Aggregation of Transport Networks Using Sensitivity Analysis
R D Connors, D P Watling, ITS, University of Leeds, UK
To address inconsistencies that can arise from different scales of network representation in transport models, an analytical method is established for the aggregation of network models, incorporating the network equilibrium condition.
Transport analysis spans many scales. At one extreme may be the design of traffic signals at an urban intersection; at a wider geographical level, transport planning over a city network may be required to examine the impact on route choice and travel demand of measures such as road user charging. At a still wider level, analysis may need to address problems of regional or national impact, such as the introduction of a national road user charging system. An element in all such analyses is that as the geographical scope of the problem changes, so does the scale of the models used, in terms of the fidelity of network representation, the size of the zones over which trip demands are modelled, and the level of disaggregation of traveller responses by, say, socio-economic group. The question then naturally arises: are these models all consistent in some sense, across the different aggregation scales? Specifically in this paper we focus on the first of these issues, that of network aggregation.
Such questions of scale and model aggregation are highly relevant in practice:
1. Many local and regional authorities maintain a range of transport models with different geographical coverage, with a coarser-scale regional/strategic model providing forecasts to a more detailed model of the urban environment, yet the underlying network models are typically based on inconsistent assumptions.
2. The advent of VADMA variable demand advice has raised questions regarding the interface between network models and complex demand models such as DIADEM, especially when the two approaches may adopt different scales of network representation.
Looking to past research on network aggregation mostly reveals empirical reports simply demonstrating that the level of aggregation alters model prediction. Moreover, as Friesz described in 1985: ?aggregation has been practised in an essentially ad hoc fashion since the advent of widespread use of network transportation planning models?. The only previous analytical method in the literature is due to Hearn (1984), who considered a focus area within a large detailed network, splitting the problem into a pair of interrelated mathematical programs, one relating to the links of the focus area and the other to its complement (the rest of the large detailed network). While the decomposed problems are individually easier to solve, it is not clear that solving them in a combined iterative fashion is more efficient than solving the original network assignment problem.
In order to address such issues, in this paper we establish a systematic methodology that allows us to make the transition from a disaggregate representation to an equivalent aggregate representation of the same network. Specifically, to achieve some generality, our focus is the aggregation of the Stochastic User Equilibrium (SUE) model, which is well known to approximate the more widely used User Equilibrium (UE) model to an arbitrary accuracy by suitable choice of perception error variances. Via sensitivity analysis of the SUE fixed point condition, our method analyses the impact of changes to the OD travel demand matrix on mean perceived OD travel costs (satisfactions). The process of re-equilibration at each stage is implicitly embedded in the sensitivity analysis, avoiding the need to re-solve equilibrium at many points. This yields an explicit functional relationship between OD demands and OD satisfactions.
For those familiar with the discrete choice modelling field, it is noted that our procedure for aggregating the network supply-side is conceptually similar to the process by which aggregation or ?nesting? of alternatives is addressed in travel demand models; in this analogy, the logsum takes the role of our ?OD satisfactions?.
There are several ways in which this aggregation method may then be subsequently applied in network analysis. The illustration used in the paper considers the interaction between a demand model operating on a simplified aggregate network, and a detailed highway network model. The application considers a problem of mode choice for urban commuters between train and car. The approach is to focus on a particular OD movement of interest, and agglomerate all other OD movements as an overall ?traffic intensity?, which reflects that as demands on other movements grow they may delay the travel of our OD movement of interest. The resulting problem is an aggregation/simplification of the original problem, consisting of only two dimensions of ?demand flow? and two dimensions of ?travel cost?, compared with the many OD movements, links and paths in the original network. Numerical results are reported, comparing the aggregate and disaggregate approaches to the combined mode choice/network assignment problem.
Association for European Transport