A few quotes from the Rabbi on 'Customs of Israel'
in which he teaches about of the Jerusalem custom of publicly welcoming the Sabbath at the Western Wall
Concerning the custom in our holy city of Jerusalem, may it be speedily built and established, Amen, whose stones and earth are revered by God's servants who seek always to bare their souls at our Western Wall, which the Shechina has not abandoned… Every holy Sabbath Eve, people go to this holy place in large numbers to welcome the holy Sabbath Queen. The area barely suffices to hold them all. Their custom is to recite the mincha afternoon prayer, Kabbalat Shabbat and the 'Arvit evening prayer. Those who leave are replaced by those arriving to pray; they come and go in large processions, the one arriving when the other leaves, well into the night. No proper individual misses this, and they are such indeed, for the group that has completed the 'Arvit prayer will tarry, to answer the Kaddish and Kedusha being recited by the preceding group that is praying Mincha. And there are even some who tarry after having prayed 'Arvit to study chapters of Mishna, recite Psalms or the like, observing one group after another, answering in each recitation of the Kaddish, Kedusha and repetition of the Eighteen Blessings.
Yismach Libi, Orach Chaim, Section 16, p. 2, Otzrot Ge'onei Sepharad Publishing, Ashdod, 1997