Stochastic Dynamic Model of Urban Traffic and Optimum Management of Its Flow and Congestion - Wang, Shi'an (Université d'Ottawa / University of Ottawa, 2018)
There are a lot more roads being built periodically in most of the countries with the advancement of modern society. In order to promote the overall traffic flow quality within different cities, city traffic management has been playing a more and more essential role during the last few decades. In recent years, a significantly increasing attention has been paid to the management of traffic flow in major cities all over the world. In this thesis, we develop a stochastic dynamic model for urban traffic along with physical constraints characteristic of intersections equipped with traffic light. We assume that the incoming traffic to each stream in an intersection is amenable to the Poisson random process with variable intensity (mean). We introduce expressions for traffic throughput, congestion as well as operator's waiting time for the typical intersection in a city and hereafter define an appropriate objective functional. Afterwards, we formulate an optimization problem and propose the sequential (or recursive) algorithm based on the principle of optimality (dynamic programming) due to Bellman. The solution if implemented is expected to improve throughput, reduce congestion, and promote driver's satisfaction. Because the dynamic programming method is computationally quite intensive, we consider the scenario that one unit traffic stream stands for a specific number of vehicles which actually depends on the volume of traffic flow through the intersection. The system is simulated with inputs described by several distinct nonhomogeneous Poisson processes. For example, we apply the typical traffic arrival rate in Canada with morning peak hour at around 7:30 AM and afternoon peak hour at around 4:30 PM whilst it is also applied with morning rush hour at about 8:00 AM and afternoon rush hour at about 6:00 PM like in China. In the meanwhile, we also present a group of numerical results for the traffic arrival rates that have shorter morning peak-hour period but longer afternoon rush hour period. This may occasionally happen when there are some social activities or big events in the afternoon. In addition, another series of experiments are carried out to illustrate the feasibility of the proposed dynamic model based on the traffic arrival rates with only one peak-hour throughout the whole day. The system is simulated with a series of experiments and the optimization problem is solved by dynamic programming based on the proposed algorithm which gives us the optimal feedback control law. More specifically, the results show that both the optimal traffic light timing allocated for each stream and the congestion broadcast level (CBL) of each road segment during each time segment are found. Accordingly, the corresponding optimal cost can be found for any given initial condition. It is reasonably believed that this stochastic dynamic model would be potentially applicable for real time adaptive traffic control system.
Keywords: Urban traffic control; Traffic flow dynamics; Nonhomogeneous Poisson processes; Dynamic programming