The "swiss" family of pairing systems are common in international tournaments. TournamentService will do pairing according to FIDE's "Dutch" rules, approved by the general assembly of 1998 (GA98). The system is based on the player's rating. You can select which rating number(s) are to be used (national/local or international/Fide) in the ranking window.
"Dutch" is a complicated set of rules, potentially involving a very high number of variants to be tested, so in special cases the pairing may take some time.
FIDE also has approved an older swiss system ("Lim", aka GA87). This is not currently supported in TournamentService.
In swiss tournaments, the pairing numbers are not random. When you do "assignment of rank no's in swiss order" the players will be ordered by (national or Fide) rating, FIDE-title and lastly by name. You may override this ordering in the ranking window.