commutation (n.)

mid-15c., "to change (something into something else), transform," from Latin commutare "to often change, to change altogether," from com-, here perhaps an intensive prefix (see com-), + mutare "to change" (from PIE root *mei- (1) "to change, go, move").

Sense of "make less severe" is from 1630s; sense of "exchange, put in place of another" is from 1630s. Meaning "substitute one sort of burden for another" is from 1640s.

Meaning "go back and forth to work" is attested by 1889, from commutation ticket "a season pass" on a railroad, streetcar line, etc. (1848), from commute in its sense of "to change one kind of payment into another" (1795), especially "to combine a number of payments into a single one, pay a single sum instead of a number of successive payments" (1845). Related: Commuted; commuting; commutable.

The noun meaning "a journey made in commuting" is attested by 1960. Also compare commuter.