  The goal of the paper is to study asymptotic behavior of the number of lost
messages. Long messages are assumed to be divided into a random number of
packets which are transmitted independently of one another. An error in
transmission of a packet results in the loss of the entire message. Messages
arrive to the $M/GI/1$ finite buffer model and can be lost in two cases as
either at least one of its packets is corrupted or the buffer is overflowed.
With the parameters of the system typical for models of information
transmission in real networks, we obtain theorems on asymptotic behavior of the
number of lost messages. We also study how the loss probability changes if
redundant packets are added. Our asymptotic analysis approach is based on
Tauberian theorems with remainder.
