Hierarchical Feedback Control Of Urban Traffic

The increasing traffic congestion in the urban area is causing problems on the social economic due to the resulting pollution,unsafety,and longer commuting time.Land use limitations and environmental constraints prevent the continued expansion of urban traffic infrastructures as a solution to congestion problems but an optimal utilization of the available infrastructure via a variety of traffic control measures.In this dissertation,the traffic lights at the intersections are regarded as control devices.Optimizing the switching times of traffic lights could lead to the minimization of the total time spent by all vehicles in an urban area.For the traffic in an urban area the complexity of the feedback control problem requires a hierarchical decomposition based on different levels of abstraction.We propose that model based local feedback controller selecting the switching times of traffic light of each intersection and operating in the low level optimizes traffic flow inside a region at a fast time scale by using a detailed traffic model.In the high level,perimeter control utilizes more aggregate traffic data and determines the flow rate of vehicles entering a region at the slower time scale in order to avoid congestion in this region.Model based traffic-responsive strategies have been given for a long time.Initially the models used in these strategies are simple traffic flow forecasting models based on the traffic data measured by inductive loop detectors that are usually located at 40-meter upstream of the stop line.Since then a number of approaches based on detailed model predicting the traffic flow dynamics and employing various numerical solution algorithm including mixedinteger linear programming,genetic algorithm,and particle swarm optimization have been proposed.However,the optimization problem is too computationally expensive to be solved on-line as the number of the controlled intersections increases due to their centralized architecture.Instead of centralized architecture,multi-agent or distributed control as adopted in control design of the low level in this dissertation only requires an agent to solve an optimization problem of a subnetwork so that the real-time feasibility is always possible.It should be pointed out that the many proposals for hierarchical control for traffic lights are based on the concept of three control variables: cycle,offset,and green spilt and the green split are usually optimized in the low level.In this research,the switching time of traffic light is treated as the control variable in proposed control framework and the high level controller only acts when the traffic in this region approaches the congestion,thus contributing to more freedom of optimization in the low level.In order to design the model based local feedback controllers in the low level,urban cell transmission model(UCTM)that is a control-oriented extension of the classical cell transmission model(CTM)for urban networks is first introduced.This model not only describes the cell dynamics of classic CTM,but also explicitly models the dynamic behaviour of traffic streams at merge and diverge locations,as well as the queue discharge phenomenon(using a modification of the sending function).The validity of this model is checked by comparing its predictions with the result from the microsimulator SUMO.UCTM is simple and intuitively easy to understand and implement.It is capable of representing all the major causes for delay of vehicles and predicting the arrival time of vehicles at the stop line of a controlled intersection at the level of detail of a few seconds.UCTM is then used for synthesis of local model predictive controllers(LMPC)and coordinated model predictive controllers(CMPC)in the low level.One local control agent only controls one intersection and selects the switching times of traffic light at this controlled intersection in the design of LMPC and CMPC.Both LMPC and CMPC employ a simulation based optimization while communications among the neighbouring control agents are allowed in CMPC but no communication in LMPC.In C++ implementation of these control strategies,a local control agent evaluates at most 9 scenarios with a prediction horizon of160 seconds at each decision time and the computation can be done within 5 seconds.This result shows that UCTM is computationally fast enough such that it can be used in a model predictive controller deciding for one intersection switching times of traffic light over a prediction horizon of a few minutes.LMPC uses local online measurements along the links connected to the intersection for estimating the initial state of the UCTM simulation runs.The performance of different scenarios each starting with this initial state but using different switching times of the traffic lights over the prediction horizon is evaluated.The local control agent then selects as optimal scenario the switching times with the smallest predicted average delay.Future arrivals in LMPC calculations are predicted using off-line information of average flow rates of upstream link of the intersection.The performance of the proposed LMPC is analysed via simulation on a simple 4 by 4 Manhattan grid,comparing its delay with an efficiently tuned pretimed control,and max pressure control.These simulations show that the proposed LMPC achieves a significant reduction in delay for various traffic conditions.CMPC improves the accuracy of the performance predictions of each scenario by allowing exchange of information about planned switching times and planed flow between neighbouring control agents.Compared to LMPC the offline information on average flow rates from neighbouring intersections is replaced in CMPC by additional online information on when the neighbouring intersections plan to send vehicles to the intersection under control.To achieve good coordination,a cost for changing the previous planned schedule is added to the cost function.The simulations on a 4 by 4 grid show that the proposed CMPC further reduces the delay compared with LMPC.Note that the system performance now becomes dependent on the communication between neighbouring agents but more robust against modelling uncertainly.LMPC could be regarded as a backup of CMPC in case of communication failure.Inspired from max pressure control which is provably stable,a prediction of the value of the local Lyapunov function,which is defined as the sum of the squared queue sizes over all links connected to an intersection,is used as a constraint for selecting the optimal scenario whenever some downstream queues of this intersection become too long.Only scenarios that decrease the value of the local Lypaunov function of this intersection are considered for possible implementation.This stabilization criterion is shown experimentally to further improve the performance of the controller.In particular it leads to a significant reduction of the queues that build up at the edges of the traffic region under control.This property will contribute to a better performance of high-level perimeter control in the hierarchical framework since perimeter control avoids the congestion of the region by reducing the inflow to it,thereby creating more temporary queues outside the region.This extra delay of vehicles incurred by perimeter control at the edge of the region becomes smaller and is thus easier to be offset by the higher speed of vehicles travelling in the region thanks to CMPC.The hierarchical control framework given in the end of this dissertation specifies how to synergistically design the low-level controller and high-level perimeter controller.The detailed analysis and simulation experiment of this hierarchical framework are left for the future work.An interesting but difficult problem is how to give a rigorous proof to the stability of CMPC possibly after further modification to the algorithm,which will contributes to the theory of distributed control.This open question is also under the investigation.