  Consider a generic data unit of random size L that needs to be transmitted
over a channel of unit capacity. The channel availability dynamics is modeled
as an i.i.d. sequence {A, A_i},i>0 that is independent of L. During each period
of time that the channel becomes available, say A_i, we attempt to transmit the
data unit. If L<A_i, the transmission was considered successful; otherwise, we
wait for the next available period and attempt to retransmit the data from the
beginning. We investigate the asymptotic properties of the number of
retransmissions N and the total transmission time T until the data is
successfully transmitted. In the context of studying the completion times in
systems with failures where jobs restart from the beginning, it was shown that
this model results in power law and, in general, heavy-tailed delays. The main
objective of this paper is to uncover the detailed structure of this class of
heavy-tailed distributions induced by retransmissions. More precisely, we study
how the functional dependence between P[L>x] and P[A>x] impacts the
distributions of N and T. In particular, we discover several functional
criticality points that separate classes of different functional behavior of
the distribution of N. We also discuss the engineering implications of our
results on communication networks since retransmission strategy is a
fundamental component of the existing network protocols on all communication
layers, from the physical to the application one.
