How long does it take l-tryptophan to convert to serotonin, melatonin

[High_Anglican]

I understand that the amino acid L-Tryptophan is metabolized into 5-htp, then serotonin, then melatonin, but I don't know what the time line is. I normally eat dinner at 8pm, and I want my serotonin levels to be high so that I am more satisfied with less food. I normally go to bed at midnight, and would hope that by that time it has turned into melatonin.

So if I want the tryptophan to have turned into serotonin by 8 and then into melatonin by 12, when and in what dosage should I take it? Or should I stagger the doses?