The Influence of Cost Assumptions on Properties of the Combined Assignment Control Problems.

The uniqueness and existence of a solution to the combined traffic assignment/signal control problem is investigated, particularly with respect to the cost functions used. The two cost functions investigated are the polynomial BPR function and Webster's two term cost function. Properties of three well-known signal control policies are investigated, and a number of new policies are developed, which guarantee a unique solution to the combined problem. The comparative performance of these policies is tested with respect to uniqueness of the resulting green times and total network travel times at the solution. To this end a streamlined version of the iterative assignment control procedure is developed and applied to three networks. It is found that potential theoretical uniqueness and existence problems do not necessarily occur in practical tests, and that enforcement of theoretical properties on signal control policies renders them rather inefficient.