The story of Alexander is that of a Greek army officer who, moved by Christ's words to the rich young ruler, sold his possessions and became a monk. But he was too energetic for a solitary life. After seven years, in a fit of enthusiasm he left his retreat and set fire to a pagan temple. For this he was imprisoned, but, like Saint Paul, succeeded in converting the governor, who was baptized with all his household.
Securing his freedom, Alexander returned to the desert and fell in with a band of robbers. The result was remarkable, for under his influence they also accepted the Christian faith, and when their leader died, Alexander turned them into a band of monks and their robber's den into a monastery. Appointing one of them as abbot, he went on his way, this time to Mesopotamia, where he established a monastery on the Euphrates.
Alexander was a somewhat restless archimandrite, fond of new places and faces. So, he formed a travelling monastery. With 150 monks he journeyed from place to place, until his followers numbered 300. These he divided into six choirs, to sing in turn the divine office and thus maintain, day and night, unceasing praise, and hence came their name of the Sleepless Ones (akoimetoi). One of these houses he established at Constantinople (Benedictines, Gill).
source: http://www.saintpatrickdc.org/ss/0223.htm
Also from the orthodox Prologue this account where Alexander is remembered on July 3 It includes this Orthodox hymn of praise
Order of CenturionsJan 2007
HYMN OF PRAISE
Venerable Alexander, saint of God,
Established the temple of the "Sleepless Ones"; holy monastery,
That in it, the Lord be glorified, hymned and magnified;
Concerning this holy monastery, the story is still related.
But brethren, even our heart the community of heaven is,
It is necessary in your heart to glorify the Living God,
In the heart, let sleepless prayer be counted,
As a flame, let unquenchable love stand,
With Grace let the Holy Spirit warm our hearts,
Let Christ, His words throughout our heart sow,
Let the angels in that temple keep vigil day and night
Farther from us, farther from them, the furious ones let them hide.
Let the Holy Virgin emit with myrrh in that temple,
Together with Her, let the apostles and all of the saints throughout,
And all the chosen ones of God; glorious martyrs,
And all the virgins for the sake of Christ and all the hermits.
In the hearts, let the Liturgy be celebrated thusly
And sleeplessly magnify the wisdom of God.
http://www.westsrbdio.org/prolog/