  The completion time for the dissemination (or alternatively, aggregation) of
information from all nodes in a network plays a critical role in the design and
analysis of communication systems, especially in real time applications for
which delay is critical. In this work, we analyse the completion time of data
dissemination in a shared loss (i.e., unreliable links) multicast tree, at the
limit of large number of nodes. Specifically, analytic expressions for upper
and lower bounds on the expected completion time are provided, and, in
particular, it is shown that both these bounds scale as $\alpha \log n$. For
example, on a full binary tree with $n$ end users, and packet loss probability
of $0.1$, we bound the expected completion time for disseminating one packet
from below by $1.41 \log_2 n+o \left( \log n \right)$ and from above by $1.78
\log_2 n+o \left( \log n \right)$.
  Clearly, the completion time is determined by the last end user who receives
the message, that is, a maximum over all arrival times. Hence, Extreme Value
Theory (EVT) is an appropriate tool to explore this problem. However, since
arrival times are correlated, non-stationary, and furthermore, time slots are
discrete, a thorough study of EVT for Non-Stationary Integer Valued (NSIV)
sequences is required. To the best of our knowledge, such processes were not
studied before in the framework of EVT. Consequently, we derive the asymptotic
distribution of the maxima of NSIV sequences satisfying certain conditions, and
give EVT results which are applicable also beyond the scope of this work. These
result are then used to derive tight bounds on the completion time. Finally,
the results are validated by extensive simulations and numerical analysis.
