  We show that in a generic case of the pre-big-bang scenario, inflation will
solve cosmological problems only if the universe at the onset of inflation is
extremely large and homogeneous from the very beginning. The size of a
homogeneous part of the universe at the beginning of the stage of pre-big-bang
(PBB) inflation must be greater than $10^{19}$ $l_s$, where $l_s$ is the
stringy length. The total mass of an inflationary domain must be greater than
$10^{72} M_{s}$, where $M_{s} \sim l_s^{-1}$. If the universe is initially
radiation dominated, then its total entropy at that time must be greater than
$10^{68}$. If the universe is closed, then at the moment of its formation it
must be uniform over $10^{24}$ causally disconnected domains. The natural
duration of the PBB stage in this scenario is $M_p^{-1}$. We argue that the
initial state of the open PBB universe could not be homogeneous because of
quantum fluctuations. Independently of the issue of homogeneity, one must
introduce two large dimensionless parameters, $g_0^{-2} > 10^{53}$, and $B >
10^{91}$, in order to solve the flatness problem in the PBB cosmology. A regime
of eternal inflation does not occur in the PBB scenario. This should be
compared with the simplest versions of the chaotic inflation scenario, where
the regime of eternal inflation may begin in a universe of size $O(M_{p}^{-1})$
with vanishing initial radiation entropy, mass $O(M_p)$, and geometric entropy
O(1). We conclude that the current version of the PBB scenario cannot replace
usual inflation even if one solves the graceful exit problem in this scenario.
