We present a semi-analytical method to calculate the global evolution of the ionized state of the inter- galactic medium, on the basis of physically motivated star formation histories in the early universe. This method incorporates not only the conventional scenarios in which the star formation rate is proportional to the growth rate of the halo collapse fraction, but also the more sophisticated scenarios in which the star formation is self-regulated. We show that this variance in the star-formation model strongly impacts the resulting reionization history, which bears a prospect for observational discrimination of these models. We discuss how observations of the anisotropic polarization of the cosmic microwave background and the global 21cm signal from the high-redshift universe, most notably by Planck and EDGES, may probe the history of reionization.