Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2005-012 (October 24, 2005)
The Traffic Equilibrium Problem with Nonadditive Costs and Its Monotone Mixed Complementarity Problem Formulation
by Rhoda P. Agdeppa, Nobuo Yamashita and Masao Fukushima
Various models of traffic
equilibrium problems (TEPs) with nonadditive route costs have been
proposed in the last decade. However, equilibria of those models are
not easy to obtain because the variational inequality problems
(VIPs) derived from those models are not monotone in general.
In this paper, we consider a TEP whose route cost functions are nonadditive disutility
functions of time (with money converted to time). We show that the
TEP with the disutility functions can be reformulated as a monotone
Mixed Complementarity Problem (MCP) under appropriate conditions.
We then establish the existence and uniqueness results for an equilibrium
of the TEP.
Numerical experiments are carried out using various sample
networks with different disutility functions for both the single-mode
case and the case of two different transportation modes in the network.