Statistical Inference for Gravity Models in Transportation Flow Forecasting

{ Gravity models are a class of log-linear regressions that have been used in studies of traac ows between geographical zones. Stochastic parameter variations on these models, and their Bayesian analyses via stochastic simulation, are explored here in connection with the development of approaches to studying variability questions in established traac ow network equilibrium models. In addition to developing methods of statistical inference and prediction speciic to gravity models, this paper provides discussion of general concepts of Bayesian modelling and stochastic simulation analysis that will be of wider interest to the transportation community. This report represents research performed under the cross-disciplinary transportation project Measurement, Modeling and Prediction for Infrastructural Systems at the National Institute of Statistical Sciences (NISS) under support of NSF grant DMS-9313013. 1. CONTEXT AND BACKGROUND In connection with current and anticipated developments in intelligent transportation systems, studies of problems of short-term traac ow forecasting and management on urban road networks raise questions about patterns of variability of link ows and travel times, and dependencies amongst such quantities across collections of links. These kinds of issues are being studied as part of the collaborative project run by the National Institute of Statistical Sciences (NISS). As prelude to wider statistical modelling and exploration of variability and dependence issues, a part of the initial stage of this project focuses on exploration of the degrees of uncertainties about, and relationships between, equilibrium link travel times arising from static network equilibrium models. The network structure and ow models of the Advance project (Boyce et al, 1992; Berka and Boyce, 1994), based on a geographic zone structure in northeastern Illinois, provides relevant context , and associated zone-to-zone ow survey information from the Chicago Area Transportation Survey (CATS{Ghislandi, 1994) provides some relevant data. In connection with this exploratory study, variations on traditional gravity models for zone-to-zone ows are examined, with a view to a further stage of the project that may address questions of uncertainty about equilibrium link ows and travel times by repeatedly simulating average zone-to-zone ows and then running such replicates through existing network ow models, such as the Advance model. This way, replicated runs produce sampled equilibrium ows and times that incorporate and represent the uncertainties about average zone-to-zone ow rates captured in the statistical measures of uncertainties about the gravity model parameters. Patterns of dependency among equilibrium characteristics are similarly represented. This program requires initial work on statistical inference for …