Sensitivity analysis for the asymmetric network equilibrium problem |
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Authors: | Stella Dafermos Anna Nagurney |
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Institution: | (1) Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, 02912 Providence, RI, USA |
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Abstract: | We consider the asymmetric continuous traffic equilibrium network model with fixed demands where the travel cost on each link
of the transportation network may depend on the flow on this as well as other links of the network and we perform stability
and sensitivity analysis. Assuming that the travel cost functions are monotone we first show that the traffic equlibrium pattern
depends continuously upon the assigned travel demands and travel cost functions. We then focus on the delicate question of
predicting the direction of the change in the traffic pattern and the incurred travel costs resulting from changes in the
travel cost functions and travel demands and attempt to elucidate certain counter intuitive phenomena such as ‘Braess' paradox’.
Our analysis depends crucially on the fact that the governing equilibrium conditions can be formulated as a variational inequality.
This work was supported by the Program of University Research, U.S. Department of Transportation (Project number DTRS 5680-C-00007). |
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Keywords: | Traffic Equilibrium Stability and Sensitivity Analysis Braess' Paradox Variational Inequalities |
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