Dynamic programming systems for modeling and control of the traffic in transportation networks

TL;DR

This thesis develops dynamic programming models for traffic control in transportation networks, utilizing algebraic and stochastic approaches to improve modeling accuracy and performance bounds.

Contribution

It introduces novel algebraic and stochastic dynamic programming methods for traffic modeling and control, including max-plus algebra and passenger demand considerations.

Findings

Max-plus algebra effectively models train dynamics on metro lines.

Network calculus provides bounds on road network performance.

Incorporating passenger demand improves train dynamic models.

Abstract

This thesis is entitled Dynamic programming systems for modeling and control of the traffic in transportation networks. Two parts are distinguished in this dissertation: 1) methods and approaches based on min-plus or max-plus algebra, where the dynamics are deterministic dynamic programming systems; 2) methods and approaches whose dynamic systems are non-linear but are interpreted as stochastic dynamic programming systems. Each of the two parts includes a chapter of necessary reviews, two main chapters and a chapter summarizing other works related to the concerned part. Part 1 includes a first chapter containing an introduction and some necessary reviews; two main chapters, one on the max-plus algebra model for the train dynamics on a metro line, the other one on the network calculus approach for modeling and calculating performance bounds on road networks; and a final chapter summarizing my other contributions on the topic of this part. Part 2 includes a first chapter containing an introduction and some necessary reviews; two main chapters, one on the microscopic modeling of traffic taking into account anticipation in driving, the other one on the modeling of the train dynamics on a metro line taking into account the passenger travel demand; and a final chapter summarizing my other contributions on the topic of this part.