

Document Type

Journal Article

Publication Date


Subject Area

place - europe, place - urban, mode - subway/metro, technology - ticketing systems, operations - reliability, planning - service improvement, ridership - behaviour


smart card data, service reliability, platform waiting time, passenger flow


The estimation of platform waiting time has so far received little attention. This research aimed to estimate platform waiting time distributions on the London Underground, considering travel time variability by using smart card data that were supplemented by performance reports. The on-train and ticket gate to platform walking times were assumed to be normally distributed and were matched with the trip time recorded by the smart cards to estimate the platform waiting time distribution. The stochastic frontier model was used, and its parameters were estimated by the maximum likelihood method. The cost frontier function was used to represent the relation between the travel time recorded in the smart card data as an output and the on-train time and walking time between the ticket gate and the platform as inputs. All estimated parameters were statistically significant, as shown by p-values. Comparing the travel time values estimated by the proposed model with the times recorded recorded in the smart card data shows a goodness-of-fit coefficient of determination of more than 95%. The estimation proved to have quick convergence and was computationally efficient. The results could facilitate improvements in transit service reliability analysis and passenger flow assignment. Matching the obtained distributions with the observed smart card data will help with estimating route choice behavior that can validate current transit assignment models.


Permission to publish the abstract has been given by Transportation Research Board, Washington, copyright remains with them.