Part II: Equilibrium Methods

This paper reviews the equilibrium assignment models, i.e. assignment techniques which are based on or make use of Wardrop's first principle. The models are classified into: (1) assignments with fixed demands, (2) assignments with elastic demands, and (3) combined models. In the first category the number of trips between zones is known and fixed. The way this assignment is mathematically formulated and the use of the Frank-Wolfe algorithm to solve it are discussed. Improved models of this category, and further models which take into account junction interactions or a system-optimal behavior are also presented. In the second category of elastic demands the number of trips between zones depends on the travel time between origin and destination. The problem formulation and the solution methodologies developed so far are described in detail. Models which include traffic control in the elastic demand assignment or use a dual problem formulation are also commented. Finally, the combined models are presented, which combine equilibrium traffic assignment with one or more of the other stages of the transport planning process. In the concluding remarks the usefulness of the equilibrium assignments in practical applications is discussed.