Empirical Investigation of the Validity of the Traffic Network Equilibrium Paradigm

Empirical Investigation of the Validity of the Traffic Network Equilibrium Paradigm


D Watling, D Milne, ITS, University of Leeds, UK


A network model is compared with time-stamped 'paths' of vehicles observed over a period of days, before and after a network change. Statistical analysis is presented and practical recommendations drawn.


Network equilibrium models have for many decades been the mainstay of transport planning. Developments to these models, to incorporate uncertain or time-dependent factors, have not changed the underlying principles. It is contended that, of the thousands of practical applications of such models, virtually none truly test the validity of the underlying hypotheses. Typically, data collection efforts are focused on origin-destination flows, travel time functions and valuation parameters, but calibration focuses only on reproducing current, observed conditions. No test is made about the plausibility of how the model responds to change, yet its key planning role is in predicting performance of future networks under hypothetical conditions. Only a handful of studies have been published which compare real before-and-after effects of a scheme with the predictions of a network equilibrium model, and in those cases only quite crude comparisons are made, e.g. of link flows.

This paper reports the findings of a completed study, which aimed to explore how a real network adapted to change. Primary data consist of a time-series of observations covering the morning peak period over some twelve weekdays, before, during and after a real network change (capacity reduction). Observations were made of time-stamped (partial) registration plates across twelve sites. Matching together these data reveals information on sequences of observation stations passed, providing path-like information, and the distribution of point-to-point journey times both within and between days.

Analysis of the primary data involved application of a statistically robust method for matching the partial registration plates across sites, based on an underlying stochastic model which allows for the possibility of spurious matches. This produces estimates of summary measures, such as the moments of the point-to-point travel time distributions and matching rates, as well as a ?most likely? complete matching of the data. Compared across different days, subtle effects on the shape of the travel time probability distribution as a result of the capacity change were observed, with impacts on the mean, variance and skewness.

In terms of routing patterns, no discernible transition (dynamic) stage was detectable, and so statistical hypothesis tests were made to compare the sequences of before and after days under an assumption of stationarity. Significant day-to-day variability in total demand was a confounding factor in identifying changes in route flows. However, the pre-intervention route shares were highly stable from day-to-day (differences in shares statistically highly non-significant), as were the with-intervention route shares, suggesting analysis on the share level (rather than absolute level) might remove the confounding effect identified. Comparing the pre- and post- intervention cases together, highly statistically significant changes in route choice proportions were observed, with signs plausible for the change made.

Comparisons were made between the observed data and an existing, calibrated network equilibrium model, based on analysis of partial route flows, recognising the need for caution due to the well-known non-uniqueness of equilibrium route flows. This was unfavourable for the model: flows and travel times were both seen to substantially underestimate the mean observed results, even though the overall traffic levels on the network were believed to be reasonable. Examination revealed under-estimation of more direct routes (in distance terms), in favour of more circuitous movements. Previous practical experience with such models pointed to the role of the value of distance, which is typically interpreted as a proxy for vehicle operating cost. The value assumed in the base equilibrium model was plausible for stated preference studies conducted on this basis. The contention that the role of distance is more complex was tested by investigating alternative values, leading to significantly improved fit between modelled and observed flows and travel times when higher values were chosen. Once a good fit to the ?before? data was achieved, the model then predicted well the impacts of the change, relative to the ?after? data.

This work suggests more investigation is required regarding the role of generalised cost parameters in network equilibrium models. This work leads us to believe that distance is not simply a proxy for operating cost, as is commonly assumed, but also represents individuals? network/spatial perceptions. Thus, parameter values derived solely from economic approaches may be insufficient.


Association for European Transport