Enforcing fuel-optimal traffic patterns

Traffic Assignment (TA) models route choices of users of a road transport network assuming a known relationship between traffic flow and travel cost, and fixed demand between origin and destination points in the network. In this paper, we consider the case where the users’ travel cost function is a weighted sum of travel time, fuel consumption, and tolls. We show the existence of speed limits and tolls whose combination induces a traffic pattern with minimum total fuel consumption as a user equilibrium. This result holds both in the case where all tolls are required to be non-negative as well as in the case where negative tolls (subsidies) are allowed but network-wide revenue neutrality of the toll scheme is required. With respect to the speed limits, arbitrary non-negative values are allowed in our model, but we additionally analyze the more realistic scenario in which only a discrete set of speed limits (e.g., integer multiples of ten) is available. While this restriction of the available speed limits may lead to an increase in the total fuel consumption achievable in a user equilibrium, we prove upper bounds showing that the increase is very small for real-world TA instances.