Day-to-day dynamics in a simple traffic network with mixed direct and contrarian route choice behaviors

Contrarian behavior is an attitude leading individuals to act “contrary to the crowd” and can be observed in a variety of collective systems. The aim of this study is to investigate the effects of such behavioral trait on the day-to-day evolution of a traffic system in a simple two-route scenario. To this end, we formulate a nonlinear, discrete-time dynamical system and analyze how the fraction of contrarian-like choices affects fixed point uniqueness and stability, as well as mean travel cost evaluated both for the network as a whole and separately for subjects adopting either type of route choice behavior. We show that uniqueness and stability of the fixed point of the dynamical system are ensured inside certain ranges of the fraction of contrarian subjects within the traveling population, and that the width of such ranges depends on the sensitivity of actual costs to flows and on the level of accuracy of individuals’ cost perception. Moreover, instability is seen to take different forms (oscillatory behavior or convergence to alternate fixed points) depending on which limit of the stability region is crossed by the fraction of contrarians. Results of the analysis also indicate that introducing memory and learning in the process of expected cost formation tends to counter the destabilizing effect of strongly flow-dependent costs and highly cost-sensitive route choices. Finally, direct and contrarian travelers attain the same mean travel cost throughout the fixed point stability region, while a competitive advantage of the minority group emerges outside such region, albeit at the price of a deteriorated global network performance. Overall, the findings of the study support the conclusion that a well-balanced diversification of the traveling population in terms of direct and contrarian route choice attitudes has the potential to protect the system against instabilities induced by other behavioral and network features, and that this beneficial effect can be amplified by the occurrence of learning in the formation of perceived travel costs. It is suggested that contrarian behavior may contribute to mitigating the adverse effects of concentration of choices on the “best” routes and overreaction to the supplied information, induced by Advanced Traveler Information Systems, and thus should be explicitly considered in the design of traffic management strategies involving the deployment of such systems.