Stochastic optimization of unmetered and metered traffic flow processes
Creators: name: Liu, Hao (Ph. D. In Civil Engineering)
name: 0000-0002-5319-9514
Publisher: name: The University of Texas at Austin
Year: 2020
Subjects: Stochastic optimization
Queueing theory
Robust control
Adaptive signal control

description: This dissertation is concerned with specific uncertainties in traffic flow control, which is the most cost effective way to reduce congestion. Although past research has studied uncertainties in many aspects, due to the large number of resources and the complexity to model them mathematically, there is still plenty room for this field. This dissertation is unique in considering certain uncertainties that have not been addressed yet, and then demonstrating the performance of the proposed models by comparing to classical models. Different types of uncertainties for freeway networks and urban networks are studied, respectively. The Lax-Hopf solution to the first order macroscopic traffic flow model, i.e. the LWR model, and queueing theory are the building blocks for the stochastic control models. In particular, the effects of uncertainties in two distinctive parameters: initial densities and turning ratios, are considered for freeway networks. They are handled by chance constraints and distributionally robust chance constraints in an optimization model with linear constraints derived based on the Lax-Hopf solution. Thanks to the monotonicity of the Lax-Hopf solution, these constriants can be converted into linear constraints which can be solved fast t Based on the same framework, an adaptive signal control method is proposed for urban networks where current traffic states (densities) are available. This method takes advantage of traffic information from upstream links to predict traffic volume and formulate the optimal signal timing at a targeted intersection. The signal optimization is modeled as a mixed integer linear program (MILP), and an approximation algorithm is proposed to improve the computational speed to make the proposed method applicable as a real-time control scheme. Traffic states are required in the method above to obtain accurate predictions, however, many intersections are not currently equipped with such devices. Therefore, another adaptive signal control method based on queueing theory is developed to deal with this situation. The arrivals at an intersection are assumed to follow Poisson processes and each signal phase is modeled as an M/D/1 queue. Stochastic traffic delay models are proposed based on the busy period analysis. Then, an adaptive signal control method in a rolling horizon scheme is derived. Through comparing to another adaptive signal control strategy derived from a classical signal design method, it is demonstrated that the proposed method can reduce traffic delay significantly when the volume is low, under which the hypothesis of Poisson arrivals is appropriate. Finally, as an extension of one intersection case, an adaptive coordinated signal control technique is proposed for one-way arterial streets. Unlike the models assuming uniform or known platoon arrival patterns, this method considers Poisson arrivals at the boundaries of the coordinated system. Another key contribution is that both project horizon and offsets are allowed to be changed, which is also beneficial for reducing traffic delay.