## Route Choice Modeling Without Route Choice

### Authors

M Fosgerau, E Frejinger, A KarlstrĂ¶m, CTS - KTH, Stockholm, SE

### Description

### Abstract

Route choice modeling is complex. The number of alternative paths is often very large, while the paths are likely to share unobserved attributes which induces correlation. When modelling this, we face a trade-off between using models that are simple enough to handle many alternative paths while at the same time being able to handle correlation. There is a substantial ongoing research effort seeking to resolve this dilemma, so far with limited success. For these reasons the multinomial logit model (path size logit and c-logit proposed by Ben-Akiva and Bierliare, 1999, and Cascetta et. al., 1996, respectively) is widely used in spite of its known limitations.

The main purpose of this paper is to present and test a dynamic discrete choice approach for the estimation of the parameters of a route choice model. In the dynamic modeling approach, the individual is seen as taking sequential decisions on which link to choose, and the choices are made at the nodes in the network. The obvious advantage with this approach is that the choice set at every stage is quite small and well defined, while a correlation structure is naturally imposed among different paths, even if each sequential decision follows a multinomial logit model. From an econometric point of view, the link choice model can be a lot simper to deal with.

The utility maximising choice of path may be broken down into a sequence of link choices, where at each stage the individual considers the utility associated with downstream link choices accumulated into a value function. However, if we were to compute the value function associated with the available link choices at every stage, the complexity of the problem would be at least the same as the original path choice problem. An exact solution method to calculate the value function runs into the curse of dimensionality when solving a dynamic programming problem. Therefore, the computational burden may be prohibitive for large networks if one tries to solve the dynamic programming problem by brute force. This is probably why the sequential approach is not used for estimating route choice models in spite of having been around for many years (e.g., Dial, 1971).

However, it is not strictly necessary to solve the dynamic programming problem in order to estimate the parameters of the route choice model consistently. It is sufficient to find a suitable approximation to the value function. So the objective of this paper is to test whether it is possible to generate good predictors for the value function such that the parameters of the route choice model may be estimated on link choices rather than path choices. If this turns out to be possible, then both the econometric and computational complexity of route choice modelling may be dramatically reduced.

The paper therefore discusses the conditions under which the route choice model can be consistently estimated. We then test the approach using simulated data for a real network (BorlĂ¤nge, Sweden), where route choice observations are generated using the exact model, i.e. solving the dynamic programming problem. This allows us to compare the exact value functions with the approximations. We show how the approximation can be defined using proxy variables such as direction and distance to destination. The paper concludes with a discussion on the use of the model for prediction (policy analysis) and related issues.

#### Publisher

Association for European Transport