Models for choice of departure time.

This paper describes ongoing work undertaken as part of a UK Government Research Council funded project investigating the potential of a range of models for the study of drivers' route and departure time choices. This paper, which focuses on departure time choice, follows on from an earlier paper focusing on route choice (Batley et al., 2000). Interest in how travellers, and in particular car drivers, select their departure times has increased recently with the recognition that a change in departure time is the second most common response, after a change in route, to changes in network conditions. This brings a need for an appropriate model to predict drivers' choices of departure time, depending on network conditions such as congestion and, potentially, time-independent user charges such as road pricing. A fundamental problem is that time is a continuous variable and, as such, not readily applicable to discrete choice methods. It is necessary, therefore, to use models that are able to accommodate complex patterns of correlation between ordered alternatives. Moreover, the departure time problem becomes one of identifying an acceptable range of departure time periods for each individual. Recent developments in behavioural modelling have established the practicability of a wider range of model forms. Several of these are based within the family of generalised logit models, such as the nested logit, paired combinatorial logit, cross-nested logit and ordered logit models. Other models are based on the normal distribution, such as the multinomial probit model, or on 'hybrid' forms, such as the error components, often called mixed, logit model. Several of these models are apparently unsuitable a priori for modelling the choice of departure time and representing the correlations inherent in the choice process. Section 2.0 of the paper presents a theoretical review of various discrete choice models. Section 3.0 reports an empirical comparison of several of these models using simulated data based on a simple departure time choice problem. Tests are made of the ways in which the alternative model forms can represent the simulated behaviour. The models are tested on their fit to the simulated data and their ability to recover the parameters that were assumed in setting up the simulations. Section 4.0 provides a summary and conclusions.