SPATIAL AND TEMPORAL ANALYSES ABOUT DISTRIBUTIONS OF WALKING SPEED AND DISTANCES
Nominated for The Neil Mansfield Award
Xiaoyan Xie, École nationale des ponts et chaussées, Fabien Leurent, École nationale des ponts et chaussées
Spatial and temporal analyses about distributions of walking speed and distance are presented by using our novel stochastic model, which could handle modern data(Big data), to estimate indirectly those distributions along an urban rail transit line.
Study of public transport Quality of Service (QoS) in cities is a topic of increasing concerns in past decade. Passenger’s walking speed and walking distance along an urban rail transit line are two key factors, which impact passenger’s journey time, a key factor of the QoS of a public transit system (TCQSM, 2013). Spatial and temporal analyses about distributions of walking speed and distance were very scarce in the literature, because the estimation of those factors is still a complicated and difficult task, even if the availability of large amounts of modern data (big data), Automatic Fare Collection (AFC) data and Automatic Vehicle Location (AVL) data, individual walking speed keeps changing throughout the inter-individual journey. Thereby, the development of an applicable analysis approach including mathematical model which is able to accommodate complex travel dynamics and deals with modern data sets is required.
To accomplish that, the objective of this paper is to depict spatial and temporal analyses about distributions of walking speed and distance based on our novel stochastic model, which could handle modern data sets to estimate indirectly the distributions of those factors, by extending the primary work of (Leurent & Xie, 2016) inspiration for the model stems from (Leurent, 2000, 2001) who have provided stochastic models of roadway individual trips. According to passengers’ tap-in and tap-out times, which include elementary times, such as walking time, waiting time and in-vehicle time, along an urban transit line and cross with vehicles’ departure and arrival times at access and egress stations, our model reconstructs the load of passengers for each train by assigning each passenger the train probabilistically during the studied period. Analytical formulae are provided for the probability to choose a vehicle run at access station, the distribution of tap-out times at egress station and the general probability density along the line. In the end, a statistic estimation problem is formulated, which can be solved by Maximum Likelihood Estimation. The model calibration is achieved by combining AVL data and a dynamic Origin-Destination (O-D) matrix generated from AFC data (Xie, Leurent, & Aguiléra, 2015). It extended the methodology based on data processing and analysis methods to infer urban rail transit O-D matrix and to generate path choice from Oyster farecard data in London (Zhao, Frumin, Wilson, & Zhao, 2013). Since the objective function is a piecewise multivariate multi-parameters function, a non-linear numerical optimization approach is used for model calibration.
Spatial and temporal evaluations about distributions of walking speed and walking distance are applied to a real case study, the line RER A in greater Paris in France, by using the AFC data provided by STIF and actual train AVL data provided by RATP. Optimal parameter values are calibrated for each O-D pair. Results are confronted with that by using AFC data and the train timetable: in real case, the mean value of walking speed is smaller, and the mean values of walking distances are longer. The spatial and temporal analyses are then achieved. Along spatial axis, the estimations of Many to One along a transit line show that the mean values of walking speed are very close for the two directions of train circulation, the distributions of walking-in distance are with respect to the complex topology structure of each access station, and the distributions of walking-out distance at each terminal are consistent. Along temporal axis, results of cross-comparison highlight that the mean values of walking speeds are smaller during peak hours on account of pedestrian congestion, and walking distances are smaller during peak hours as well. That work paves the way for further refinement of stochastic model of passengers’ journeys and for economic appraisals for both transit client and transit agency.
Keywords: Spatial and temporal analyses, distributions of walking components, modern data, maximum likelihood estimation, genetic algorithm, rail transit line
Association for European Transport