## Uncertainty in Traffic Forecasts: Literature Review and New Results for the Netherlands

### Authors

G de Jong, A Daly, RAND Europe, NL and ITS, University of Leeds, UK; M Pieters, RAND Europe, NL; S Miller, RAND Europe, UK; F Hofman, AVV, Ministry of Transport, NL

### Description

This paper describes the methods that are used in the literature to quantify uncertainty in traffic forecasts. The Dutch national and regional transport models are used to produce confidence intervals for both input and model uncertainty.

### Abstract

Although thousands of papers on transport model forecasts can be found in journals, conference proceedings and reports, the literature on quantifying uncertainty in traffic forecasts is fairly limited. In this paper, we provide an overview of the literature on uncertainty in transport modelling and outcomes of interviews with a number of experts, but we also present uncertainty estimates for traffic forecasts from the Dutch National Model System and a regional model. We distinguish between input uncertainty (e.g. on the future incomes) and model uncertainty (including specification error and error due to using parameter estimates instead of the true values).

All the methods found in the literature for quantifying the amount of input uncertainty use some form of repeated model simulation (sensitivity testing). Many of the studies investigated postulate statistical distributions for the input variables and then draw (usually at random, sometimes at specific percentiles) input values from these distributions. The resulting values are then used in model runs. Final outcomes for uncertainty are calculated from the variance over all the runs for the different input values. This is also what we used for input uncertainty in the national and regional model runs. Most studies use univariate distributions for the input variables; correlation between inputs is ignored (in contrast to what is done in scenario studies). More realistic estimates of uncertainty can be derived if one takes account of correlations between inputs (e.g. income and car ownership) by drawing from multivariate distributions, but this requires knowledge of the correlations. We took existing time series data as the key source of information on means, standard deviations and correlations of input variables, and used these to get multivariate distributions for the model input variables.

For quantifying model uncertainty in transport forecasts, we found a wider diversity of approaches than for input uncertainty. Some studies used analytic expressions for the variance of the endogenous variable that results from using parameter estimates for the influence of the exogenous variables. This can only be done if the model equations are relatively straightforward. For complicated models, these expressions become very cumbersome and often only approximations (e.g. from Taylor series expansion) can be given. The volume of calculation and computer storage required can also limit the use of analytical methods.

To obtain proper standard errors for the model coefficients in situations with some kinds of specification error (such as repeated measurements in panel and SP data, or cases with mis-formulated variables), the Jackknife or the related Bootstrap method can be used. After having calculated the proper standard errors, these can be used either in an analytic calculation of the standard error (due to estimation) of the model outcomes, or as information on the statistical distribution of the parameters of the model, from which values can be drawn for model simulation runs, similarly to the method recommended for input uncertainty. Again, it is important to take account of the correlations (between the parameter estimates), either in the analytic equations or in sampling from a multivariate distribution.

For quantifying the model errors we used the bootstrap method to correct for specification error and Monte Carlo simulation for the uncertainty due to estimation. We also investigated whether analytic expressions for the variance of the outcomes could be used for the tour frequency or mode-destination choice models, but found that these would require too much computer run time and storage for evaluation.

In estimating errors for traffic forecasts, particular account must be taken of the phenomenon of congestion. Of course this itself is subject to forecasting error, which must be considered. But it also plays a particular ?damping? role in estimating errors in traffic flow. Thus if traffic is forecast too high, feedback from congestion will tend to reduce the volume, while the converse effect will apply to a forecast which is too low. Account has to be taken of this effect to derive correct estimates of the error in traffic volumes.

The National Model System LMS and the New Regional Models NRM are regularly used in The Netherlands to forecast the national and regional transport volumes and traffic flows on specific network links for a single or a limited number of scenarios. The same models are also used to give the likely impacts of transport infrastructure projects (e.g. new roads, wider roads, new railway lines) and transport policies (e.g. road pricing). All these predictions are point estimates, and, even when produced for several scenarios, do not give confidence intervals around the forecasts.

In this context, the objectives of the project ?Uncertainty in traffic forecasts? that RAND Europe has carried out for the Transport Research Centre of the Dutch Ministry of Transport, Public Works and Water Management were:

? to develop a methodology to estimate the amount of uncertainty in forecasting for new infrastructure (especially roads); and

? to implement and test this methodology in two case studies (using the Dutch National Model System LMS and the New Regional Models NRM respectively).

This methodology was developed and implemented in the LMS and NRM. In this paper we present the outcomes of the literature review on quantifying uncertainty in traffic forecasts as well as the outcomes from a large number (100) of model runs with the LMS (for the whole of The Netherlands) and the NRM (for the Province of Noord-Brabant) to derive uncertainty margins around the mean traffic forecasts. Margins are given for overall traffic volumes (by mode and by purpose) and for flows on links in the highway network.

#### Publisher

Association for European Transport