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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.
