Risk-Averse Traffic Assignment with Elastic Demands: NCP Formulation and Solution Method for Assessing Performance Reliability

How reliable the transport network is greatly affects the mobility and economy of a country. To assess the reliability of the network accurately and design a reliable transport network properly, one should consider the risk taking and elastic behaviour of travel demand. This paper develops a Nonlinear Complementarity Problem (NCP) formulation considering this behaviour. The NCP formulation is transformed to a smooth and unconstrained mathematical program via a Fischer function and then solved by the proposed modified αBB (branch and bound) algorithm, while guaranteeing finite convergence to a point arbitrarily close to the global minimum (ɛ-convergence). To speed up the computation, a sampling method is suggested. A small numerical study is set up to illustrate the properties and the performance of the algorithm. The results show that the bound improving strategy, the sampling size on estimating the value of α for the convex lower bounding function, and choice of α have a strong influence of the rate of convergence. Copyright Springer Science + Business Media, LLC 2006