2 research outputs found
Geometric Approximations of Some Aloha-like Stability Regions
Most bounds on the stability region of Aloha give necessary and sufficient
conditions for the stability of an arrival rate vector under a specific
contention probability (control) vector. But such results do not yield
easy-to-check bounds on the overall Aloha stability region because they
potentially require checking membership in an uncountably infinite number of
sets parameterized by each possible control vector. In this paper we consider
an important specific inner bound on Aloha that has this property of difficulty
to check membership in the set. We provide ellipsoids (for which membership is
easy-to-check) that we conjecture are inner and outer bounds on this set. We
also study the set of controls that stabilize a fixed arrival rate vector; this
set is shown to be a convex set.Comment: Presented at IEEE ISIT 2010 (Austin, TX