origindestinationmatrices

An origin-destination matrix (OD matrix) or origin-destination matrices are tabulations that quantify flows between pairs of geographic zones within a study area. Each row represents an origin zone and each column a destination zone, with the cell value indicating the volume of trips, shipments, or other movements from the origin to the destination. The matrix may include intra-zonal trips in the diagonal. OD matrices are central to travel demand modelling and transportation planning, supporting tasks such as forecasting traffic, assessing network performance, and evaluating policy impacts such as land-use changes or tolls.

Data sources include travel surveys, censuses, transit card data, vehicle counts, GPS or mobile phone records, and freight manifests. Creating a usable OD matrix requires a defined set of zones (a zoning system) and, often, a method to estimate or balance the matrix to ensure consistency with total observed trips. Matrices can be static, representing a single period, or dynamic, spanning multiple time periods to capture diurnal or seasonal variation.

Typical analysis treats OD matrices as asymmetric, since trips from A to B may differ from B to A. They can be expressed in absolute trips or as shares or probabilities, and can be weighted by person, vehicle, or freight tonnage. Methods for estimation include direct tabulation from surveys, distribution models such as gravity models or intervening opportunities, and matrix estimation techniques that reconcile observed counts with known totals.

Applications extend beyond transportation to epidemiology, logistics, and urban planning, where OD flows inform network design, capacity expansion, and spatial interaction patterns. Limitations include data quality, spatial resolution, privacy concerns, and temporal variability, which require careful validation and updating.