We perform numerical simulation of a lattice model for the compaction of a granular material based on the idea of reversible random sequential adsorption. Reversible random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The growth of the coverage rho(t) above the jamming limit to its steady-state value p. is described by a pattern rho(t) = rho(infinity) - Delta rho E-beta[-(t/tau)(beta)], where E-beta denotes the Mittag-Leffler function of order beta is an element of (0, 1). For the first time, the parameter r is found to decay with the desorption probability P- according to a power law tau = A P--(-gamma) Exponent gamma is the same for all shapes, gamma = 1.29 +/- 0.01, but parameter A depends only on the order of symmetry axis of the shape. Finally, we present the possible relevance of the model to the compaction of granular objects of various shapes.