Knowing that most students submit assignments right around the deadline, is it advisable not to set deadline that is very late at night?

First of all, I think the distribution that you're seeing is not very unusual, and indeed looks very similar to the distribution of times that I see coming from mature scientists submitting conference papers and grants.

It is simply that people, including your students, tend to overcommit themselves and to underestimate the difficulty of work. When that is combined with tasks on which there is a flexible amount of effort that can be invested (e.g., quality of work on an assignment), it is generally the case that "this work is done" is an ill-defined notion, and instead it gets triaged at some point of time shortly before the assignment. Better and more prepared students (or whoever) simply climb farther up in quality before triaging.

Given that, I generally advocate for a policy of "tight deadlines, lots of mercy." That means setting the deadline slightly before when you really want the assignment turned in, and then being very liberal about accepting requests for extension up until your secret "real deadline."

Addressing your specific question about timing, I think that if you want your students to get more sleep, moving the deadline up a couple of hours is a totally reasonable tactic: given the phenomena at work, it is unlikely to affect the distribution or quality of the assignments you receive. Depending on how your automated system works, you may also be able to explicitly support an official deadline of 10pm, with the de facto ability to leave the submission system open longer to receive the main tranche of "just a little bit late" assignments.

While I admire your concern for the students, I feel that ultimately your endeavor is quixotic.

To be sure, I see nothing wrong with making your deadline be at 10 pm. It won't change anything, so you might as well. But I wouldn't expect it to have any notable effect, and I would be wary of the slippery slope that leads to you blaming yourself for the students' errors.

The reason I am so pessimistic is that I don't think procrastination and irregular sleep are caused by deadline timing (unless the work demanded is truly overwhelming, but in college it never is). They are caused by poor personal discipline and bad habits acquired over many years leading up to the present. Regardless of what you do, the procrastinators will still invent ways to procrastinate, because the problem is rooted in their own behavior, not yours. You therefore cannot solve the problem by changing your behavior.

For instance, if you have the deadline at 10 pm, the procrastinator will drop everything that evening to work on your assignment and submit it around 10. Then he will still stay up doing the things he just postponed for the sake of your assignment. Because, recall, this person is not selectively procrastinating on your course only - they have also other courses that have deadlines. Even if all courses had the same early deadline policy, the students would still have their own errands with self-imposed deadlines at later times that they stay up for.

By the same logic that makes you consider 10 pm, we can explore other alternatives:

• 5 pm is a fair time, since it would presumably encourage students to concentrate their last ditch effort in the typical working day. However, there will also be students who have classes right up to the deadline that day, and if they procrastinate (as some certainly shall) they will now skip class to do the assignment, which is arguably worse than staying up!
• Noon is another time that sounds like a good idea. Being too early, you might expect that it will make students feel they have no choice but to start working on it early since the morning isn't nearly enough time, and if they can't finish it the night before they can safely go to bed, get some sleep, and finish in the morning. But realistically, the procrastinators who stay up late and hand it in at midnight now will just start working at 1 am and stay up all night to finish it.
• 9 am can be argued for as a realistic time - it's not like you will start grading at midnight, so there isn't really a point in requiring the assignment by midnight - instead of having the students rush their submission to a deadline just so it could sit in your mailbox for several hours, you could tell them to that you will start grading at 9 am and they should have it done by then. This makes the deadline less arbitrary, since there is now a clear logic to being required to meet it (ie. you will be delayed if they don't do their part). But of course you will again have the same problem of students staying up all night because they procrastinated.

For what it's worth, I think the midnight deadline came about as codification of an unspoken tradition. Often deadlines are given as days, without time - with this, there is always much controversy about what exactly counts as meeting an August 6 deadline: Does it have to be done at the beginning of Aug 6? Does it have to be before the instructor leaves the office? Does it have to be before the end of the day, ie. before you go to sleep? Well, what if you never go to sleep, can you squeeze out a few more hours and still "meet your Aug 6 deadline" by submitting at 3:14 am on [technically] Aug 7?

Even though informally "today" means "until I go to sleep", the convention is that the date changes at midnight, which is also reinforced by how computer clocks show the date. Hence, I think the midnight deadline came about as an extension of this - it's just a date delimiter.

As for the students, since you are concerned about how late they go to sleep, surely you will agree that planning ahead and not leaving everything to the last minute is an important skill to be learned as part of tertiary education. This, then, the students must learn on their own, you cannot help them by tinkering with deadlines, since indeed the deadline is not what is preventing their learning. In fact, one could argue that you should maximize the negative reinforcement, and set the deadline at the worst possible time - say 6 am: The more misery you inflict on the procrastinators, the better they will appreciate how important it is to learn discipline, and the sooner they will take steps to unlearn their bad habits.

Granted, I'm not seriously suggesting you do the above, since it seems like it could go horribly wrong. Realistically, I could instead suggest the following:

• Set your deadline at some reasonable, early time such as noon.
• Secretly (ie. do not tell this part to the students) have the "real deadline" (for instance, the one you lose points for missing) be quite a bit later, say 5 pm.
• In class, say that it is very important they not miss the deadline even by a minute (don't say why), and they should come talk to you if they feel they won't make it.
• When they inevitably come asking for more time, be liberal with the extensions, but not before making them explain why they were late and lecturing them on the importance of planning ahead. When giving the extension, explain that they absolutely cannot miss the extended deadline, because then you would not be able to meet your own deadline for grading (whether true or not).
• If anyone misses the noon deadline (but not the 5 pm deadline), confront them about it to discourage submitting late without asking for an extension (which allows bypassing the social discomfort of asking for more time).

With this, you might create something like a low stakes environment (you don't lose massive points just for being a few minutes late) while still creating a fair amount of social pressure to increase the likelihood of a lightbulb appearing and the student thinking, "Hey, Dr. Ward is very nice and reasonable about deadlines and everything, but maybe it's worth for me to try to stop leaving everything to the last minute?". Furthermore, if you force them into an explicit discussion about their procrastination, they have an opportunity to ask you for advice on how to plan their work.

But all of this requires quite a bit of effort from you (much more than just replacing "midnight" with "10 pm" on your syllabus). So if you are not willing to commit the energy, there isn't really much that can be achieved with quick fixes.

I would consider a deadline at around 10p.m. very wise and student-friendly. I remember staying up late night as long as the submission system allows to post a new version and polishing the hell out of my assignment, although it probably made little difference.

As a lecturer I have always readily given small extensions to people who asked at least a little (about a day) in advance before the deadline, because I think that this fosters good habits in life: it is OK to fail sometimes, but you should handle the failure responsibly and warn people depending on you in advance.

I like the "tight deadlines, lots of mercy" policy mentioned in another answer (which I think is one of the good solutions). If you are worried that students will learn and exploit this policy, you can have a deadline that is openly less strict: for example subtracting 10 points from the evaluation of the assignment for every hour of delay or letting the students to submit until the next lecture, but for half the points. I experienced this a few times as a student and it was motivational yet forgiving to small lapses.