Modelling equilibrium for a multi-criteria selfish routing network equilibrium flow problem

Abstract

The selfish routing of network flow often considers a single objective, namely travel time or travel distance, and optimisation models are often guided by the principle of user equilibrium (UE). A more challenging approach is to consider multiple objectives simultaneously, as for example distance, travel time and pollution.In this paper we present a bi-criteria problem whereby the road users selfish objective of minimising their travel time is at odds with the objective of minimising the overall fuel consumption of all road users. The approach taken is to manipulate “free” parameters, namely speed limits, in an attempt to coerce the road users into behaviour which helps the latter objective. Motivated by the work done on the Price of Anarchy (PoA) into classifying the suboptimality of equilibrium with respect to the minimum total travel time we look to classify the equilibrium solutions with respect to a weighted sum model of the minimum total travel time and overall fuel consumption.Our results show that small changes to these “free” parameters can result in solutions which Pareto dominate other solutions. Whilst our measure for the suboptimality of equilibrium solutions can highlight the inefficiency of a network configuration itself, it does not allow insight into the overall quality of the solution when compared with other network configurations.