## Trip-based Route Choice Models ? a Method to Eliminate Aggregation Bias in Activity-based Models

### Authors

O Anker Nielsen, Technical University of Denmark, DK and TUDelft, NL

### Description

Trip-based assignment models are compared with traditional matrix-based. The benefits are that full trip information from demand is used, and that calculation of Level of Service is consistent. It is shown that calculation complexity is efficient.

### Abstract

Activity-based models provide more insight in persons? trip making than traditional demand models. The newest types of activity-based models simulate individuals? activity patterns over the day, i.e. the fundamental modelling unit is the individual (integer). The insight into the characteristics of each trip is therefore higher; Income, Value of Time (VoT), gender, etc. may be related directly to the individual trip. Especially VoT is interesting, since it may depend on e.g. the person?s income, the time use of the trip (trip length), the trip purpose and the time of the day.

Individual-based disaggregate approaches are different from traditional matrix-based models (whether activity-based or not), where the fundamental unit is the cell in the matrices and the unit is a floating point. With the increasingly segmentation of models into time-of-the-day, trip purposes and number of zones, the size of this fundamental unit may be quite small ? often even much lower than one on average. Whilst one (integer) is the fundamental unit in disaggregate activity-based models. An example is the Copenhagen model (OTM), where there are 2.2 million car trips, distributed between 835x825 zones, 7 time-periods and 6 trip purposes (Nielsen et.al. 2006). This equals 42 trip matrices and 0.07 trips in average per cell.

Activity-based models are often used to evaluate network effects, where the Value of Time may be a core element in the decision making. An example is congestion reducing projects or road pricing schemes. The information of the individual trip characteristics from the demand models are however seldom used directly in the assignment procedures. Hence, a very often used approach is that the detailed trips from the activity-based models are aggregated to zones and trip matrices, which are then assigned by ?traditional? assignment procedures. The LoS matrices produced by the assignment procedure are hereby only an average. There are therefore both socio-economic and geographic aggregation bias. This is relatively larger for short trips due to the Zonal aggregation of the start and end point of the trip.

The problem of aggregation bias may be solved partly by segmenting the demand into more trip purposes and VoT intervals, and carry out a multi-purpose assignment. This increase ? however ? the number of matrices and reduce the cell-sizes further. In the case of the Copenhagen model, 5 VoT intervals would increase the number of car matrices from 42 to 210, and the average cell-size would be reduced from 0.07 to 0,015. If the trips are also to be split into trip-length segments, this will increase the number of matrices further, and also introduce a need of sorting the matrices at cell-level before the splitting.

Therefore, an intuitive improvement of assignment procedures in activity-based modelling is to assign the trips directly onto the network. The obvious benefits have been described above;

? Direct use of trip attributes in the assignment, e.g. VoT depending on the individual?s income, trip length, trip purpose and time-of-the-day.

? Correct LoS calculations for feedback from assignment to demand.

Another benefit is that there is no need for a zonal aggregation, and the trips can therefore be assigned directly from node to node rather than from zone to zone. The need for zones and zonal connectors are therefore eliminated. The usual problems with too much traffic at the roads near the end of the connectors are hereby eliminated, as well as problems to get the right distribution of traffic onto the different connectors from/to a zone.

Trip-based assignment procedures are often claimed to increase calculation time compared to matrix based. However, the paper shows based on a paper by Nielsen accepted for the Triennial Symposium on Transportation Analysis that the theoretical calculation complexity of trip-based assignment models used within large-scale activity-based models may even be lower than the traditional matrix-based approaches. This is illustrated empirically in the present paper by tests on the network from the Copenhagen OTM model. In addition it is shown that the equilibrium scheme of the trip-based approach converge faster than the matrix-based, whereby an additional benefit is a need for fewer iterations in the solution algorithm.

Due to the many potential benefits of using a trip-based assignment model in terms of more refined casual relationships and consistency between the activities based model and the assignment, trip-based assignment seems to be a promising way forward.

#### Publisher

Association for European Transport