We characterize the transient behavior of the time-dependent linear stochastic systems in presence of an external force, by means of the integration of the nonlinear relaxation time (NLRT), supported by the quasi-deterministic (QD) theory. The formalism is applied to study the transient dynamics of the switch-on times of a single mode semiconductor laser, in presence of an external optical signal, as a prototype model. The time scale, for this laser model is essentially given in terms of a relevant scaling parameter.