  We present here a real-time control model for the train dynamics in a linear
metro line system. The model describes the train dynamics taking into account
average passenger arrival rates on platforms, including control laws for train
dwell and run times, based on the feedback of the train dynamics. The model
extends a recently developed Max-plus linear traffic model with
demand-dependent dwell times and a run time control. The extension permits the
elimination of eventual irregularities on the train time-headway. The resulting
train dynamics are interpreted as a dynamic programming system of a stochastic
optimal control problem of a Markov chain. The train dynamics still admit a
stable stationary regime with a unique average growth rate interpreted as the
asymptotic average train time-headway. Moreover, beyond the transient regime of
the train dynamics, our extension guarantees uniformity in time of the train
time-headways at every platform.
