Mixed Integer Linear Programming for Traffic Signal Control

Abstract

As urban traffic congestion is on the increase worldwide, it is critical to maximize capacity and throughput of existing road infrastructure through optimized traffic signal control. This thesis builds on the body of work using mixed integer linear programming (MILP) approaches that attempt to jointly optimize traffic signal control over an entire traffic network and specifically improve the scalability of these methods to larger numbers of intersections. The main contribution of this thesis is the Queue Transmission Model (QTM), a MILP formulation for traffic signal control, which can be evaluated at non-homogeneous time intervals. This property can be used to extend the planning horizon of a traffic signal controller by strategically adjusting the spacing between samples. By using more samples near the start, and fewer at later stages, the planner can adapt to long term changes in traffic flow, while improving the short-term fidelity. The performance of this approach is evaluated on several networks of differing topology, and the results show that, compared to homogeneous time control with the same number of intervals, this method is able to produce solutions with substantially lower overall travel times, and better per vehicle delay distribution. Another contribution of this thesis is modeling light rail systems that share intersections with vehicle traffic, to aid the many cities considering light rail in understanding its impact on signal timing and delay. A method is described to incorporate light rail schedules and fixed time control as additional constraints on QTM signal timing, such that the controller is able to produce signal plans that take the light rail into account when optimizing for the vehicle traffic. A micro simulator is then used to evaluate the performance of all these extensions, comparing fixed time control to optimized adaptive control, using multiple scenarios of network topology, light rail schedules and traffic levels. The results show that optimized adaptive control plans have substantially lower average delay, better per vehicle delay distribution and lower numbers of stops. In some scenarios, switching to optimized adaptive control nullifies the impact on signal timing of introducing light rail, while persisting with fixed time control requires a significant reduction in traffic levels to achieve the same outcome. The final contribution of this thesis is to compare QTM with several different formulations for MILP based traffic signal optimization both theoretically and empirically. First, it is demonstrated using variational theory, that all the models find equivalent discrete solutions to kinematic wave theory. This result is used to finally address the issue of unintended vehicle withholding, and to show for the first time that withholding has no impact on the optimality of the solutions. Finally, a series of experiments is run on networks of increasing size, using vehicle platoons of varying length and arrival time. The results show that when comparing both the solve time and the quality, QTM is able to find better policies with lower delay, and in less time than the other formulations. Show more