  Recent observations have revealed that at least several old globular clusters
(GCs) in the Galaxy have discrete distributions of stars along the Mg-Al
anti-correlation. In order to discuss this recent observation, we construct a
new one-zone GC formation model in which the maximum stellar mass (m_max) in
the initial mass function (IMF) of stars in a forming GC depends on the star
formation rate (SFR), as deduced from independent observations. We investigate
the star formation histories of forming GCs. The principal results are as
follows. About 30 Myr after the formation of the first generation (1G) of stars
within a particular GC, new stars can be formed from ejecta from asymptotic
giant branch (AGB) stars of 1G. However, the formation of this second
generation (2G) of stars can last only for [10-20] Myr, because the most
massive SNe of 2G expel all of the remaining gas. The third generation (3G) of
stars are then formed from AGB ejecta ~ 30$ Myr after the truncation of 2G star
formation. This cycle of star formation followed by its truncation by SNe can
continue until all AGB ejecta is removed from the GC by some physical process.
Thus, it is inevitable that GCs have discrete multiple stellar populations in
the [Mg/Fe]-[Al/Fe] diagram. Our model predicts that low-mass GCs are unlikely
to have discrete multiple stellar populations, and young massive clusters may
not have massive OB stars owing to low m_max ([20-30] M_sun) during the
secondary star formation.
