Rolling resistance is one of the key factors that affect the fuel efficiency of the national pavement system. In addition to pavement texture and pavement roughness, the dissipation of mechanical work provided by the vehicle because of viscous deformation within the pavement structure has been recognized as a relevant factor contributing to the environmental footprint of pavement systems. This dissipation depends on material and structural parameters that can be optimized to increase the fuel efficiency of pavements. Identifying the key material and structural parameters that drive this dissipation is the focus of this paper. This identification is achieved by a combination of dimensional analysis and model-based simulations of the dissipation of a viscoelastic beam on an elastic foundation. For linear viscoelastic systems, the dissipation is found to scale with the square of the vehicle weight and with the inverse of the viscous relaxation time, in addition to distinct power relations of top-layer stiffness, thickness, and subgrade modulus. These scaling relations can be used by pavement engineers to reduce such pavement-inherent dissipation mechanisms and increase the fuel efficiency of a pavement design. An example shows the application of these scaling relations with data extracted from FHWA's Long-Term Pavement Performance database for seven road classes. The scaling relations provide a means for evaluating the performance of the various road classes in terms of the fuel efficiency related to dissipation.