  We compare two versions of deformed dispersion relations (energy vs momenta
and momenta vs energy) and the corresponding time delay up to the second order
accuracy in the quantum gravity scale (deformation parameter). A general
framework describing modified dispersion relations and time delay with respect
to different noncommutative kappa -Minkowski spacetime realizations is firstly
proposed here and it covers all the cases introduced in the literature. It is
shown that some of the realizations provide certain bounds on quadratic
corrections, i.e. on quantum gravity scale, but it is not excluded in our
framework that quantum gravity scale is the Planck scale. We also show how the
coefficients in the dispersion relations can be obtained through a
multiparameter fit of the gamma ray burst (GRB) data.
