A Hybrid Gravity Modelling Approach For Trip Matrix Synthesis

A Hybrid Gravity Modelling Approach For Trip Matrix Synthesis


Stefanos Psarras, AECOM, Rawle Prince, AECOM, Reza Tolouei, AECOM


We develop an approach to build synthetic matrices based on a gravity model that consists of different deterrence functions, the parameters of which are calibrated simultaneously to match different Trip Cost Distributions, discussing relative errors.


Synthetic matrices are commonly used in the UK to complement observed trip information sourced from roadside interviews (RSI) or more recently, from mobile phone data. Particularly, these could be used to infill short trips when building matrices from mobile phone data, since these are poorly represented, as well as for spatial disaggregation or segmentation of trips by purposes (Tolouei et al., 2016).

The standard approach to developing synthetic matrices is to calibrate the parameters of a single deterrence function across the entire matrix to observed Trip Cost Distribution (TCD). It is generally understood that, whilst achieving an overall good fit with the observed data, this approach will result in matrices which are subject to large errors, as well as poor fits at some sub-matrices or for specific areas of the model.

The errors are largely due to differences in travel patterns, resulting in insufficient set of explanatory variables in the calibrated gravity models. The extra explanatory power could potentially be achieved using one, or a combination of the following methods:

- using a set of sector-based constraints (referred to as ‘k’ factors); and
- calibrating different deterrence functions, reflecting differences in TCDs between sub-matrices within the whole matrix.

Whilst sectored constraints have been regularly used is developing synthetic matrices, and has shown to result in significant improvements in the performance of the matrices (e.g. Feldman et al, 2012), it is heavily dependent on the availability of reliable sectored trip estimates. The second method above however has not been investigated sufficiently in the past.

While calibrating different sub-matrices has been considered before (e.g. Feldman et al (2012)), this has been mainly based on splitting a TCD into two parts, and calibrating two separate functions. This approach requires both the trip-ends and TCD for each sub-matrix to be known a priori. The calibration of such models could result in substantial discontinuities around cut-off points, which then may require derivation of weights to smooth the ‘joins’ between different TCDs.

Besides, it may be more appropriate to consider differences in trip patterns geographically. For example, trips produced in urban areas are expected to have a different TCD, with a higher proportion of short distance trips, in comparison to trips produced in rural areas (reflecting different travel patterns). When synthetic matrices are intended to be used to represent short trips in matrices sourced from mobile phone data, for instance, the above inconsistency would result in large errors in the representation of local trips.

In this study, we develop an approach to build synthetic matrices based on a gravity model that consists of different deterrence functions, the parameters of which are calibrated simultaneously to match different TCDs, representing distinct travel patterns for specific areas in the model. Not only does this approach potentially reduces errors within sub-matrices, or for different model areas, but it also enables individual subsets of the matrix to be calibrated using different functional forms. This is demonstrated by testing ‘Tanner’ and lognormal density functions.

Applying the approach described above, synthetic matrices are developed for one of the county-wide transport models recently developed by AECOM. Availability of partially observed matrices based on RSI Data for this model provides the opportunity to use these as sector constraints in developing synthetic matrices. Different set of synthetic matrices will be developed, with and without sector constraints, and with single or multiple deterrence functions (of different functional forms) as described above. Different deterrence functions will be calibrated to corresponding area-specific TCDs based on National Travel Survey (NTS) data.

The developed matrices will be compared in order to investigate whether and to what extent using a gravity model composed of multiple deterrence functions, reflecting different TCDs by area, improves the performance of the synthetic matrices. This will be investigated through the following comparisons
• TCDs versus estimates from NTS;
• sectored trips vs. RSI matrices (for synthetic matrices with no sector constraints); and
• assigned flows versus traffic count data across screenlines.

The paper will include a detailed discussion on the expected relative errors of the alternative synthetic matrices, drawing on the comparison of the resulting trip estimates with those observed from the RSI data, taking into account the 95% confidence intervals of the RSI trip estimates.

Tolouei, R., Psarras, S., Prince, R. (2016). “Origin-Destination Trip Matrix Development: Conventional Methods vs. Use of Mobile Phone Data”, proceedings of the European Transport Conference, Barcelona, 2016.
Feldman, O., Forero-Matrinez, J., Coombe, D. (2012). “Alternative Gravity Modelling Approaches For Trip Matrix Synthesis”, proceedings of the European Transport Conference, Glasgow, 2012


Association for European Transport