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

Buffer occupancy asymptotics in rate proportional sharing networks with heterogeneous long-tailed inputs