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This thesis is entitled Dynamic programming systems for modeling and controlof the traffic in transportation networks. Two parts are distinguished in thisdissertation: 1) methods and approaches based on min-plus or max-plus algebra,where the dynamics are deterministic dynamic programming systems; 2) methodsand approaches whose dynamic systems are non-linear but are interpreted asstochastic dynamic programming systems. Each of the two parts includes achapter of necessary reviews, two main chapters and a chapter summarizing otherworks related to the concerned part. Part 1 includes a first chapter containingan introduction and some necessary reviews; two main chapters, one on themax-plus algebra model for the train dynamics on a metro line, the other one onthe network calculus approach for modeling and calculating performance boundson road networks; and a final chapter summarizing my other contributions on thetopic of this part. Part 2 includes a first chapter containing an introductionand some necessary reviews; two main chapters, one on the microscopic modelingof traffic taking into account anticipation in driving, the other one on themodeling of the train dynamics on a metro line taking into account thepassenger travel demand; and a final chapter summarizing my other contributionson the topic of this part.

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