Destination Sampling in Forecasting: Application in the Prism Model for the UK West Midlands Region
S Miller, A Daly, J Fox, RAND Europe, UK; S Kohli, Mott MacDonald, UK
We describe the implementation of destination sampling in forecasting, in the PRISM West Midlands model. We offer results to show the run time savings achieved, and the amount of error in the assigned outputs.
Model run time is a key consideration in strategic transport modelling, because it determines the speed with which model runs can be carried out and the cost of those runs. Run times are also seen as the key measure of flexibility of strategic models as they determine the number of scenarios that can be evaluated for a scheme appraisal, or the number of policy options that can be compared in a finite amount of time.
At the leading edge of disaggregate modelling, model runs can take several days even on ?state of the art? computers and run time increases with model complexity. The greater the range of policy options a model is required to embrace, the greater the level of complexity that is required.
The PRISM model is a highly complex strategic transport model for the West Midlands region, developed by RAND Europe and Mott MacDonald for the Highways Agency of the UK and seven local authorities of the West Midlands. In a normal application of PRISM the demand response models and assignment models are iterated with a feedback loop amongst them several times to achieve overall convergence. The run time of the PRISM model is a critical issue, especially since it has been extended to include an income segmentation module in order to allow charging policies to be assessed in more detail. The addition of the income segmentation module has increased run times by about a factor of two to three.
Destination sampling is a method by which the run time of a disaggregate demand model can be significantly reduced with a minimal loss of accuracy. This is achieved by only performing utility calculations for a sample of destinations, for each origin. Destination sampling in forecasting should be distinguished from alternative sampling in estimation using the method of McFadden (1978).
For a given origin zone (in a tour based model), the majority of demand will be concentrated over a small number of nearby, large and highly accessible/attractive destinations. Destination sampling involves selecting a limited sample of destinations for each origin, taking advantage of this concentration of demand, and carrying out detailed demand calculations for only those destinations. Demand for the remaining destinations is forecast approximately, as a function of demand for the sampled destinations. Using destination sampling, a large proportion of the total demand can be forecast accurately using a fraction of the total number of destinations.
In this paper we will describe the implementation of destination sampling in the PRISM demand model, covering:
-Creating destination samples for each travel purpose, using importance sampling to select the most attractive destinations whilst ensuring some coverage of distant zones
-Forecasting demand using a sample of destinations, which includes:
--Tour generation based on incomplete accessibility information
--Approximating changes in demand for unsampled destinations in terms of the change in demand for sampled destinations. Proportional changes in demand are taken forward into pivoting, where they are applied to observed base matrices to produce pivoted forecast matrices.
--Accounting for mode share changes, mode availability and destination availability
We will present results to demonstrate:
-The run time savings achieved by destination sampling
-The amount of error in the model forecasts when compared to a model run with no destination sampling, including a comparison of assigned flows at the corridor level
We will highlight the assumptions implicit in the destination sampling calculations, and outline how a theoretical measure of the amount of error in the forecasts might be obtained.
Association for European Transport