Inference of dynamic origin–destination matrices with trip and transfer status from individual smart card data
Authors: Cerqueira Sofia , Arsenio Elisabete , Henriques Rui 
Published: September 2022

Abstract
Background
The provision of seamless public transport supply requires a complete understanding of the real traffic dynamics, comprising origin-to-destination multimodal mobility patterns along the transport network. However, most current solutions are centred on the volumetric analysis of passengers’ flows, generally neglecting transfer, walking, and waiting needs, as well as the changes in the mobility patterns with the calendar and user profile. These challenges prevent a comprehensive assessment of the routing and scheduling vulnerabilities of (multimodal) public transport networks.

Research aims/questions
The research presented in this paper aims at addressing the above challenges by proposing a novel approach that extends dynamic Origin-Destination (OD) matrix inference to dynamic OD matrix inference with aggregated statistics, highlighting vulnerabilities and multimodal mobility patterns from individual trip record data.

Methodology
Given specific spatial and temporal criteria, the proposed methodology extends dynamic Origin-Destination (OD) matrices with aggregated statistics, using smart-card validations gathered from (multimodal) public transport networks. More specifically, three major contributions are tackled; i) the data enrichment in the OD matrices with statistical information besides trip volume (e.g., transfer and trip features); ii) the detection of vulnerabilities on the network pertaining to walking distances and trip durations in a user-centric way and iii) the decomposition of traffic flows in accordance with calendrical rules and user (passenger) profiles. The set of contributions are validated on the bus-and-metro public transport network in the city of Lisbon.

Results
The proposed approach for inferring OD matrices yields four unique contributions. First, we allow inference to consider multimodal commuting patterns, detecting individual trips undertaken along with different operators. Second, we support dynamic matrices’ OD inference along with parameterizable time intervals and calendrical rules, and further support the decomposition of traffic flows according to the user profile. Third, we allow parameterization of the desirable spatial granularity and visualisation preferences. Fourth, our solution efficiently computes several statistics that support OD matrix analysis, helping with the detection of vulnerabilities throughout the transport network. More specifically, statistical indicators related to travellers’ functional mobility needs (commuters for working purposes, etc.), walking distances and trip durations are supported. The inferred dynamic OD matrices are the outcome of a developed software with strict guarantees of usability. Results from the case study using data gathered from the two main public transport operators (Bus and Metro) in the city of Lisbon show that 77.3% of alighting stops can be estimated with a high confidence degree from bus smart-card data. The inferred OD matrices (Bus and Metro) in the city of Lisbon reveal vulnerabilities along specific OD pairs, offering the bus public operators in Lisbon new knowledge and a means to better understand dynamics and validate OD assumptions.