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Assessing the Demand Vulnerability of Equilibrium Traffic Networks via Network Aggregation

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Abstract

Studies of network vulnerability mostly focus on changes to the supply side; whether considering a degradation of link capacity or complete link failure. However, the level of service provided by a transport network is also vulnerable to increases in travel demand, with the consequent congestion causing additional delays. Traffic equilibrium models can be used to evaluate the influence of travel demand on level of service when interest is restricted to only a small number of pre-specified demand scenarios. A demand-vulnerability analysis requires understanding the impact of unknown future changes to any possible combination of OD demands. For anything but the smallest networks, this cannot be accomplished by re-computing network equilibrium at all possible demand settings. We require a representation of the functional relationship between demands and levels of service, avoiding the need to re-evaluate the equilibrium model. This process—of collapsing the demand and network representations onto a single, coarse-level network with explicit functional relationships—is referred to here as ‘network aggregation’. We present an efficient method for network aggregation for networks operating under Stochastic User Equilibrium (SUE). In numerical experiments, we explore the nature and extent of the aggregation errors that may arise.

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Notes

  1. Our classification covers only those approaches which begin with a discrete graph representation and aim for some kind of simplified representation from that graph. Hence, although they have some relation, we exclude from this classification continuum models, whereby a dense urban network is represented as a continuum, with flows comprising a vector field (e.g. Dafermos 1980; Wong 1998; Daniele, Idone and Maugeri 2003).

  2. Indeed the equilibrium link flows and costs themselves cannot typically be expressed as explicit functions of the network parameters and OD demands.

  3. While a map is provided on Bar-Gera’s website the map node numbers do not match the data file(s) and hence it cannot be used to identify ODs.

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Authors and Affiliations

  1. Institute for Transport Studies, University of Leeds, Leeds, LS2 9JT, United Kingdom

    Richard D. Connors & David P. Watling

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  1. Richard D. Connors
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  2. David P. Watling
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Correspondence to Richard D. Connors.

Appendix: Toy City Link Cost Function Parameters

Appendix: Toy City Link Cost Function Parameters

$$ t(x)= ff+ B{\left(\frac{x}{C}\right)}^{\beta} $$
Table 3 Link Cost Function Parameters for Toy City Network
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Connors, R.D., Watling, D.P. Assessing the Demand Vulnerability of Equilibrium Traffic Networks via Network Aggregation. Netw Spat Econ 15, 367–395 (2015). https://doi.org/10.1007/s11067-014-9251-9

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