  This paper presents a mathematical model for the train dynamics in a
mass-transit metro line system with one symmetrically operated junction. We
distinguish three parts: a central part and two branches. The tracks are
spatially discretized into segments (or blocks) and the train dynamics are
described by a discrete event system where the variables are the $k^{th}$
departure times from each segment. The train dynamics are based on two main
constraints: a travel time constraint modeling theoretic run and dwell times,
and a safe separation constraint modeling the signaling system in case where
the traffic gets very dense. The Max-plus algebra model allows to analytically
derive the asymptotic average train frequency as a function of many parameters,
including train travel times, minimum safety intervals, the total number of
trains on the line and the number of trains on each branch. This derivation
permits to understand the physics of traffic. In a further step, the results
will be used for traffic control.
