Abstract
© 2015, Springer Science+Business Media New York. 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→ + ∞ 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→ + ∞, r being a scale parameter, the workload limit process converges to a reflected fractional Brownian motion on a polyhedral cone.
Original language | English |
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Pages (from-to) | 461-479 |
Journal | Telecommunication Systems |
Volume | 62 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jun 2016 |
Keywords
- Bandwidth sharing
- Elastic flows
- Heavy-traffic
- On/Off sources
- Packet-switched network
- Reflected fractional Brownian motion