  We calculate two transport coefficients -- the shear viscosity over entropy
ratio $\eta/s$ and the ratio of the electric conductivity to the temperature
$\sigma_0/T$ -- of strongly interacting quark matter within the extended
$N_f=3$ Polyakov Nambu-Jona-Lasinio (PNJL) model along the crossover transition
line for moderate values of baryon chemical potential $0 \leq \mu_B \leq 0.9$
GeV as well as in the vicinity of the critical endpoint (CEP) and at large
baryon chemical potential $\mu_B=1.2$ GeV, where the first-order phase
transition takes place. The evaluation of the transport coefficients is
performed on the basis of the effective Boltzmann equation in the relaxation
time approximation. We employ two different methods for the calculation of the
quark relaxation times: i) using the averaged transition rate defined via
thermal averaged quark-quark and quark-antiquark PNJL cross sections and ii)
using the 'weighted' thermal averaged quark-quark and quark-antiquark PNJL
cross sections. The $\eta/s$ and $\sigma_0/T$ transport coefficients have a
similar temperature and chemical potential behavior when approaching the chiral
phase transition for the both methods for the quark relaxation time, however,
the differences grow with increasing temperature. We demonstrate the effect of
the first-order phase transition and of the CEP on the transport coefficients
in the deconfined QCD medium.
