Seneca, On Consolation to his Mother Helvia
6.2-4 (tr. John W. Basore):
 "To be deprived of one's country is intolerable," you say. But come now, behold this concourse of men, for whom the houses of huge Rome scarcely suffice; most of this throng are now deprived of their country. From their towns and colonies, from the whole world, in fact, hither have they flocked. Some have been brought by ambition, some by the obligation of a public trust, some by an envoy's duty having been laid upon them, some, seeking a convenient and rich field for vice, by luxury, some by a desire for the
higher studies, some by the public spectacles; some have been drawn by friendship, some, seeing the ample opportunity for displaying energy, by the chance to work; some have presented their beauty for sale, some their eloquence for sale —  every class of person has swarmed into the city that offers high prizes for both virtues and vices. Have all of them summoned by name and ask of each: "Whence do you hail?" You will find that there are more than half who have left their homes and come to this city, which is truly a very great and a very beautiful one, but not their own.  Then leave this city, which in a sense may be said to belong to all, and travel from one city to another; everyone will have a large proportion of foreign population.
"carere patria intolerabile est." aspice agedum hanc frequentiam, cui vix urbis immensae tecta sufficiunt; maxima pars istius turbae patria caret. ex municipiis et coloniis suis, ex toto denique orbe terrarum confluxerunt. alios adduxit ambitio, alios necessitas officii publici, alios imposita legatio, alios luxuria opportunum et opulentum vitiis locum
quaerens, alios liberalium studiorum cupiditas, alios spectacula; quosdam traxit amicitia, quosdam industria laxam ostendendae virtuti nancta materiam; quidam venalem formam attulerunt, quidam venalem eloquentiam —  nullum non hominum genus concucurrit in urbem et virtutibus et vitiis magna pretia ponentem. iube istos omnes ad nomen citari et "unde domo" quisque sit quaere. videbis maiorem partem esse, quae relictis sedibus suis venerit in maximam quidem ac pulcherrimam urbem, non tamen suam.  deinde ab hac civitate discede, quae veluti communis potest dici, omnes urbes circumi; nulla non magnam partem peregrinae multitudinis habet.
In general see Laurens E. Tacoma, Moving Romans: Migration to Rome in the Principate
(Oxford: Oxford University Press, 2016).