A packet-switched network with On/Off sources and a fair bandwidth sharing policy: state space collapse and heavy-traffic

We consider a flow-level model for packet-switched telecommunications networks handling elastic flows with concurrent occupancy of resources, in which digital objects are transferred at a rate determined by capacity allocation on each route. The capacity of each node is dynamically allocated to the routes passing by it through a weighted proportional fair sharing policy, and the arrival request for transfer on each route is generated by N heavy-tailed On/Off sources. Under heavy-traffic, we combine state space collapse (SSC) and an Invariance Principle to show that when $$N\rightarrow +\infty $$ N → + ∞ the conveniently scaled workload and flow count processes converge. SSC establishes a relationship between the corresponding limits by means of a deterministic operator. In Theorem 1 we prove that assuming the other hypotheses hold, SSC is not only sufficient for the convergence, but necessary. In Theorem 2 we prove that when $$r\rightarrow +\infty $$ r → + ∞ , r being a scale parameter, the workload limit process converges to a reflected fractional Brownian motion on a polyhedral cone.