Dynamics of Highly Connected Queuing Networks

Опубликовано 6 сентября 2016, 16:51

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 particle system, if started from a reasonable initial state, relaxes to its equilibrium in time independent of the size of the network. We show that 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. Such transition can happen only when the load per server exceeds some critical value, while in the low load situation the PH behavior holds. Thus, the load plays here the same role as the inverse temperature in statistical mechanics.