Abdullah bin Umar (may Allah be pleased with them both) used to send the weak members of his household ahead, and they would stand by al-Mash'ar al-Haram at Muzdalifah at night and remember Allah as much as they were able; then they would leave before the Imam stood. Some of them would arrive at Mina at the time of the Fajr prayer and some after that; when they arrived, they would stone the Jamrah. And Ibn Umar (may Allah be pleased with them both) used to say that the Messenger of Allah (peace and blessings be upon him) had granted a concession for these people.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9511