1) Ambient music group 2) Be half asleep 3) Be half-asleep 4) Be half-awake 5) Be on the verge of sleeping 6) Be sleepy 7) Close lids lightly 8) Daydream 9) Doze 10) Drift off 11) Drop off 12) Nod off 13) Nod off, sort of 14) Not stay alert 15) Sadcore and slowcore group 16) Sleeping 17) Start to nod off 1) Doze 2) Snooze 
• (n.) A slight or imperfect sleep; a doze. • (v. i.) To sleep imperfectly or unsoundly; to slumber; to be heavy with sleepiness; to doze. • (v. t.) To make heavy with sleepiness or imperfect sleep; to make dull or stupid.
Drowse intransitive verb [ imperfect & past participle Drowsed ; present participle & verbal noun Drowsing .] [ Anglo-Saxon dr...sian , dr...san , to sink, become slow or inactive; confer OD. droosen to be sleepy, fa...Drowse noun A slight or imperfect sleep; a doze. « But smiled on in a drowse of ecstasy.» Mrs. Browning. Drowse transitive verb To make heavy with sleepiness or imperfect sleep; to make dull or stupid. Milton. 
[v] - be on the verge of sleeping
verb be on the verge of sleeping; `The students were drowsing in the 8 AM class`