  This thesis proposes mathematical traffic models and control laws for metro
lines with one junction. The models are based on the ones developed for linear
metro lines (without junction) in [12, 14]. The train dynamics are described
with a discrete event traffic model. Two time constraints are considered. The
first one imposes lower bounds on the train run and dwell times. The second one
fixes a lower bound on the safe separation time between two trains. A model of
the train dynamics on the junction is proposed, as well as control laws for the
train run and dwell times, as a function of the passenger travel demand. Most
of these models are written as linear systems in the max-plus algebra
(polynomial matrix algebra), which permits the characterization of the
stationary regime, and the derivation of traffic phase diagrams.
