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We investigate, by numerical simulation, the dynamical response of a granular system to an abrupt change in shaking intensity within the framework of the reversible random sequential adsorption models. We analyse the two-dimensional lattice model in which, in addition to the adsorption-desorption process, there is diffusion of the adsorbed particles on the surface. Our model reproduces qualitatively the densification kinetics and the memory effects of vibrated granular materials. An interpretation of the simulation results is provided by the analysis of the insertion probability function. The importance of the diffusional relaxation is discussed. We conclude that a complex time-evolution of the density could be explained as a consequence of the variation of the diffusion rate during the compaction. We study the nonequilibrium time-dependent density-density autocorrelation function and show that the model displays out-of-equilibrium dynamical effects such as aging.