The collision-induced subduction transference is a composite dynamic process including both the terrane collision/accretion and the subduction initiation (SI) at the neighboring passive margin. This process occurred repeatedly during the evolution of Tethyan systems, with multiple ribbon-like continents or micro-continents drifting from Gondwana in the southern hemisphere and accreting to the Eurasian continent since Paleozoic. In the previous numerical studies, the dynamics of terrane collision and induced SI are investigated individually, which however need to be integrated to study the controlling factors and time scales of collision-induced subduction transference. Systematic numerical models are conducted with variable properties of converging plates and different boundary conditions. The model results indicate that the forced convergence, rather than pure free subduction, is required to trigger and sustain the SI at the neighboring passive margin after terrane collision. In addition, a weak passive margin can significantly promote the occurrence of SI, by decreasing the required boundary force to reasonable value of plate tectonics. The lengths of subducted oceanic slab and accreting terrane play secondary roles in the occurrence of SI after collision. Under the favorable conditions of collision-induced subduction transference, the time required for SI after collision is generally short within 10 Myrs, which is consistent with the general geological records of Cimmerian collision and the following Neo-Tethyan SI. In contrast, the stable Indian passive margin and absence of SI in the present Indian Ocean may due to the low convergent force and/or the lack of proper weak zones, which remains an open question.