  In this paper, we investigated the issue of black hole masses and minimum
timescales of jet emission for blazars. We proposed a sophisticated model that
sets an upper limit to the central black hole masses $M_{\bullet}$ with the
minimum timescales $\Delta t^{\rm{ob}}_{\rm{min}}$ of variations observed in
blazars. The value of $\Delta t^{\rm{ob}}_{\rm{min}}$ presents an upper limit
to the size of blob in jet. The blob is assumed to be generated in the
jet-production region in the vicinity of black hole, and then the expanding
blob travels outward along the jet. We applied the model to 32 blazars, 29 of
which were detected in gamma rays by satellites, and these $\Delta
t^{\rm{ob}}_{\rm{min}}$ are on the order of hours with large variability
amplitudes. In general, these $M_{\bullet}$ estimated with this method are not
inconsistent with those masses reported in the literatures. This model is
natural to connect $M_{\bullet}$ with $\Delta t^{\rm{ob}}_{\rm{min}}$ for
blazars, and seems to be applicable to constrain $M_{\bullet}$ in the central
engines of blazars.
