It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him), in his Hajj, walked briskly (ramal) in the first three circuits from the Black Stone to the Black Stone, and walked normally in the remaining four.
Hadith Referenceالمعجم الكبير للطبراني / باب العين / 12003