Sahih Muslim Book 7, Hadith Number 2969.

Chapter : It is excellent that the aged and the weak, especially among the women, should hasten from Muzdalifa to Mina at the latter part of the night before the people moving in multitude. and excellence of staying there for others until they observe the dawn prayer at Muzdalifa.

Salim b. ‘Abdullah reported that ‘Abdullah b. ‘Umar (Allah be pleased with them) used to send ahead of him the weak members of his household to stay during the night at Mash’ar al-Haram at Muzdalifa. They remembered Allah so long as they could afford, and then they proceeded before the stay of the Imam, and before his return. So some of them reached Mina for the dawn prayer and some of them reached there after that; and as they reached there, they stoned al-Jamra; and Ibn ‘Umar (Allah be pleased with them) used to say: Allah’s Messenger (may peace be upon him) has granted this concession to them.