  In this paper, we adopt combinatorial Ricci curvature flow methods to study
the existence of cusped hyperbolic structure on 3-manifolds with torus
boundary. For general pseudo 3-manifolds, we prove the long-time existence and
the uniqueness for the extended Ricci flow for decorated hyperbolic polyhedral
metrics. We prove that the extended Ricci flow converges to a decorated
hyperbolic polyhedral metric if and only if there exists a decorated hyperbolic
polyhedral metric of zero Ricci curvature. If it is the case, the flow
converges exponentially fast. These results apply for cusped hyperbolic
structure on 3-manifolds via ideal triangulation.
