  We calculate the nuclear modification factor ($R_{AA}$) of light hadrons by
taking into account the initial state momentum anisotropy of the quark gluon
plasma (QGP) expected to be formed in relativistic heavy ion collisions. Such
an anisotropy can result from the initial rapid longitudinal expansion of the
matter. A phenomenological model for the space time evolution of the
anisotropic QGP is used to obtain the time dependence of the anisotropy
parameter $\xi$ and the hard momentum scale, $p_{\rm hard}$. The result is then
compared with the PHENIX experimental data to constrain the isotropization time
scale, $\tau_{\rm iso}$ for fixed initial conditions (FIC). It is shown that
the extracted value of $\tau_{\rm iso}$ lies in the range $0.5 \leq \tau_{\rm
iso} \leq 1.5$. However, using fixed final multiplicity (FFM) condition does
not lead to any firm conclusion about the extraction of the isotropization
time. The present calculation is also extended to contrast with the recent
measurement of nuclear modification factor by ALICE collaboration at
$\sqrt{s}=2.76$ TeV. It is argued that in the present approach, the extraction
of $\tau_{\rm iso}$ at this energy is uncertain and, therfore, refinement of
the model is necessary. The sensitivity of the results on the initial
conditions has been discussed. We also present the nuclear modification factor
at LHC energies with $\sqrt{s} = 5.5$ TeV.
