-A bi-level modelling approach is proposed to represent the interaction between the vehicle loading practices of road freight transport carriers, and the decisions of a road planning authority responsible both for road maintenance and for the enforcement of overloading control. At the lower (reactive) level, the overloading decisions of the carriers impact on road maintenance expenditure, while at the upper (anticipatory) level the planner decides fine and enforcement levels by anticipating the responses of the carriers. A case study using data from Mexico is used to illustrate the method.

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The issue of route choice is a key factor for the freight transport performance. Congestion at roads encourages hauliers to change routes to minimize the delays and keep lead times in a reliable range. In the context of transport planning, the route choice problem can be assessed by modelling the travel times needed to reach a destination through the different routes in a road network. Is in this point where the volume-delay functions become relevant. A Volume-Delay Function (VDF) is a mathematical representation of the increase of the travel time as more and more vehicles utilize the routes, causing congestion on the road networks. The related literature and practitioners report on the use of some known functional forms, as the BPR function, the Conical volume-delay function or the Akcelik's function, which are widely utilized in flow's assignation modelling in transport planning. A successful application of VDFs requires a proper fitting of the function's parameters. In a classical focus these parameters can be deduced from speed-flow surveys carried out at the routes or links of interest; these surveys generally require time money and personnel. As an alternative to this classical focus, particularly when facing scarcity of resources, this work carries out a mathematical analysis of the VDF functional forms, as well with an interpretation of their parameters in relation to road's operation. The results of these analyses clarifies the meaning of the functional forms for the VDFs and their parameters, and suggest other ways to assess those parameters which may be more practical for the purpose of modelling the choice of route in freight transport. Some considerations to put into practice this in Mexico are discussed at the end of this work.