Combining Choice Models with Assignment

Combining Choice Models with Assignment


A Daly, RAND Europe, UK


Problems concerning the consistency of mode and destination choice models and assignment are discussed and improved practice recommended. These combinations of models are important in many forecasting systems.


In models of travel demand, sub-models for mode and destination choice almost invariably predict that apparently identical travellers will make different choices. The choice probabilities for the alternative modes or destinations lie strictly between zero and one. However, the sub-models used for route choice, both for cars and for public transport, are usually based on the "assignment" concept: that all travellers will use the route with the lowest cost (Wardrop, 1952) and multiple routes will only be used when the costs are equal. There is thus a fundamental inconsistency between the choice and assignment sub-model components, which can lead to confusion and inconsistency in the application of the models.

A particular issue is the definition of "modes". When considering variants of modes, such as toll roads, or variants of public transport modes, sometimes called "sub-modes" such as mixed bus and metro services or high-speed rail services, or in considering park-and-ride and station choice, there is particular difficulty in separating the issues of choice and assignment.

Several difficulties arise from the inconsistent modelling of these two model components.
- One issue is the extent to which utility can be modelled consistently throughout the system. The time taken by assignment processes means that a relatively simple approach has to be taken, so that some degree of simplification is inevitable.
- In particular, mode and destination models often require a non-linear utility, which is difficult to handle in an assignment sub-model.
- In practice, it is often the case that the two components have different specifications (e.g. values of time) and practical considerations may make it difficult to achieve consistency.
- The models of mode and destination choice require input of a measure of the composite cost resulting from the route choices travellers make.

An important consideration in the assignment process is how multiple routes arise. If they arise because of the equalisation of travel costs under the Wardrop principle, or if they arise because of system performance (e.g. one bus arriving before another) then an averaging process is appropriate. But if they arise because of different preferences in the population (e.g. different values of time) then a more sophisticated composite measure (e.g. a logsum) is needed.

The paper explains the inconsistencies and discusses the methods that are available to avoid or reduce the problems arising. Reference is made to a number of studies undertaken by the author in recent years, including both high-speed-rail or other long-distance studies and studies of conurbations.

A final issue is the inconsistency of both choice and assignment components with the appraisal procedures often used. Again here the issue of consistency of the specification of cost is important, but for a number of reasons this cannot always be achieved. The issues arising from this problem are discussed.

Wardrop, J. G. (1952), Some theoretical aspects of road traffic research, Proceedings, Institute of Civil Engineers, PART II, Vol.1, pp. 325-378.


Association for European Transport