  Tent and Ziegler proved that the automorphism group of the Urysohn sphere is
simple and that the automorphism group of the Urysohn space is simple modulo
bounded automorphisms. A key component of their proof is the definition of a
stationary independence relation (SIR). In this paper we prove that the
existence of a SIR satisfying some extra axioms is enough to prove simplicity
of the automorphism group of a countable structure. The extra axioms are chosen
with applications in mind, namely homogeneous structures which admit a
"metric-like amalgamation", for example all primitive 3-constrained metrically
homogeneous graphs of finite diameter from Cherlin's list.
