Analytical Methods in Transportation: Left-Turn Penalties in Traffic Assignment Models

TLDR: The simplex computational technique and an equivalent geometric algorithm are presented side-by-side in the solution of a sample problem so that the relationship of the two methods can be seen.

Abstract: An examination of the use of linear programming is presented for the assignment of traffic to routes in a network when the origins and destinations of the trips are known. The formulation of the traffic assignment problem as a linear programming problem is given. The simplex computational technique and an equivalent geometric algorithm are presented side-by-side in the solution of a sample problem so that the relationship of the two methods can be seen. Also mentioned is an intersection mode that permits time penalties to be assigned to individual turning maneuvers within the intersection. Essentially the intersection node is broken into several sub-nodes so that, for visualization purposes, a spacial separation can be substituted for the temporal one. Adaptations of the model for several types of intersections are presented. The intersection model can be applied equally well to the linear programming approach to assignment or to presently used techniques.