Pivoting in travel demand models

In forecasting travel demand it is quite common, and required in the UK, to base future-year forecasts on a well-established base-year pattern of observed flows. By focussing the modelling effort on predicting changes it is possible to make significant reductions in the expected forecast error. The process of taking a fixed base point and making forecasts relative to that is called pivoting. However, the methods used for pivoting are diverse, sometimes giving substantially different results, and little has been published to help analysts to choose an appropriate method for their particular study. This paper reviews such literature as exists and discusses the apparent strengths and weaknesses of the methods that are presented in each paper. A set of criteria by which pivoting methods should be judged are presented. These include: the insight into the model that is available to the analyst, the plausibility of the methods in general terms and the likelihood that counter-intuitive results can be obtained. For example, if a synthetic forecast matrix is generated as part of the process, that matrix can be inspected and judgement made about its plausibility. Also, if a method is fully compatible with utility maximisation, it is not possible that it can generate counter-intuitive results. These criteria can help in judging the suitability of alternative methods. In maintaining consistency with utility maximisation specific functional forms need to be used and these will be described and justified. An important issue is that pivot methods must be applied both to sparse and to well-filled base matrices. To deal with sparse matrices, methods must be robust in dealing both with zero cells and in dealing with cells that contain survey data to which large expansion factors have been applied. It may be appropriate to aggregate cells in the matrix before applying the pivoting, even to restrict the influence of base data to providing key numbers such as trip length distributions. The sparseness of the base matrix may be paralleled by sparseness in the synthetic matrix, if a sampling scheme is used to speed run times; the ways in which these issues can be dealt with will be discussed. The paper develops from an ERSA paper of 2005, largely by the same authors, but takes account of theoretical developments and practical experience since then. This experience now extends from the Netherlands National Model, the Netherlands Railways Model and the model of East Denmark to include a model of the West Midlands and of Long-Distance travel in Britain.