Metastability and phase transitions associated to dynamic routing in networks

Abstract

The nature of the empirically observed metastability is studied by using particle system techniques. One of the questions examined is whether the metastability in large finite systems can be studied through an explicit phase transition in an infinite limit. Metastability in large finite systems is often associated with phase transitions in an infinite limit, i.e. the finite systems can be thought of as embedded in a single Markov process that admits multiple invariant distributions for certain parameter values. An example of this is discussed in the context of the well-known contact process. The phase transition suggested by circuit switched networks with alternate routing is of an unlikely kind because the system has positive rates and appears to be ergodic for both very small and very large arrival rates and to have multiple equilibria only in an intermediate range of parameters. >