%0 Journal Article
%T Stability of processor sharing networks with simultaneous resource requirements
%A Jennie Hansen
%A Cian Reynolds
%A Stan Zachary
%J Mathematics
%D 2006
%I arXiv
%X We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to met demand, the requirement for simultaneous availability of resources means that a network may nevertheless be unstable. We show that instability occurs through poor control, and that, for a variety of network topologies, only small modifications to controls are required in order to ensure stability. For controls which possess a natural monotonicity property, we give some new results for the classification of the corresponding Markov processes, which lead to conditions both for stability and for instability.
%U http://arxiv.org/abs/math/0605477v2