First come, first served: “Written more fully this is, ‘the FIRST item to COME here is the FIRST one SERVED.’”
Webster’s Second Unabridged, 1934:
“first come, first served. Ellipsis for: He who is FIRST COME is FIRST SERVED;—used in stores, restaurants, etc., to indicate service of patrons in the order of arrival.”
You might also find the linguistically more mysterious “first come, first serve”, but when in doubt, just acronymize: FCFS.