On a Ramp-Flow Assignment Problem

The formulation of ramp-flow assignment problem in the operations of controlled expressways during the rush-hour period is presented here. In order to discuss the problem on a quantitative basis, a simple unidirectional expressway system with multiple entrance-ramps has been selected as the model. When the flow throughout the system can be maintained below the bottleneck capacity of the expressway, the condition of steady flow prevails, and the model may be regarded as a dynamic process in the direction of flow. The ramp-flow regulation problem in an expressway system is then formulated as a multistage decision process by considering the ramp-flows as decision variables. Various criteria for selecting the optimum ramp-flow assignment are discussed and their implications in the regulation of rush-hour traffic are illustrated through a simple example. In the example, the technique of dynamic programming was used successfully to determine the optimum policy that minimizes the system congestion period and the results led to the conclusion that the two-switching policy is the best optimum policy with respect to the stated objective for a three-stage process.