Switching times in absorptive optical bistability

We give analytic expressions for the up-switching and the down-switching times of an optical bistable device in the limit of large C. In the case of up-switching the jump time is proportional to the atomic relaxation time. In the case of down-switching, the jump time is proportional to the cavity relaxation time. No assumption on the relative magnitude of the cavity and the atomic relaxation times is introduced.