  Nuclear modification factor $R_{AA}$ for large $p_T$ single hadron is studied
in a next-to-leading order (NLO) perturbative QCD (pQCD) parton model with
medium-modified fragmentation functions (mFFs) due to jet quenching in
high-energy heavy-ion collisions. The energy loss of the hard partons in the
QGP is incorporated in the mFFs which utilize two most important parameters to
characterize the transport properties of the hard parton jets: the jet
transport parameter $\hat q_{0}$ and the mean free path $\lambda_{0}$, both at
the initial time $\tau_0$. A phenomenological study of the experimental data
for $R_{AA}(p_{T})$ is performed to constrain the two parameters with
simultaneous $\chi^2/{\rm d.o.f}$ fits to RHIC as well as LHC data. We obtain
for energetic quarks $\hat q_{0}\approx 1.1 \pm 0.2$ GeV$^2$/fm and
$\lambda_{0}\approx 0.4 \pm 0.03$ fm in central $Au+Au$ collisions at
$\sqrt{s_{NN}}=200$ GeV, while $\hat q_{0}\approx 1.7 \pm 0.3$ GeV$^2$/fm, and
$\lambda_{0}\approx 0.5 \pm 0.05$ fm in central $Pb+Pb$ collisions at
$\sqrt{s_{NN}}=2.76$ TeV. Numerical analysis shows that the best fit favors a
multiple scattering picture for the energetic jets propagating through the bulk
medium, with a moderate averaged number of gluon emissions. Based on the best
constraints for $\lambda_{0}$ and $\tau_0$, the estimated value for the
mean-squared transverse momentum broadening is moderate which implies that the
hard jets go through the medium with small reflection.
