A theoretical model for numerical simulation of the nonlinear spin-wave transient processes in magnonic active-ring oscillators (MAROs) with variable gain has been developed. The model employs the formalism of the Landau-Ginzburg equation to describe the nonlinear propagation of spectrally narrow magnonic wave packets in a magnetic film. We show that the model allows one to simulate ring's operation above the self-generation threshold as a magnonic physical reservoir computer for which the control of ring gain is employed as a method of data input into the physical reservoir. Performance of the reservoir computer was evaluated by carrying out numerical simulations using the developed model. To this end, we simulated the completion of the short-term memory and the parity-check tasks by the model. We found that the simulation results are in good agreement with experimental data. This evidences that the constructed model can be used for investigating physics underlying the performance of the MARO as a physical reservoir computer and for reservoir optimization with the final goal of maximizing reservoir performance.