Date Published: May 7, 2018
Publisher: Public Library of Science
Author(s): Mehmet Yildirimoglu, Osman Kahraman, Peng Chen.
Cities around the world are inundated by cars and suffer traffic congestion that results in excess delays, reduced safety and environmental pollution. The interplay between road infrastructure and travel choices defines the level and the spatio-temporal extent of congestion. Given the existing infrastructure, understanding how the route choice decisions are made and how travellers interact with each other is a crucial first step in mitigating traffic congestion. This is a problem with fundamental importance, as it has implications for other limited supply systems where agents compete for resources and reach an equilibrium. Here, we observe the route choice decisions and the traffic conditions through an extensive data set of GPS trajectories. We compare the actual paths followed by travellers to those implied by equilibrium conditions (i) at a microscopic scale, where we focus on individual path similarities, and (ii) at a macroscopic scale, where we perform network-level comparison of the traffic loads. We present that non-cooperative or selfish equilibrium replicates the actual traffic (to a certain extent) at the macroscopic scale, while the majority of individual decisions cannot be reproduced by neither selfish nor cooperative equilibrium models.
Our lives are trains of decisions, many are made individually in a matter of seconds as in changing lanes in busy traffic , some others are crafted as carefully as possible to harvest the best of outcomes despite a deceptive lack of a clear foresight of the future and may involve collectives of people of varying size, as in choosing a place to set up a firm . The dynamics of how these decisions come together and interact with each other within a resource limited setting is what fuels and shapes our languages , markets , and social lives . In line with such a fundamental importance, a great deal of intellectual effort has been devoted to elucidate the principles governing decision making at various scales, giving birth to many now established disciplines such as rational choice theory , game theory , as well as relatively recent fields including sociodynamics [8, 9], behavioural economics  and algorithmic game theory . Leveraged with the massive amounts of data on our social and economic actions being gathered with increasing accuracy thanks to the widespread access to information and communication technologies, such theoretical approaches hold the promise of addressing many challenges our modern societies face today, including the questions of sustainability and efficiency of our cities under their rapid urbanization.
Traffic equilibrium models concern the selection of routes given the demand between origins and destinations in transportation networks, and they can be formulated as variational inequality, nonlinear complementarity or fixed-point problems [38, 39]. In fact, these models present a system of nonlinear equations, and the most efficient solution approach would be Newton’s method which is based on replacing the nonlinear function with its first-order approximation. However, traffic simulation tools, which are becoming increasingly popular, involve a large number of parameters and do not have an analytical form. Therefore, the first-order derivatives are usually not available in the traffic equilibrium context. Fixed-point formulations, which do not require the computation of derivatives, are deemed the most efficient approach to establish equilibrium conditions.
Understanding the interaction between agents in a resource limited setting has far reaching implications for many aspects of our society ranging from economic markets to social circles. In the context of traffic, the sum of all travel decisions is what defines the economic and social cost of congestion, and the coupling between travellers has fundamental importance in further steps taken to alleviate congestion.