Dynamic Optimal Control Of Urban Expressway Via Variable Message Signs

The traffic guidance system (TGS) based on variable message signs (VMS) is an important component of the intelligent transportation system. Providing traffic information via VMS potentially leads to a more efficient traffic network. By use of the TGS, the traffic is better distributed through the roads in the network, so no road is congested due to a heavy demand.The key different aspect of the TGS comparing with the traditional signal control system is the uncertainty of the guidance effect. Unlike other control devices, VMSs are not supported by mandatory regulations. Consequently, it is uncertain whether drivers obey or disobey the guidance. This kind of uncertainty makes the design of information provision strategy challenging. Improper provision of guidance information may move the congestion from one road to another, and degrade the overall mobility of the network.Designing the information provision strategy is important for the TGS, and is studied in the dissertation. The optimal control method is adopted to get the optimal information provision strategy via VMS. We innovatively propose a dynamical optimal control method for the TGS considering the uncertain behavior of driver, and a clustering method for the control location selecting problem in network with multi-VMS and on-ramps. Moreover, the switches between several countable states of VMS are used as the control variables in the dissertation. It makes the derived optimal strategy easier to understand and more manipulatable in compare with most current works. The main contributions of the dissertation are summarized as follows:First, assuming that drivers have a constant compliance rate with respect to the messages via VMS, a second-order macroscopic traffic flow model is adopted to formulate the basic optimal control problem for the TGS. The control variables in the problem are the on-off states of VMS, i.e. binary variables, so the optimal control problem is transformed to an easy-to-solve optimal parameter selecting problem. The problem is then solved by use of revised gradient based on the maximum principle. It is shown by simulation that the proposed method performs best in scenarios with critically saturated flow demand.Second, assuming that drivers’ compliance rate to VMS follows a given stochastic distribution, the optimal control for the TGS with stochastic parameters is studied. The problem is formulated in the format of a bi-level optimal control problem, which consists of a deterministic lower level problem about the traffic network and a stochastic upper level problem about drivers’ stochastic compliance. Then, the sensitivity of cost function with respect to drivers’ compliance is utilized to convert the upper level problem to a deterministic one, and the convexity of cost function with respect to drivers’ compliance is proved. The proposed conversion method makes it able to avoid the complexity and difficulty of solving a stochastic optimal control problem. Simulation shows that the expectation of the cost criterion is improved, and the improvement is rather robust while parameters change.Third, drivers are assumed to choose a route that maximizes their individual utility according to their perception of travel time, and drivers’ diversion rate turns out a time-varying parameter. A discrete choice model named the logit model, together with a vehicle queuing model named the point queue model are adopted to formulate the new optimal control problem, in which whether or not providing real-time travel time information via VMS is used as the control variable. The proposed method is tested via numerical examples that use real-world traffic demand levels in a commuting network in Minneapolis, MN. It is found that always giving information may not be the optimal strategy, while the proposed on-off control method always performs best. The sensitivity of the solution to varying demand patterns is also analyzed.Finally, the problem of designing optimal strategy for coordinated control of route guidance via VMS and ramp metering is considered. To conquer the side effect arising from the big number of control variables, the gradients of control variables are utilized and a K-means cluster algorithm is applied to select the best control locations. Simulation of a real-world traffic network shows that the proposed method can dynamically select control locations and efficiently reduce the total time spent of drivers. In some specific scenario, the selective control method performs even better than the one employing all control variables.