Bridging the user equilibrium and the system optimum in static traffic assignment: a review

Solving the road congestion problem is one of the most pressing issues in modern cities since it causes time wasting, pollution, higher industrial costs and huge road maintenance costs. Advances in ITS technologies and the advent of autonomous vehicles are changing mobility dramatically. They enable the implementation of a coordination mechanism, called coordinated traffic assignment, among the sat-nav devices aiming at assigning paths to drivers to eliminate congestion and to reduce the total travel time in traffic networks. Among possible congestion avoidance methods, coordinated traffic assignment is a valuable choice since it does not involve huge investments to expand the road network. Traffic assignments are traditionally devoted to two main perspectives on which the well-known Wardropian principles are inspired: the user equilibrium and the system optimum. User equilibrium is a user-driven traffic assignment in which each user chooses the most convenient path selfishly. It guarantees that fairness among users is respected since, when the equilibrium is reached, all users sharing the same origin and destination will experience the same travel time. The main drawback in a user equilibrium is that the system total travel time is not minimized and, hence, the so-called Price of Anarchy is paid. On the other hand, the system optimum is an efficient system-wide traffic assignment in which drivers are routed on the network in such a way the total travel time is minimized, but users might experience travel times that are higher than the other users travelling from the same origin to the same destination, affecting the compliance. Thus, drawbacks in implementing one of the two assignments can be overcome by hybridizing the two approaches, aiming at bridging users’ fairness to system-wide efficiency. In the last decades, a significant number of attempts have been done to bridge fairness among users and system efficiency in traffic assignments. The survey reviews the state-of-the-art of these trade-off approaches.