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This work has its ultimate background in the problem of road traffic congestion. A road traffic network is an infrastructure used for transportation of—among many other things—people to and from work, goods from factories to stores and firetrucks or ambulances in duty. In view of society a heavily congested traffic network is costly, since it delays the traffic in it. Therefore, there is a ground for doing research on how to reduce congestion.

The problem of road congestion has long been subject to research and there are well-established mathematical models for traffic networks using cost and demand functions and the behavior of road users through equilibrium definitions ([BMW56],[Pat94],[She85]). Means for reducing congestion have also been developed and formalized to mathematical models. In this work, capacity expansions of roads and toll pricing are the means considered, which formalized as mathematics constitute mathematical programs with equilibrium constraints (MPEC) with continuous decision variables. This class of optimization problems is called network design problem (NDP). Recently ([Pat08]), stochastics has been added to the models, allowing for modeling of unpredictable phenomena such as varying weather conditions, fluctuating demand or uncertainty in investment budget calculations. These problems are formalized as stochastic mathematical programs with equilibrium constraints (SMPEC).