  We establish the proportionality principle between the Riemannian volume and
locally finite simplicial volume for Q-rank 1 locally symmetric spaces covered
by products of hyperbolic spaces, giving the first examples for manifolds whose
cusp groups are not necessarily amenable. Also, we give a simple direct proof
of the proportionality principle for the locally finite simplicial volume and
the relative simplicial volume of Q-rank 1 locally symmetric spaces with
amenable cusp groups established by L\"oh and Sauer.
