There was one and only one migration of the ancestors of the Roma to Europe.

That migration occurred very early, as Romanes does not show any influences of Semitic languages, and effectively, all the Persian words in Romanes are in their pre-Islamic forms.

In addition, Romanes words of Armenian origins, such as momelin [a candle] are also in a linguistically early form, having kept the “l” and not in the later Armenian form of a “gh”. This switch occurred in the IXth century, meaning that Roma passed through the Armenian lands prior to this change.

Note that Armenia at that time stretched from present day Armenia to the Mediterranean, encompassing all of nowadays Eastern Turkey up to Syria.

Syriac, a semitic language that was spoken at that time in Anatolia and in present day Turkey has left no traces in Romanes. This hints at a fast travel through that region to arrive in the European part of the Byzantine Empire in the IXth or Xth century. The most probable cause of the move to Europe was the mass deportation of Armenians following the Byzantine victory against the Paulician Heresy which was prevalent in Armenia in the IXth century.

From there, Roma slowly migrated towards the Carpaths, towards Wallachia and Moldova, parts of present-day Romania, and due to the Ottoman invasions, at the turn of the XVth century, towards Western and Northern Europe.