[n] migration into a place (especially migration to a country of which you are not a native in order to settle there)
[n] the body of immigrants arriving during a specified interval; "the increased immigration strengthened the colony"
in-migration - (4 syllables)
\Im"mi*gra"tion\, n. [Cf. F. immigration.] The act of immigrating; the passing or coming into a country for the purpose of permanent residence. The immigrations of the Arabians into Europe. --T. Warton.