A mixed integer linear programming formulation of the dynamic traffic assignment problem

The authors propose a new model for dynamic traffic assignment, modeling the traffic system by a mixed integer linear program solvable in finite time. The model represents link travel times, which must be the same for all vehicles which enter a link together during a single time period by means of 0-1 integer variables. Given the values of these variables, the problem is to assign traffic, modeled as multiperiod multicommodity flow, subject to constraints on capacity implied by the link travel times. An optimal solution to the model gives the vehicle routings corresponding to minimum total travel time, achieving the most efficient use of road capacity. The solution gives unambiguous link travel times as a function of time of entry to the link, suitable for individual route optimization if all but a small priority class of traffic accepts the system-optimal routing