On Dynamic Traffic Assignment

Abstract

Traffic assignment is one of the most important steps in the mathematical theory of traffic flow and there is a lot of literature dealing with this subject (confer to Potts and Oliver (1972) or Florian (1976)). But almost all the papers have in common that only a static version of the assignment or the traffic equilibrium problem is treated. This means that there is always the assumption in the models that there are no changes in the structure of the network during the trip from an origin to a destination. Alternatively one can also say that there is no time dependancy for the trips considered. Relatively little attention has been paid to the solution of the assignment problem in a dynamic framework, which means that demand structure and trip costs are varying over time. There are basically two models which consider dynamic assignment problems. One is by Yagar (1976) which gives heuristic principles for a dynamic assignment by an “emulation technique”. This technique uses a dynamic demand structure, but there is no explicit dynamic flow model. The other model is by Merchant and Nemhauser (1978 a,b), who formulated a dynamic flow model and also presented an algorithm which obtains system- optimized flows. Perhaps one should mention in this context also the work of Maher and Akcelik (1977) about route control. Although there is no dynamic assignment model presented there the authors try to connect traffic assignment and dynamic flow structure by a combination of incremental loading and simulation in order to evaluate different strategies of traffic control. This is of interest because in urban networks traffic control strongly influences the flow dynamic and therefore also route choice as it is shown in an example given by Smith (1979).