  We construct a generalization of the Chalker-Coddington network model to the
case of fractional quantum Hall effect, which describes the tunneling between
multiple chiral edges. We derive exact local and global duality symmetries of
this model, and show that its infrared properties are identical to those of
disordered planar Josephson junction array (JJA) in a weak magnetic field,
which implies the same universality class. The zero frequency Hall resistance
of the system, which was expressed through exact correlators of the tunneling
fields, is shown to be quantized both in the quantum Hall limit and in the
limit of perfect Hall insulator.
