## An Alternative Approach to Route Choice Simulation: the Sequential Models

### Authors

Guido Gentile, Università di Roma "La Sapienza", IT; Andrea Papola, Università di Napoli "Federico II", IT

### Description

In this paper the sequential models are proposed as an alternative approach to route choice simulation. These models seems to be more convincing from a behavioural point of view and surely much simpler from a computational point of view.

### Abstract

A path is, by definition, a sequence of links connecting an origin to a destination.

As a consequence, two different approaches to the estimation of route choice probabilities can be considered in principle within the random utility theory which can be called ?joint? and ?sequential?.

The joint approach assumes the user to choose a path among all those available for a given od pair, that is he/she jointly chooses all the links belonging to that path.

The sequential approach assumes the user to reach his/her destination through a sequence of link choices at nodes; the choice probability of a path can be deduced by multiplying the choice probabilities of all the links belonging to that path.

All the models proposed so far to simulate route choice probabilities adopt the first approach, in spite of the fact that it leads to some problems due to the large number of overlapping acyclic paths which generally connect an od pair, especially in urban contexts.

The first problem is that such a complex choice context needs a model which is from one hand sophisticated enough to deal with a very general correlation pattern and from the other hand simple enough to deal with a very large number of alternatives (and an even larger number of od pairs) so as to guarantee acceptable computational times; this is still an open question.

Moreover, when dealing with extremely large choice sets, the assumption that the decision maker is able to perceive and evaluate all the alternatives taking into account the effects of the correlations among them can be unrealistic. Indeed, in these cases, the decision maker generally tends to simplify his/her choice process, so that the sophisticated model mentioned above isn?t always the most consistent with the actual behaviour.

The main idea of this paper is that, in route choice contexts, the simplification introduced by the user in his/her decisional process consists in adopting a sequential approach, i.e. ?building? his/her route to reach the destination through successive link choices at nodes.

In more detail, concerning for example a systematic trip, each user is assumed to ?come? to his/her final route choice through a learning process made up by tests experiments, attempts, randomness, etc. which lead him/her to improve the network knowledge by performing different costs to reach some nodes starting from some other nodes. Obviously this learning process leads the user to a partial network knowledge. During this learning process, the initial route is successively modified by substituting part of it with some others more efficient, i.e. by successively modifying one or more sequences of link choices.

If this is the case, the model which probably best approximate users final route choice (this is of interest for static route choice simulation) could:

a) assume the user, in virtue of his/her learning process, to have performed at least once each efficient (with respect to the destination) link and therefore to have a knowledge - which become better when getting closer to the destination - of an average cost needed to reach the destination from each of these links;

b) be a sequential model where each link choice occur at a specific node j among all efficient links jh belonging to the forward star of j (two-three at the most) by associating to each of these links their costs cjh plus the cost to reach the destination from the end of that link chd; the latter can be computed as the expected maximum utility among all the efficient paths connecting the end of the link h with the destination d; moreover the correlation among the link alternatives of each link choice is given by the overlapping degree among the correspondent chd.

To simulate these link choices, taking into account the correlations mentioned above, different random utility model can be used and consistently different sequential route choice models are derived. In any case, this behavioural paradigm avoids the problem of identifying all available paths for any od pair. Moreover it generally leads to different link choice probabilities than those resulting from the joint approach ? by definition they become independent from the trip origin ? and consequently to different route choice probabilities. However, for two very well known route choice models ? deterministic and Logit ? the probabilities coincide in the two cases.

In this paper, different sequential route choice models are proposed and compared among each other and with the standard route choice models (Logit, C-Logit, Probit, etc.). Numerical results show the sequential models (above all the sequential Probit) perfectly able to reproduce expected route choice probabilities in a number of test networks. Obviously from a computational point of view the performances of the sequential models are clearly much better.

Dealing with new behavioural hypothesis, testing the models with experimental data is clearly particularly important.

#### Publisher

Association for European Transport