I've never felt the Traveller rules really model sleep deprivation very well. I use these alternative rules to supplement them for periods long periods of time that aren't going to be RP'd out in detail (such as setting up schedules during the week in Jump) and similar "routine schedule" tasks.
A bit of background:
While sleep is surprisingly not well understood, iirc current studies say that the amount your exercise actually reduces the amount of sleep you need. Like someone who is in very good physical condition can pretty easily get by on 6 hours (or sometimes even less) normally.
Otherwise honest people will lie about how much sleep they need, both to themselves and to other people, almost always quoting a low amount. I can't tell you the number of people who claim they only need X amount of sleep a night; in the modern Western world, it is our version of machismo to claim that you naturally only need a handful of hours of sleep and are "perfectly fine." It's like some macho thing (except women to do it too).
Lack of sleep is treated as a trivial matter by most people, but it's actually quite deadly. I have friends in the Highway Patrol who tell me that someone who is driving on a lack of sleep is indistinguishable from a drunk driver. Caffeine and similar stimulants are of limited use - they maintain consciousness but the problems in reaction time and judgement usually persist.
Studies have shown that the human body actually gets its minimum sleep amount in the long run, by hook or by crook. People who claim to only need five hours may put their heads down at their desks "for a few minutes", may "zone out" for a "few minutes", doze off in front the TV at home, and similar things, all of which those he-men and she-women who claim they only need a handful of hours of sleep don't count in their sleep totals.
Children need more sleep than adults. Older people tend to need as much sleep as younger adults, but the sleep they get isn't as restful, some researchers think this is purely related to the brain while others believe it is tied to the general degradation of the body due to age, but old people might only sleep a few hours every night but tend to nod off often during the day.
Throughout these rules END (Endurance) will be used. However, a character with Athletics skill may modify the END modifier with levels in Athletics. In no case can the penalty or bonus be greater than +/- 3, however.
Amount of sleep required out of every 24 hours: 7 +/- END Modifier
A character requires 7 hours of sleep for every 24 hours, naturally (yes most studies suggest 8, but 7 yields better numbers for game purposes). People in good physical condition require less sleep; people in poor physical condition require more. This is modeled by the 7 hours modified by a character's END modifier (so someone with a high END requires less sleep out of 24 hours). This is the "normal" amount of sleep a character needs; a character with a high END who only needs 5 hours of sleep can live off 5 hours indefinitely and without penalty. This rule replaces the p74 MongTrav rule under the bullet of "After staying awake for a number of hours..."
If the character does not meet the minimum sleep requirement, he or she takes the standard fatigue penalty. The player must be warned his or her character feels the lack of sleep.
The sleep deficit cannot be recovered in the way that normal fatigue is. It can only be made up by making up the lack of sleep. A character who requires 7 hours of sleep who only gets 5 in a 24 hour period is at a deficit of 2 hours and suffers fatigue penalties. In the next 24 hours, the character only gets 6 hours of sleep and is now at a 3 hour deficit. In the next 24 hours, the character gets 7 hours, but remains fatigued as the character still has a 3 hour deficit. If, at any time, the deficit is 6 hours or more, the fatigued penalty doubles.
A character which is feeling the lack of sleep is particularly in danger if he or she is doing something dull and repetitive alone. Common examples of this: Standing sentry duty over the party's camp, driving or piloting a vehicle, cramming for tests, doing officework.
In some situations, this may be averted by taking stimulants, having someone to talk to (they must be actively interacting - two partymembers standing watch silently doesn't count). Otherwise, the check must be made as usual.
If in these situations, the GM should require the player to make an END check at a DM+2 for every hour of the task (plus any END modifiers), the actual task is DM+4, but the -2 for fatigue is already factored in. This check has degrees of success:
A marginal, average, or exceptional success means the character can continue doing whatever or he or she intended to do.
A failure means the character has nodded off to some degree at some point during that hour. If the character was attempting a task that produces something (such as programming a computer), this hour is considered wasted as far as counting towards completing the task.
Marginal Failure: The character is "almost awake" - They're unconscious but may be startled by hitting the "road braille" if driving (only to start nodding off again after a few seconds or minutes), or might not be able to quite account for some time while standing watch, and so on. It may not be immediately obvious to others that the character has nodded off; the sentry is still standing, the programmer is at his desk, and so on. Any extended observation will reveal the truth; the sentry is not looking around, the programmer isn't inputting data, the student isn't really reading. If the character is standing watch, any observational or awareness task is rolled at Very Difficult (if the task already was Very Difficult or Formidable, then no roll is possible).
Average Failure: The character has nodded off. The character has decided to close his or her eyes for "a few seconds" (actually minutes). If the character is standing watch, any observational or awareness task is automatically failed. After a few minutes of this, the character has the option to take some drastic action or he or she will fall asleep as described under "Exceptional Failure." Drastic action might be to go wash his or her face with cold water, go wake someone up to take over their task, or simply decide it cannot be done and take a nap. There is a golden lining to this level of failure: Regardless of the action, the character has rested sufficiently that he or she will not have to make fatigue checks for next 1 + (END modifier) hours. If this total is 0 or less due to poor END, the character will have to make an END check as usual.
Exceptional Failure: The character has fallen asleep, without quite realizing it. This is literally "asleep at the wheel" and the kind of thing Roman Legionaries used to get beat to death over. The character falls asleep doing the task; vehicles will roll off the road or hit barriers, aircraft may plunge into the ground, the character is deeply asleep for all intents and purposes and will remain so until he or she is woken up (either by another person or by some stimulus great enough to wake the player up at the GM's discretion), or sleeps to drop the sleep deficit to 0. It is blatantly obvious to others the character has nodded off. If the character is standing watch, any observational or awareness task is automatically failed.
