  The average time delay of photons due to multiple interactions with gravitons
of the background is computed in a frame of the model of low-energy quantum
gravity by the author. The two variants of evaluation of the lifetime of a
virtual photon are considered: 1$)$ on a basis of the uncertainties relation
(it is a common place in physics of particles) and 2$)$ using a conjecture
about constancy of the proper lifetime of a virtual photon. It is shown that in
the first case Lorentz violation is negligible: the ratio of the average time
delay of photons to their propagation time is equal approximately to
$10^{-28}$; in the second one (with a new free parameter of the model), the
time-lag is proportional to the difference $\sqrt{E_{01}}-\sqrt{E_{02}}$, where
$E_{01}, E_{02}$ are initial energies of photons, and more energetic photons
should arrive later, also as in the first case. The effect of graviton pairing
is taken into account, too.
