We consider a fully-connected loss network with dynamic alternative routing, each link of capacity K. Calls arrive to each link {i, j} at rate λ. If the link is full upon arrival, a third node k is chosen uniform and the call is routed via k: it uses a unit of capacity on both {i, k} and {k, j} if both have spare capacity; otherwise, the call is lost.

We analyse the asymptotics of the mixing time of this process, depending on the traffic intensity α := λ/K. In particular, we determine a phase transition at an explicit threshold α_c: there is fast mixing if α < α_c or α > 1, but metastability if α_c < α < 1.

**Date**: 9 May 2022, 12:00 (Monday, 3rd week, Trinity 2022)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: Lecture Room 4**Speaker**: Sam Olesker-Taylor (University of Bath)**Organising department**: Department of Statistics**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: James Martin