Time of Day and Demand Equilibrium in Large Scale Models

Time of Day and Demand Equilibrium in Large Scale Models


J. Zantema, DAT.Mobility, M. Heynickx, Provincie Noord-Brabant, L. Brederode, DAT.Mobility


The research on the next generation regional traffic models within the province of Noord-Brabant. This paper focusses on the demand and departure time choice models, describing the methods and level of convergence reached on a large scale model.


This paper focusses on the research and application of a Time of Day model and Demand Equilibrium on the province wide traffic model of Noord-Brabant. The Province of Noord-Brabant is a region that is considered to be the second largest urban region in the Netherlands with approximately 2,5 million inhabitants, a large concentration of high-tech companies and the highest patent density of all European regions.

During 2014 the Province of Noord-Brabant commissioned an audit of the current regional traffic model system (BBMA). Prime amongst the results stood the necessity for:
- a network loading model which incorporated spillback effects for more realistic travel times;
- a departure time model to predict ‘return to the peak’ behaviour for forecasting models.

Two research projects were initiated in 2015. As the departure time model intersected with the main structure of the demand estimation, the effects on the entire model structure needed to be reviewed. This paper focusses on the research for the Time of Day and the Demand model, and how to reach an equilibrium. The use of the network loading model with incorporated spillback effects is a given for this research.

The Time of Day model is an extension of the original schedule delay model from Vickrey in 1969 and Small in 1982. It closely resembles the MD-Pit model from Van Amelsfort from 2005. The most important difference between the models is that the original model from Small used a continuous time scale and a bottleneck model, where Van Amelsfort distinguished short time periods (5 minutes). The model within the BBMA only has 3 different time periods (am peak, pm peak and off peak). The Time of Day model needed to be changed to incorporate only these three time periods.

Using travel survey data from the OViN (Onderzoek Verplaatsingsgedrag in Nederland, the Dutch national travel survey), the preferred arrival times and actual departure times of drivers are determined. Using the differences between actual and preferred departure time the shift from the peak hour is determined. This shift is used to calibrate the departure time model parameter.

The Time of Day model converged relatively quick given that the solution space is defined in the first two iterations. Equilibrium is defined when no people switch to another departure time in order to minimize their cost function. To keep the model runs acceptable for the regions using the BBMA the calculation time should be kept to a minimum. On the base model within the BBMA (3.300 zones, 140.000 links, 100.000 nodes, of which 1900 nodes are defined for junction modelling) equilibrium was reached within 5 iterations.

For the Demand model (consisting of car, PT and bicycle) over 10 different convergence methods have been tested. In an easy to explain theoretical test network in Excel each method was tested to make a preselection for the large scale model. Methods as MSA Polyak (Method of Successive Averages, at a different power as described by Polyak) and fixed fractions performed very well on this theoretical network. A selection was made within the convergence methods by their performance and need for tuning. On the large scale network, the effectiveness of these methods was surpassed by the MRA (method of repeated approximations) in the first few iterations.

Given that the Time of Day module and a new traffic assignment model have been incorporated in the BBMA, it proves necessary to re-estimate the demand parameters. In the model runs with the original demand parameters an unrealistic amount of traffic was shifted to the modes of public transport and bicycle.

Early 2016 the results of both research projects, have been incorporated in the tender of the BBMA model actualization. The research in this paper therefore describes one of the steps to the next generation in regional traffic models in the Netherlands.


Association for European Transport