Networks and Spatial Economics

, Volume 7, Issue 3, pp 213–240

A Study on Network Design Problems for Multi-modal Networks by Probit-based Stochastic User Equilibrium


  • Kenetsu Uchida
    • Graduate School of EngineeringHokkaido University
    • Department of Civil and Structural EngineeringThe Hong Kong Polytechnic University
    • Institute for Transport StudiesUniversity of Leeds
  • David Watling
    • Institute for Transport StudiesUniversity of Leeds
  • Richard Connors
    • Institute for Transport StudiesUniversity of Leeds

DOI: 10.1007/s11067-006-9010-7

Cite this article as:
Uchida, K., Sumalee, A., Watling, D. et al. Netw Spat Econ (2007) 7: 213. doi:10.1007/s11067-006-9010-7


This paper develops a multi-modal transport network model considering various travel modes including railway, bus, auto, and walking. Travellers are assumed to choose their multi-modal routes so as to minimise their perceived disutilities of travel following the Probit Stochastic User Equilibrium (SUE) condition. Factors influencing the disutility of a multi-modal route include actual travel times, discomfort on transit systems, expected waiting times, fares, and constants specific to transport modes. The paper then deals with the multi-modal network design problem (NDP). The paper employs the method of sensitivity analysis to define linear approximation functions between the Probit SUE link flows and the design parameters, which are then used as constraints in the sub-problem of the NDP instead of the original SUE condition. Based on this reformulated NDP, an efficient algorithm for solving the problem is proposed in the paper. Two instances of this general NDP formulation are then presented in the paper: the optimal frequency design problem for public transport services (FDP), and the anti-freezing admixture dispersion problem (AADP).


Network designMulti-modal networksStochastic user equilibriumSensitivity analysis

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© Springer Science+Business Media, LLC 2006