Consider a fluid queue with a finite buffer $B$ and capacity $c$
fed by a superposition of $N$ independent On--Off processes. An
On--Off process consists of a sequence of alternating independent periods of
activity and silence. Successive periods of activity, as well as
silence, are identically distributed. The process is
active with probability $p$ and during its activity period
produces fluid at constant rate $r$. For this queueing system,
under the assumption that the excess activity periods are
intermediately regularly varying, we derive explicit and
asymptotically exact formulas for approximating the stationary
overflow probability and loss rate. In the case of homogeneous
processes with excess activity periods equal in distribution to
$\tau^e$, the queue loss rate is asymptotically, as $B\rightarrow
\infty$, equal to
\[
\Lambda^B = (r_0 -c) \pmatrix{N\cr m} \Bigl(p \,\Pr\Bigl[\tau^e
> \frac{B}{r_0-c}\Bigr]\Bigr)^{m} (1+o(1)),
\]
where $m$ is the smallest integer greater than
$(c-N\rho)/(r-\rho)$, $r_0= m r + (N -m)\rho$, $\rho=r p$ and $N
\rho < c$; the results require a mild technical assumption that
$(c-N\rho)/(r-\rho)$ is not an integer. The analyzed queueing
system represents a standard model of resource sharing in
telecommunication networks. The derived asymptotic results are
shown to provide accurate approximations to simulation
experiments. Furthermore, the results offer insight into
qualitative tradeoffs between the overflow probability,
offered traffic load, capacity and buffer space.