1520s, probably ultimately from Old English drusan, drusian "sink," also "become languid, slow, or inactive" (related to dreosan "to fall"), from Proto-Germanic *drus- (see dreary). But there is no record of it in Middle English. Related: Drowsily; drowsiness.
drowsiness drows·i·ness (drou'zē-nĭs)
A state of impaired awareness associated with a desire or inclination to sleep. Also called hypnesthesia.