sochinho, are you being asked to determine the latency between and new character arriving/leaving the UART and the point at which the Pi is actively dealing with it or between characters arriving/leaving the UART.
If it's just leaving/arriving in the UART the internal buffering will hid all of it. Remember that in async transmission each character has an overhead of one start bit and one, one and a half or two stop bits depending of baud rate (high baud rates tend to have one start and one stop bit). So for every 8 bit character, 10 (or more) bits are transacted. This extra time is more than enough for most computer systems deal with characters without any delays or gaps in the character stream.
If the task is response time from new character event to event completion it'll depend on what else is happening in the system and relative priories in any scheduling system.
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