  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.
