Research On Synergetic Signal Optimization And Road Guidance Problem Based On Space-phase-time Network

Accompanied by the advent of big data,the focus of urban traffic problem is to realize the intellectualization of urban transportation.It forebodes the transform of traffic control and management.Analyzing and mining mess data in the transportation industry are challenge and chance for the development of transportation.By collecting traffic data,it can adjust the path of multiple vehicles and make guidance to individuals in traffic network and optimize traffic signal.The purpose of intelligent traffic control is to make traffic unobstructed and safe.The rapid development of intelligent transport system(ITS)makes it possible to make full use of interactive information between vehicles and intelligent transport system.ITS can promote coordination of traffic guidance and signal control systems.It can make vehicle guidance and signal optimization more effectively,reduce vehicle delay and alleviate road congestion.For intelligent transport system,part of the traffic information is known.Based on those known information,giving route guidance for each vehicle in the network while adjusting the traffic signal timing at the same time,Minimizing the total travel time of all the vehicles in the network is the research goal of synergetic problem.The traditional simultaneous route guidance and signal control problem has two aspects.One is to predict traffic flow,and then adjust the signal timing to passively adapt to changing traffic flow.The predicted traffic flow is obtained by collecting real-time traffic data.The other one is to provide dynamic traffic information and path suggestion to the vehicles in the network.Drivers convert the path after receiving the information and suggestion.But the path always restricted by the fixed signal timing.The connection between route guidance and signal optimization is not strong enough.Since Allsop proposed the concept of synergetic problem,many researchers have studied the road capacity,vehicle delay and signal optimization models and analyzed the impacts of the factors related to the synergetic models.Many mathematical models have been established and have good results.In these models,the solution of the signal optimization problem is provided to the solving process of traffic assignment problem,and then the solution of the traffic assignment returns to the signal optimization problem,such iteratively feedback regulation is repeated.The coupling between the two problems is basically point-to-point.Most of the formulation of the synergetic model are non-linear.The feasible region is non-convex,so the solution is more likely to be a local optimal solution which would impact the reliability and practicality of the model.Although the solution of path guidance and signal optimization model is not unique,it is possible to combine modern optimization algorithm and software technology to solve synergetic model.If the number of constraints can be reduced in the original problem,the difficulty of solving synergetic problem can be lower.Therefore,we put forward to use Lagrangian relaxation algorithm.The algorithm can make the problem easier to solve through absorbing constraints into the objective function.The algorithm has two purposes,one is that it can be supplied to get lower bound for the mathematical models,the other one is for the Lagrangian relaxation heuristic.In this paper,route guidance problem is not dynamic traffic assignment.Routh guidance refers to the individuals and dynamic traffic assignment refers to whole vehicles in the network.By analyzing the relationship between the traffic guidance model and the signal optimization model,it can be found that both of them have underlying traffic flow evolution model.In essence,the synergetic problem is to deal with the relation between the traffic flow and the intersection delay index.The process of route guidance depends on the delays most of which are caused by signal control.Signal control is based on the aggregated trajectories of vehicles.Many previous optimization models have underlying assumption of fixed flow during the signal timing.So it always be cycle timing for intersection signal control according to traffic demand.The optimization process lose sight of flexible phase and phase sequence,so it can't reflect the redistribution of vehicle over time.The CTM(cellular transport model)is a discretization approximation of the macro continuous traffic flow model(LWR model).The dynamic network traffic flow model based on CTM can successfully capture the dynamic process of vehicles queue and dissipation at signalized intersections.Inspired by the CTM and the "storage-and-delivery" method,we consider to discretize the space node,phase node to analyze the change of the vehicle trajectories and the signal phase state over time.The establishment of space-time network and phase-time network can intuitively reflect the time-varying vehicle trajectories and phase sequence.The space-time network discretizes the link nodes according to the time,which reflects path of the vehicle and specifies the waiting time of the vehicles.The phase-time network discretizes the signal phase according to the time,which can reflect the impact of signal timing on vehicle redistribution.The synergetic problem is a combinatorial optimization problem.By imposing Lagrange multiplier,the original model can be decomposed and relaxed.Putting forward an optimization framework of Lagrangian relaxation algorithm to separate the simultaneous problem into two sub-problems,route guidance and traffic signal optimization problem.In the route guidance sub-problem,the path provided for each vehicles depends on the time-varying link capacity according to given OD and the departure time windows,in the meanwhile,the time-varying link capacity depends on the solution of the signal optimization sub-problem.In the signal optimization sub-problem,the signal timing optimization is based on the aggregated vehicle trajectories and the link demand.Link demand is rely on the solution of the route guidance problem.Also,the route guidance dual price provide the search direction for signal timing optimization.The phase of each intersection adopts the flexible eight-phase method,fully taking into account the redistribution of traffic flow during signal timing period.By placing route guidance and signal optimization problem in the space-phase-time network,we can solve the two sub-problem by searching shortest path in the network.Shortest path can be found by using MATLAB program,and then a system lower bound can be found.Upper bound of the system optimal solution is from a simulation software NeXTA-DTAlite.In the iteration process,the upper bound and the lower bound get closer.Numerical experiments show that the system optimal solution can be achieved quickly on relatively smaller gaps.