Sensitivity Analysis of Stochastic User Equilibrium Flows in a Bi-Modal Network with Application to Optimal Pricing

Document Type

Journal Article

Publication Date


Subject Area

operations - traffic, ridership - commuting, policy - congestion, economics - pricing, economics - economies of scale, mode - mass transit


Transit, Traffic congestion, Stochastic user equilibrium model, Sensitivity analysis, Roads, Public transit, Pricing, Optimization, Optimisation, Networks, Network equilibrium, Mass transit, Local transit, Links (Networks), Gridlock (Traffic), Equilibrium (Systems), Economies of scale, Cost functions, Algorithms


This paper examines sensitivity analysis methods for transportation systems having an automobile road network and a physically separate transit network. A general computational method is presented for the case where both the automobile and transit networks are congested in the sense that link cost functions increase with the flow. Conditions under which sensitivity analysis can be properly conducted are investigated for another case where the automobile network is congested but the transit network simply consists of independent lines connecting origin-destination pairs and may have economies of scale with the increase of the passengers. The sensitivity analysis algorithm is applied to the optimal pricing problem in a combined network with transit lines exhibiting economies of scale as well as congestion diseconomies. This research is successful in providing a general methodological framework for dealing with the two-fold non-convexity in optimal design and management of transportation systems. Directions for further research are discussed.


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