Senya Shlosman: Dynamics of Highly Connected Queuing Networks: Synchronization Phase Transition and the Coherent States
Abstract:
We study particle systems corresponding to highly connected queuing networks. We examine the validity of the so-called Poisson Hypothesis (PH), which predicts that the Markov process, describing the evolution of such particle system, started from a reasonable initial state, approaches the equilibrium in time independent of the size of the network. This is indeed the case in many situations. However, there are networks for which the relaxation process slows down. This behavior reflects the fact that the corresponding infinite system undergoes a phase transition. It is characterized by the property that different nodes of the network start to evolve in a synchronous way. Such transition can happen only when the load per node exceeds some critical value, while in the low load situation the PH behavior holds. The load thus plays here the same role as the inverse temperature in statistical mechanics.