## The Effect of Correlated Value of Travel Time Savings in Public Transport Assignments

### Authors

Otto A Nielsen, Stefan Mabit, Centre for Traffic and Transport, Danish Technical University, DK

### Description

In the paper we investigate how theoretically imposed correlations in Value of Travel Time Savings affect the estimation of VTTS. Furthermore we look into how these new VTTS estimates effect assignment in a public transport network.

### Abstract

In research in general and also in many cases in applied work the mixed logit (ML) model is used to estimate the willingness-to-pay for travel time savings. The majority of ML models assume that the distributions of the coefficients are independent. This assumption may not hold in models with various time components, e.g. access time, waiting time, and in vehicle time distributed on various public transport modes in a transit network. A person with a generally high value of time can e.g. be assumed to have generally higher time coefficients compared to cost, and visa versa.

From the microeconomic framework of De Serpa and others we know that Value of Travel Time Savings (VTTS) can be seen as the sum of the resource value of time and the direct disutility of travel. In the discrete choice model it is not possible to estimate these two elements separately. On the other hand the resource value of time is an element in both in vehicle time and waiting time. So if the resource value of time is distributed this induces a correlation structure in the mixed logit model.

In this paper we therefore investigate how theoretically imposed correlations in VTTS affect the estimation of VTTS. We then investigate how these new VTTS estimates effect assignment in a public transport network.

The estimation of VTTS may be based on a commonly accepted framework derived from microeconomic theory and the general theory on discrete choice models. This framework has shown its use both with revealed preference data (RP) and stated preference data (SP). We therefore base our estimation of VTTS on this framework.

The data used for the analyses consists of 6 unlabelled SP experiments for the public transport modes: regional train, city train and bus, covering the Copenhagen Region. From the data we model willingness-to-pay for saving in vehicle time, access and egress time, waiting time and other components of a travel with public transport. This is done with a nested mixed logit model, using various Lognormal distributions on the coefficients (dependent on the specific model being tested).

Different formulations were tested, e.g. MNL, standard ML without correlation, and ML with correlation. Different utility functions were tested as well, e.g. with different income specifications, VTTS dependent on journey time, and estimation in standard formulation versus VTTS space.

Looking at the final mean estimates from these different models, the effect of imposing correlations is minor in terms of mean VTTS estimates as well as model fit. Though, the models based on micro-economic theory performed slightly better than the traditional models with linear utility functions.

The second part of the paper tests the estimated utility functions in a schedule-based public transport assignment model. The model is applied on the transit network in the Copenhagen region.

The usual shortest path algorithms assumes linear cost functions. An approximation method was used to overcome this when applying the models with increasing VTTS as function of journey time. The utility functions were applied by simulation, whereby individual travelers VTTS could be simulated instead of just the mean estimates from the entire population.

The main conclusion of the assignment tests was that the actual route choices in the network changes significantly when the simulated VTTS were applied in the assignment procedure, instead of just the mean over the population. Furthermore, models with uncorrelated versus correlated VTTS were tested and compared.

The paper shows, that it indeed improves assignment models if correlation between VTTS components are applied in a mixed logit framework instead of using mean estimates only. The work also shows ? maybe not very surprisingly ? that the more complex utility functions based on micro economic theory performed slightly better in terms of model fits than traditional linear functions.

#### Publisher

Association for European Transport