The Reflected Fbm Process On A Convex Polyhedron As Limit For The X−model With On/off Sources Under Heavy-traffic

AUTHOR(S):

Rosario Delgado

TITLE

The Reflected Fbm Process On A Convex Polyhedron As Limit For The X−model With On/off Sources Under Heavy-traffic

KEYWORDS

reflected fractional Brownian motion; convex polyhedron; On/Off sources; heavy-traffic limit; Skorokhod problem; X−model

ABSTRACT

We consider a X−model with fluid queues that can be approximated under heavy-traffic conditions by a two-dimensional reflected fractional Brownian motion (rfBm). Specifically, we prove a heavy-traffic limit theorem for this single-server two-station model in which each server helps the other when free, with feedback allowed and a non-deterministic arrival process generated by a large enough number of heavy-tailed On/Off sources, say N. Scaling conveniently by a factor r and by N, and letting N and r approach infinity (in this order), we prove that the scaled (total) workload process converges under heavy-traffic to a rfBm process on a convex polyhedron.

Cite this paper

Rosario Delgado. (2017) The Reflected Fbm Process On A Convex Polyhedron As Limit For The X−model With On/off Sources Under Heavy-traffic. International Journal of Mathematical and Computational Methods, 2, 41-52