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 ρ(t) above the jamming limit to its steady−state value ρ∞ is described by a pattern ρ (t) = ρ∞ − ρEβ[−(t/τ)β], where Eβ denotes the Mittag−Leffler function of order β ∈ (0, 1). For the first time, the parameter τ is found to decay with the desorption probability P− according to a power law τ = A P− −γ. Exponent γ is the same for all shapes, γ = 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.