  Fundamental diagrams describing the relation between pedestrians speed and
density are key points in understanding pedestrian dynamics. Experimental data
evidence the onset of complex behaviors in which the velocity decreases with
the density and different logistic regimes are identified. This paper addresses
the issue of pedestrians transport and of fundamental diagrams for a scenario
involving the motion of pedestrians escaping from an obscure tunnel. We capture
the effects of the communication efficiency and the exit capacity by means of
two thresholds controlling the rate at which particles (walkers, pedestrians)
move on the lattice. Using a particle system model, we show that in absence of
limitation in communication among pedestrians we reproduce with good accuracy
the standard fundamental diagrams, whose basic behaviors can be interpreted in
terms of the exit capacity limitation. When the effect of a limited
communication ability is considered, then interesting non-intuitive phenomena
occur. Particularly, we shed light on the loss of monotonicity of the typical
speed--density curves, revealing the existence of a pedestrians density
optimizing the escape.
  We study both the discrete particle dynamics as well as the corresponding
hydrodynamic limit (a porous medium equation and a transport (continuity)
equation). We also point out the dependence of the effective transport
coefficients on the two thresholds - the essence of the microstructure
information.
