Tryptophan is metabolized into melatonin by the enzymes arylalkamine N-acetyl transferase and H-indolyl O-methyl transferase. Melatonin is used in mammals as a hormonal signal of night. This is why it is taken by many people with sleep disorders, in an attempt to "normalize" their circadian rhythms.

Of course, it's probably not that simple. In some mammals studied, melatonin levels did not increase until significantly into the dark period. Also, melatonin does not alter human sleep patterns unless ingested during certain times of day. This might rule out a simple "melatonin->sleepiness" trigger.

Sources:
Reppert and Weaver (1995) Cell 83: 1059-1062.
Ribelayga et al. (2000) Am. J. Physiol. Regulatory Comp. Physiol. 278: R1339-R1345.