Coupling model analyses of short-time relaxation data of glycerol from quasielastic neutron scattering and ortho-terphenyl (OTP) by molecular dynamic simulation are shown to account for both the time dependence of the correlation function and its temperature dependence. The latter is expressible over a limited temperature range as an Arrhenius relation with an apparent activation energy for the fast alpha-relaxation process, with E(A) = 6.2 and 3.9 kcal/mol for glycerol and OTP, respectively. The viscosities of these glass formers have also been measured up to temperatures sufficiently high that the mean viscosity relaxation time, [tau(n)(T)], becomes short, approaching the crossover time, t(c) approximate to 2 ps, of the coupling model. When this condition is realized, [tau(n)(T)] becomes comparable to tau(D)(T) in both magnitude and temperature dependence. Hence, the asymptotic high temperature activation energy of [tau(eta)(T)] approximately equals the apparent activation energy of tau(D). The experimental data, supporting this connection between macroscopic variables such as viscosity and microscopic dynamics from neutron scattering and molecular dynamics simulation, indicate the significance of the fast cr-relaxation process in both fragile and strong liquids.