Ph.D Student | Haddad Jack |
---|---|

Subject | Optimal Control for Isolated Signalized Intersections |

Department | Department of Civil and Environmental Engineering |

Supervisors | Professor David Mahalel |

Professor Emeritus Per-Olof Gutman | |

Full Thesis text |

The traffic control is one of the tools that traffic engineers can utilize as an answer for congested transportation networks. This thesis focuses on optimal control for simplified Isolated Signalized Intersections (ISI) with two one-way movements.

Like any other dynamic process, the queue dynamics of vehicles at isolated signalized intersections has transient and steady-state periods. In this thesis, the two periods are considered and two control problems for isolated signalized intersections are investigated: N-stages control and steady-state control. The N-stages control deals with an initially oversaturated traffic condition, i.e. at least one movement has a residual queue at the end of its green light, while steady-state control deals with undersaturated traffic conditions such that queues are dissolved during the green lights.

Our research goal is to determine the optimal traffic control policy that minimizes total delay at isolated signalized intersections for the transient and the steady-state periods. The total delay is defined as the time integral of the sum of all queue lengths at the intersection.

The steady-state control seeks the optimal control decisions, i.e. green duration for each movement, that imply cyclic queues, i.e. initial queue lengths at the start of the green light are equal over sequence of cycles, with minimum total delay. The N-stages control seeks to decrease the initial queue lengths at the intersection to the optimal steady-state queue lengths by optimizing control sequences over N cycles and determining the “switching point”, i.e. the optimal time instant when the traffic timing plans, i.e. constant green durations, are switched.

Different types of models are proposed for the traffic control problems: discrete-event models and a continuous-time model. Discrete-event piecewise and discrete-event max-plus models are proposed to optimize the control sequences for ISI in steady-state and N-stages control. The formulated discrete problems for steady-state and N-stages control are converted to be solved by linear programming, mixed-integer programming, and mixed-integer linear programming.

Furthermore, a continuous dynamical model of a simplified isolated signalized intersection is derived in order to find and analyze an optimal control policy to minimize total delay. An analytical solution of the optimal control problem with constrained signal light control is presented. The optimal synthesis is found for the four principal control constraint cases.

A new algorithm is proposed for solving the discrete N-stages optimization problem by simple calculations, based on the optimal solution of the corresponding continuous-time problem. The new algorithm is useful for real-time implementation.