This study explores dynamic ramp control strategies for a simple transportation network with stochastic travel time. The objective of the ramp metering under consideration is not only to mitigate congestion in a freeway but also to achieve dynamic system optimal (DSO) assignment on a network with two parallel links: one of the links is a freeway with a single bottleneck, and the other is a local bypass link that can be regarded as an aggregation of a local street network. Travel time on the bypass link is assumed to follow a stochastic process due to many factors that cannot be controlled or predicted. A road network manager is expected to control the inflow rate in the freeway at each time point so as to attain the DSO assignment for a certain time horizon. The problem is approached by formulating it as a stochastic control problem (SCP) and then feedback control rules are provided that exploit the real time observation of the realization of the stochastic state variable (such as random travel times). It was found thatthe optimal control (ramp metering) strategies at each time period can beclassed into seven patterns, depending on the realization of the queue length in the freeway and the observed travel time of the bypass link. In order to obtain more detailed properties of the optimal control strategies, the problem requires to be solved numerically. After presenting the stochastic control formulation of the DSO assignment model developed by the authors, Hamilton-Jacobi-Bellman (HJB) equations of the SCP are derived. Some qualitative properties of the optimal control policies are demonstrated. The HJB equations were then reformulated to develop an efficient solution method for the DSO assignment. For the covering abstract see ITRD E144727. Reprinted by permission of Elsevier.
Abstract