There are specific actions which cause a character to become fatigued. These are called Fatiguing Actions. A Fatiguing Action could be sprinting for 30 seconds, marching/walking for an hour, participating in combat for 1 minute, or anything else the DM thinks would cause a character to tire.
When a character performs a Fatiguing Action that character loses a set value of HP (this could be variable based on the class of the character, 4 for a magic-user, 6 for a cleric, or 8 for a fighter, or based on HD, etc), 1 constitution point, and takes a -1 penalty to all rolls.
(When I run D&D, PCs don't die at 0 hp, they receive a wound instead. Hp represent the PCs ability to avoid wounds, so this loss of hp reflects a loss of combat ability without being a direct threat to their life. If you run the game so that PCs die at 0 hp, you may want to forego the hp loss depending on how harsh you want your game to be.)
Characters can recover from fatigue by taking a short rest of 10 minutes (1 Turn). (this ties into the rule that PCs have to rest for 1 Turn in 6, and also spend a Turn resting after every combat) This will restore the hp lost, the constitution point, and negate the penalty to rolls. If a character performs a 2nd Fatiguing Action without taking this short rest in between the actions, he must make a system shock roll. If he fails this roll he receives twice the penalty as normal; on a success only the normal penalties apply. This extra penalty also applies if the character has not rested to fully recover from their fatigue.
Example: If a character had performed 3 sequential Fatiguing Actions and had succeeded his system shock roll both times he would have a -3 constitution and a -3 penalty to all rolls. He rests for 1 Turn, bringing his penalties to a -2. He then performs another Fatiguing Action and must make a system shock roll. If he succeeds he receives only the normal -1 penalty, putting him at -3 again; if he fails he receives a -2 penalty bring him down to a -4.
When a character's constitution score reaches 3 they become Exhausted (PCs that start with a 3 constitution are always exhausted). A character will also become exhausted by being active (awake and doing stuff) for extended periods of time (16 hours for humans, if they are awake but physically inactive this period of time can be stretched out to say 24 hours). An Exhausted character will be so tired they have no energy to do anything; their movement rate drops to practically 0 and they can only perform basic actions which require little mental power and cannot perform Fatiguing Actions.
An Exhausted character can try to shrug off the effects of Exhaustion by making a system shock roll. On a success the character can function normally for 1 hour before making another system shock roll. If a character who has shrugged off the effects of Exhaustion wants to perform a Fatiguing Action they must make a system shock roll. On a success they are able to perform the Fatiguing Action and takes the -2 penalties. On a failure the character simply does not have the energy to continue on and isn't able to perform the action, and the character also takes another -1 penalty for their effort.
The effects of both Exhaustion and Fatigue will be completely negated by sleeping For a requisite number of hours (8 for humans). If a character ever reaches a Constitution score of 0, that character dies from exhaustion.
There are details that need to be filled in, like what actions constitute fatiguing actions. I also haven't taken food/water into account. The effects of dehydration and/or lack of food can be very similar to just being extremely tired. This is just an idea, and I'm putting it out there to see what others think of it.
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