  In this paper, we consider a network of rate proportional processor sharing
servers in which sessions with long-tailed duration arrive as Poisson
processes. In particular, we assume that a session of type $n$ transmits at a
rate $r_n$ bits per unit time and lasts for a random time $\tau_n$ with a
generalized Pareto distribution given by $P \{\tau_n > x\} \sim \alpha_n
x^{-(1+\beta_n)}$ for large $x$, where $\alpha_n, \beta_n > 0$. The weights are
taken to be the rates of the flows. The network is assumed to be loop-free with
respect to source-destination routes. We characterize the order $O-$asymptotics
of the complementary buffer occupancy distribution at each node in terms of the
input characteristics of the sessions. In particular, we show that the
distributions obey a power law whose exponent can be calculated via solving a
fixed point and deterministic knapsack problem. The paper concludes with some
canonical examples.
