Origin–destination matrix estimation for public transport: A multi-modal weighted graph approach

Estimating the large-scale Origin–Destination (OD) matrices for multi-modal public transport (PT) in different cities can vary largely based on the network itself, what modes exist, and what traffic data is available. In this study, to overcome the issue of traffic data unavailability and effectively estimate the demand matrix, we employ several data sets like the total boarding and alighting, smart card as well as the General Transit Feed Specification (GTFS) in order to capture the PT dynamic patronage patterns.

First, we propose a new method to model the dynamic large-scale stop-by-stop OD matrix for PT networks by developing a new enhancement of the Gravity Model via graph theory and Shannon’s entropy. Second, we introduce a method entitled “Entropy-weighted Ensemble Cost Features” that incorporates diverse sources of costs extracted from traffic states and the topological information in the network, scaled appropriately. Last, we compare the efficiency of a single travel cost versus various combinations of travel costs when using traditional methods like the Traverse Searching and the Hyman’s method, alongside our proposed “Entropy-weighted” method; we demonstrate the advantages of using topological features as travel costs and prove that our method, coupled with multi-modal PT OD matrix modelling, is superior to traditional methods in improving estimation accuracy, as evidenced by lower MAE, MAPE and RMSE, and reducing computing time.