Modelling and optimising fuel consumption in traffic assignment problems

The Traffic Assignment (TA) Problem models route choices of users of a road transport network assuming a known relationship between traffic flow and travel time, and fixed demand between origin and destination points in the network. By modelling network user route choices, TA is able to derive network wide flows, for instance to understand the effects of modifications of the transport system in terms of congestion, travel times, or generalised cost. A basic assumption of TA is that network users selfishly minimise their own travel time and that a TA solution follows the so-called user equilibrium. It is well known that user equilibrium traffic flow does not necessarily follow a system-optimal travel pattern (in terms of travel time or generalised cost). Such a system-optimal travel pattern can be computed and congestion pricing theory shows that it can be enforced in a user equilibrium TA by charging network users an appropriate congestion toll (cf. Patrikkson 1994). In this paper, we develop a model of fuel consumption within the TA framework. Our aim is to derive a system-optimal distribution of traffic with respect to fuel consumption and to devise congestion pricing and speed limits to encourage traffic flow to follow this system-optimal distribution when network users minimize a weighted sum of their travel time, fuel consumption, and tolls. We initially propose to apply a simplified model of fuel consumption (Song et al., 2013). Unfortunately, fuel consumption is not an increasing function of speed or arc flow – a basic assumption required to ensure that TA models converge to user equilibrium or system optimum solutions. Hence, considering fuel consumption in TA models provides new methodical challenges. Despite this, we analyse the proposed fuel-consumption TA model from a theoretical point of view and are able to show that, under appropriate assumptions, system-optimal traffic patterns can be derived and enforced by congestion pricing and appropriate speed limits. Moreover, we present results for standard TA instances (Transportation Networks for Research, 2016).