  We investigate the collective interaction of a multi-atom three-level ladder
system with an environmental incoherent reservoir. The exact solution of the
master equation that describes such a system of atoms emitting distinguishable
or indistinguishable photons on interaction with an incoherent reservoir is
obtained. The quantum decay interference effects have no influences over
steady-state distribution of population among the energy levels. However, the
photon statistics of the collectively emitted photons are different in this
case. In particular, the normalized second-order photon correlation function
shows a minimum in its value for the photons generated on lower atomic
transition in a system with orthogonal dipoles. The minimum is due to the
steady-state amplified spontaneous emission by the incoherent applied fields.
