Estimation of Transfer Time Distribution Parameters with Automatic Fare Collection Data: Stochastic Frontier Model

Abstract

The uncertainty in walking and waiting transfer times at transit stops depends on the environmental conditions, vehicle schedule punctuality, and variations among individuals. Relying only on the mean values ignores such uncertainty and leads to improper transfer coordination. This paper provides a general framework to estimate the time distribution parameters of walking and waiting based on automatic-fare-collection data under the assumption that the distribution function is known. The proposed methodology contributes to the existing literature by providing a stochastic frontier model (SFM) that is adaptable to transit assignment models. The normal/exponential SFM is utilized to estimate distribution parameters based on the maximum-likelihood method. The methodology was applied to smart-card data from Japan to estimate the transfer walking- and waiting-time distributions between bus stops and rail stations. The results indicate a low disturbance in the observed data for walking time and that our assumptions regarding walking-time estimation were reliable. Furthermore, we quantified how the waiting time at a bus stop depends on variations in the service headway. These findings are expected to help in making more informed decisions to optimize transit schedules.