The practice of sleeping in a sitting posture can be explained as one of the 13 Dhutanga.
- Sitter's Practice (nesajjik'anga) — living in the three postures of walking, standing and sitting and never lying down.
The advantages of sleeping less as described by the Buddha can be found in Jāgariyasutta
This was said by the Lord…
"Bhikkhus, a bhikkhu should be vigilant; he should live mindful, clearly comprehending, concentrated, happy and calm, and should know when it is suitable to cultivate those things that are wholesome. Bhikkhus, for a bhikkhu who is vigilant and living thus, one of two fruits is to be expected: final knowledge here and now or, there being some residual defilement, the state of non-returning."
You vigilant ones hear this:
Wake up, you who are asleep!
Vigilance is better than sleep:
There is no fear for the vigilant.
One who is vigilant and mindful,
Comprehending and concentrated,
Joyful and calm in his thoughts,
By rightly investigating the Dhamma
With unified mind, will in time
Destroy the darkness of ignorance.
Therefore be devoted to vigilance,
An ardent, discerning, meditative bhikkhu.
Having severed the fetter of birth and decay,
One may here and now attain
Enlightenment which is supreme.
Note that the pali word 'Jāgaro' which means 'deprive sleep' is translated as 'vigilant' in the above sutta translation.