A strategy-based recursive path choice model for public transit smart card data

https://doi.org/10.1016/j.trb.2018.01.002Get rights and content

Highlights

  • A sequential choice model is proposed for transit path choice modeling with smart card data.

  • The model uses a link-based formulation and includes all path/hyperpath alternatives without enumeration.

  • Extends the conventional notion of “attractive sets” by introducing a measure of “attractiveness” that allows for randomness in the choice of attractive routes.

  • Developed and tested a bi-level maximum likelihood estimation for calibration.

Abstract

A recursive logit model is proposed for path choice modeling with transit smart card data in higher-frequency bus and rail services. In such circumstances, it is commonly assumed that passengers may arrive randomly to a stop and may behave according to a “strategy”; such a strategy is associated with a so-called “attractive” set of routes: a passenger selects a set of routes departing from the stop, and will board the next vehicle to depart from among that set of routes. We extend the conventional notion of attractive sets by introducing a measure of “attractiveness” that allows for randomness in the choice of attractive routes.

The proposed model uses a link-based (recursive, or sequential choice) formulation, rather than a path-based formulation, which has the advantage of including all path alternatives without the need for path set enumeration. The recursive formulation is also very suitable for smart card data because it allows model calibration with incomplete path choice observations.

The link-based approach was originally advocated by Nguyen et al. (1988) in the strategy-based transit assignment context, but without investigating methods for model calibration or empirical analysis. Recently, Fosgerau et al. (2013) and Mai et al. (2015) have presented methods to empirically estimate traffic path choice models using a link-based formulation. Our framework builds off these previous works to formulate and estimate a strategy-based path choice model with smart card data. The proposed model is tested with a 6 months extract from the smart card transactions in Brisbane, Australia, for two popular origin-destination pairs with diverse path alternatives.

Introduction

Since its development by Spiess and Florian (1989), the strategy-based transit assignment has been widely accepted and extensively used in travel demand forecasting models. In high frequency services, it is commonly assumed that passengers may arrive randomly to a stop, rather than timing their arrival with a specific scheduled vehicle departure. Further, it has been hypothesized that passengers arriving to stops may actually behave according to a “strategy”, by choosing among different services (routes1or route segments) that will take them toward their destination (Spiess and Florian, 1989). In a deterministic choice context, such a strategy is associated with a so-called “attractive” set of routes: a passenger selects a set of routes departing from the stop, and will board the next vehicle to depart from among that set of routes. Therefore, the strategy-based formulations can capture the behavior of passengers when they adapt their path decisions according to the service arrivals in real time. Computationally, the problem has been modeled as a linear program (LP) minimizing the expected travel time between the origin and destination. An efficient network labeling algorithm is proposed (Spiess and Florian, 1989) that is effective in handling real-sized transit assignment problems. In parallel, Nguyen and Pallottino (1988) proposed the concept of transit hyperpath and modeled travel strategies in a hyperpath/hypergraph network structure. They proved that a strategy-based transit assignment can be found in a hypergraph structure using a network flow procedure.

Some extensions have been proposed to allow randomness in travel strategies. Florian and Constantin (2012) argued that the optimal strategy (deterministic) calculation may result in extreme solutions and thus could be highly sensitive to small fluctuations in the service, especially at critical values. In order to account for this, Nguyen et al. (1988) proposed a strategy-based transit assignment method with an implicit logit formulation to model the stochastic choices of boarding stops and transfer locations. This allows randomness in the model to account for variations in passengers’ preferences and their knowledge of the transit service and may improve the path choice estimation particularly in the choice of departure or transfer stops. However, the selected set of routes to a destination is assumed identical for all passengers and equal to the attractive set of the fastest strategy to the destination. This characteristic could be potentially restrictive because the variability in passengers’ boarding strategy choices, which is known to exist in dense and complex transit systems, is ignored. An empirical analysis with transit smart card data of Brisbane, Australia over a six-month period indicates significant variability of boarding strategies among regular passengers of high-demand origin-destination (O-D) pairs (Nassir et al., 2017).

In this paper, we extend the conventional notion of attractive sets by incorporating randomness in passengers’ choices of attractive routes. We propose a measure of “attractiveness” for any alternative route and use this measure to model path choice strategies of passengers. Attractiveness of an alternative route is defined as the probability that passenger n will select that route in his/her attractive set, and is estimated based on utility of boarding that route as compared with the utility of waiting for other alternative routes.

Section snippets

Background

In the review of methodological background, we present a summary of advancements in two main research streams which our proposed model is building on. These two streams are “transit path choice strategies” and “recursive path choice models”.

Model structure

The proposed recursive model comprises two interrelated systems of equations to be evaluated for traveling to a destination, in order to realize boarding, alighting and transfer choice probabilities to that destination from any location in the network. At the system of equations in the upper level (network level), the utility of boarding, alighting, and transfer alternatives are defined recursively; and at the system of equations in the lower level (stop level), the attractiveness of every

Model estimation data

In order to use the proposed model for understanding and prediction of passenger path choices in a large-scale and dense transit network, the stochastic parameters of the model should be calibrated with actual path choice observations in the network of interest. Transit smart card transaction data represents a valuable source of passively-collected information on passenger choices. With geographic coordinates and time stamps for these transactions, it is possible to identify a passenger's

Case study and results

A case study experiment in the network of Brisbane, Australia, is carried out for demonstration purposes, particularly, in order to clarify the use of smart card observation data for model estimation and also to demonstrate the interpretation and use of the estimated model parameters. The transit network of Brisbane includes extensive segments of grade separated dedicated busways. As a result, many routes overlap in various sections of the busway network and for many OD pairs in the network of

Access and egress

Given that the choice observations on access (from actual origin to the chosen boarding stop) and egress (from chosen alighting stop to actual destination) behaviors are missing in the smart card data, if the proposed model is used for predicting the path choice for door-to-door OD pairs, the access and egress choices can be estimated using transfer and alighting choice equations, respectively. With the assumption that the passenger access choice behavior is similar to their choices of transfer

Conclusions and future works

Probably the most important complexity in modeling and prediction of transit path choices in urban transport networks is related to representation of the choice set. These sets are usually unknown to modelers and research has revealed that path choice model outcomes could be significantly affected by the configuration of the choice set (Prato and Bekhor, 2013, Bliemer and Bovy, 2008). Considering that the set of alternative paths in a transport network can grow exponentially with the number of

Acknowledgments

This research was funded by Queensland Department of Transport and Main Roads (TMR), under the ASTRA agreement with the University of Queensland. The authors would like to thank TMR for the financial support, and also Translink for providing the data and invaluable consultations.

The authors also wish to thank anonymous reviewers for their constructive comments that helped improve the quality of paper substantially.

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