The observation of various cosmic ray particles at the Earth had been done with the PAMELA space detector for almost 10 years, from June 2006 to January 2016. The AMS-02 space experiment provides similar cosmic ray data. The purpose of this work is to utilize the available state-of-the-art numerical modulation model for the transport of cosmic rays in the heliosphere to compute the modulation of galactic protons from minimum to maximum solar activity. These modeling results, which simulate realistic heliospheric conditions, are compared to proton observations from PAMELA taken between 2006 and 2010 and to similar AMS-02 observations after 2011. It will be shown how differently modulation mechanisms influence the time-evolution of the proton spectra when modulation conditions change from minimum to maximum, including a reversal of the polarity of the heliospheric magnetic field.