When you are exhausted, nothing is worse than lying in bed desperately trying and failing to fall asleep. You might have better luck drifting off into dreamland if you try to stay awake instead.
In this video from the In59seconds YouTube channel, Professor Richard Wiseman from the University of Hertfordshire explains a recent study that looked at insomniacs and methods for falling asleep. The University of Glasgow study, led by Niall M Broomfield, followed two different groups of insomniacs and monitored their sleep patterns.
One of the groups was asked to lie in bed with their eyes open without any television, computers, phones, were only allowed to blink, and basically asked to try to stay awake for as long as possible. That group managed to fall asleep faster every night. The next time you're having trouble sleeping, get comfortable, stop moving, and try to keep your eyes open. You might find that trying to stay awake is way more tiring than focusing all your energy on falling asleep.
How to fall asleep [YouTube]