Abstract
This study reveals basic properties of dynamic system optimal (DSO) assignment problem in a 2-link network, which consists of a freeway with a single bottleneck and an arterial road with stochastic travel time. We first formulate a DSO problem under travel time uncertainty as a stochastic control problem, in which the manager controls the freeway inflow rate at the ramp according to the rule based on the realtime observation of the traffic condition (i.e. the queue length and the travel time). Our analysis uncover that the optimality condition of the problem reduces to a dynamical system of GLCP (generalized linear complementarity problem). This enables us to develop an efficient solution algorithm for the stochastic DSO assignment problem. Numerical analysis obtain an improvement in expected total travel time by proposed feedback dynamic ramp metering, which can be interpreted as an option value of the realtime observation.
