A Heavy-Traffic Limit of a Two-Station Fluid Model with Heavy-Tailed On/Off Sources

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A Heavy-Traffic Limit of a Two-Station Fluid Model with Heavy-Tailed On/Off Sources, Feedback and Flexible Servers

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ABSTRACT

We consider a two-station fluid model that can be approximated under heavy-traffic by a reflected fractional Browian motion (rfBm) process on a convex polyhedron. Specifically, we prove a heavy-traffic limit theorem for a two single-server workstation fluid model with feedback and flexible servers. Flexibility here means that one of the servers is capable to help the other. The non-deterministic arrival process is generated by a large enough number of heavy-tailed On/Off sources, N. We introduce the adequate definition of workload, and scaling conveniently by a factor r and by N, and letting N and r approach infinity (in this order), we prove that the scaled workload process converges to a rfBm on a convex polyhedron.

KEYWORDS

fluid network, flexible servers, reflected fractional Brownian motion, convex polyhedron, On/Off sources, workload process, heavy-traffic limit, Skorokhod problem

REFERENCES

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[4] R. Delgado, State space collapse and heavytraffic for a packet-switched network with On/Off sources and a fair bandwidth sharing policy, to appear in Telecommunication Systems (2015). http://dx.doi.org/10.1007/s11235- 015-0086-6

[5] R. Delgado, A heavy-traffic limit of cascade fluid networks with heavy-tailed On/Off sources, submitted for publication (2015).

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Cite this paper

Rosario Delgado. (2016) A Heavy-Traffic Limit of a Two-Station Fluid Model with Heavy-Tailed On/Off Sources, Feedback and Flexible Servers. International Journal of Mathematical and Computational Methods, 1, 149-158