  We develop a new quantum-mechanical approach to scattering a particle on a
one-dimensional (1D) system of two identical rectangular potential barriers,
which implies modelling the dynamics of its subprocesses -- transmission and
reflection -- at all stages of scattering. On its basis we define, for each
subprocess, the dwell time as well as the local (exact) and asymptotic
(extrapolated) group times. Our concept of the asymptotic transmission group
time confirms the validity of the Wigner phase time in the opaque limit, as
well as the existence of the usual and generalized Hartman effects predicted on
its basis. On the energy scale, this concept is valid everywhere in the high
energy region as well as in the low energy region, excepting resonance points
and their neighborhoods. On the contrary, the Buttiker dwell time is valid, as
the transmission time, just only at the resonance points. Our concept of the
transmission dwell time predicts monotonous growth of the tunneling time when
the distance between the opaque barriers increases. By our approach only this
time scale yields the true time spent, on average, by transmitted particles in
the region occupied by the system. We explain why the asymptotic and local
transmission group times cannot play this role and why the concept of {\it
transmission group} velocity lies beyond the scope of special relativity. And
else, all the transmission times admit only indirect measurements. Hence the
unambiguous interpretation of all tunneling-time experiments is impossible when
the transmission dynamics at all stages of scattering is unknown.
