Dynamic O-D trip matrices for public transportation systems provide a valuable source of information of the usage of public transportation system that may be used either by planners for a better design of the transportation facilities or by the administrations in order to characterize the efficiency of the transport system both in peak hours and off-peak hours. Since all these evaluations are intended to be done off-line as a part of an evaluation/planning process, the estimation models have also been aimed at processing off-line large amounts of data comprising one or several journeys. Also, initially, on-board equipments have been oriented at sending the collected information after the operational journey of the transportation units. In this context there are currently several models and methods for estimating dynamic O/D trip matrices using observed volumes. In operational environments, however, such trip tables should be dynamic. The literature on methods for estimating dynamic O/D matrices for public transport systems is much smaller than in the static case. Recently, the use of dynamic O-D trip matrices has been suggested for other contexts, such as for instance the management of alleviation strategies in disrupted systems. Typically, these recovery systems have been planned off-line using static O-D information from historical data. This paper presents a dynamic O/D trip matrix estimation model for transit networks which may be aimed at an on-line usage, that incorporates emerging information and communication technologies (ICT), especially those based on the electronic signature detection of devices used by passengers on board that provide a rich source of data of higher quality than simple counts. The procedure presented is based on the statement of a mathematical programming-based model for the adjustment of passenger counts on a diachronic network model. The distinctive approach presented in the paper takes advantage of a detection system, capable of measuring not only the passenger's load on segments, but also to track, up to some extent, the passenger trajectories on the network, comprising but not limited to end-to-end trajectories. The estimation model is not limited to a single line but is a formulation for a general public transportation network. The formulation of the estimation model permits to include requirements on passenger's route choice which may be estimated either by historical or survey data or may come from static passenger transit assignment models. As a first paper of a series of three, this one only presents and justifies the model's formulation showing how it is oriented for being solved effectively, leaving for a second one the advantges and the enhancements in the quality of the estimation of combining all the types of passenger counts. Finally, a third one would discuss algorithmic solution to the proposed model.
Department of Statistics and Operations Research. Universitat Politècnica de Catalunya. July 2021