  We investigate the role of inelastic processes in the strongly interacting
quark-gluon plasma (sQGP) based on the effective dynamical quasi-particle model
(DQPM). In the DQPM the non-perturbative properties of the sQGP at finite
temperature $T$ and baryon chemical potential $\mu_B$ are described in terms of
strongly interacting off-shell partons (quarks and gluons) with dynamically
generated spectral functions whose properties are adjusted to reproduce the
lQCD EoS for the QGP in thermodynamic equilibrium. For the first time the
massive gluon radiation processes from the off-shell quark-quark ($q+q$) and
quark-gluon ($q+g$) scatterings are calculated explicitly within leading order
Feynman diagrams with effective propagators and vertices from the DQPM without
any further approximations. We present the results for the energy and
temperature dependencies of the total and differential radiative cross sections
and compare them to the corresponding elastic cross sections. We show that our
results reproduce the pQCD calculations in the limit of zero masses and widths
of quasiparticles. Also we study the $\mu_B$ dependence of the inelastic cross
sections. Moreover, we present estimates for the transition rate and relaxation
time of radiative versus elastic scatterings in the sQGP.
