# Lindberg 200801

### From NA-Wiki

Computation of Traffic Equilibria

Traffic Equilibria are the equilibrium flows that appear when several independent users (travellers) with different origins and destinations travel through a network with congestion effects. There are several ways to model Traffic Equilibria, more or less complex. The more complex ones build on the simplest: the static, deterministic, single user problem (a.k.a. the Traffic Assignment Problem, TAP). In TAP (as well as the other problems) users want to travel the shortest (quickest) route to their destination. Their route choice gives route flows, which give link flows, which give link travel times which in turn determine the route times and hence the route choice. At equilibrium, nobody has any incentive to change their route choice. (This is a Nash equilibrium.) I will survey Traffic Equilibrium problems and their computation, starting with TAP and moving to more complex problems if time permits. Hopefully I can present some of my own ideas for improvement In all these problem versions a heavy recurring problem is computing shortest paths from all (relevant) origins to all (relevant) destinations. In large networks there are thousands of origins and destinations.