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 6GG

Venue 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