Abstract
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 \(N\rightarrow +\infty \) 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 being a scale parameter, the workload limit process converges to a reflected fractional Brownian motion on a polyhedral cone.
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Acknowledgments
The author wishes to thank the anonymous referees for reading and helpful comments that resulted in an overall improvement of the readability of the paper. The research of the author is supported by the Ministerio de Economía y Competitividad (MEC) of Spain and ERDF (European Regional Development Found) “A way to build Europe” through project MTM2012-33937.
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Delgado, R. A packet-switched network with On/Off sources and a fair bandwidth sharing policy: state space collapse and heavy-traffic. Telecommun Syst 62, 461–479 (2016). https://doi.org/10.1007/s11235-015-0086-6
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DOI: https://doi.org/10.1007/s11235-015-0086-6
Keywords
- Bandwidth sharing
- Elastic flows
- Heavy-traffic
- On/Off sources
- Packet-switched network
- Reflected fractional Brownian motion