How to react to some students who book an appointment and do not show up?
Back when this was something I had to deal with, I would:
Always have something to do if someone doesn't show up for their appointment, or if their question gets resolved very quickly.
Write brief emails to no-shows along the lines of
Dear X: I'm following up on our appointment today at 14:00. I hope everything is OK with you. Let me know if your question is still relevant and you would like to reschedule. If you answered your own question, I'm glad, but next time I'd appreciate a heads up for scheduling purposes. Ditto if something came up and you just couldn't make it. See you in class tomorrow, I hope!
- Get progressively more direct if people missed several appointments, to the extent of refusing to make further appointments (leaving the student the option to come for the office hour I had for appointment-free visits every week).
Note the tone of the email in point 2 is not demanding of an explanation (or indicating a desire to judge whether excuses provided are adequate), but is also openly asking for a change in behaviour, without pulling rank or going passive-aggressive. Generally I got belated apologies and improved future behaviour. And a couple of times the "I hope everything is OK", meant genuinely, surfaced that something pretty dire had happened (where a pure chastising email soliciting an apology would have been cringingly tone-deaf!), including a student on the verge of an emotional breakdown where we were able to get them help.
Now, a couple of decades later, I'd still do the same -- and suspect I've written stuff not too dissimilar in tone to peers and superiors too!
Basically: be frank about what you need to change, don't make an investigation of it, and open the door to empathy.
Editing to add: Comments/other answers have pointed out potential different cultural expectations, and/or that the tone is not optimal if there turns out to have been a real emergency. Regarding the first, agreed: needs to be tempered by cultural norms. But if student behaviour feels outside of local norms, do go ahead and address it. Regarding the 2nd, also true. At the risk of going very math/stats-nerdy, there is a Bayesian prior regarding what caused the missed appointment. My answer assumes the Bayesian prior is fairly flat between emergency, forgetfulness, student self-absorbtion/failure to consider from others' point of view, and overall excessive academic stress. The tone tries to be acceptable and hopefully effective in all these instances. If your Bayesian prior is more heavily weighted to one pole, your optimal tone will change. This includes repeat offenders (where the Bayesian prior weighs more heavily on self-absorbtion), reason to suspect emergencies, etc.
It’s not just students who do this. Every professional I know - doctors, lawyers, professors, psychotherapists etc - regularly has experiences with people who make appointments and don’t show up. I think the best course of action is to accept that this happens and save your energy and outrage for other things. There is no point in contacting the student. They may contact you later to apologize and/or try to reschedule, or they may not; it’s up to them and beyond your control.
At least be thankful that as a professor you don’t lose income when this happens (unlike many other professionals) and are free to use the time to do other useful work. One trick I’ve learned is that when I have an appointment coming up with a student, especially one that I don’t know well, I sometimes prepare in advance some unrelated work to do while I wait for them to show up (usually minor tidbits like sending off some emails), keeping in mind that I could be waiting a lot longer than I expected...
I disagree with the posted answers, asking for an explanation is not necessary, and it would strike me as pretty rude and weird if a professor emailed me back to say "Why didn't you make the meeting?" Especially if I missed it for highly personal reasons. They aren't my parent or mentor.
Give them until the end of the workday or so, and if they haven't apologized or reached out, something appropriate to say would be:
Student,
Please give me a heads-up if you aren't able to make your meeting, so that I don't wait too long for you. If you would still like to meet, please (let me know/schedule online).
If the student has a reasonable excuse (got sick, personal emergency), they will likely let you know. Sometimes they'll let you know even if it's unreasonable. If not, they will still have learned their lesson about oversleeping, etc. by understanding they disappointed you and interrupted your day.