Cost versus time equilibrium over a network

Most traffic assignment models assume that the generalized cost experienced by a traveller making a given trip on a network results from a combination of time and money expanses that is the same for everybody. To represent with more relevance different tradeoffs between time and money, the paper designs a model that allows for differentiating travellers by means of an attribute, ‘value-of-time’, that is continuously distributed over a real interval. After giving a formal definition of the cost versus time equilibrium, it characterizes it as a solution of a convex extremal program, before showing that there exists a unique cost versus time equilibrium. The paper then designs an algorithm to compute this equilibrium. It uses it to carry on a small numerical experiment that emphasizes the importance of considering continuously distributed values-of-time in the evaluation of toll highway projects.