Is there a term for the moment when a lot of users visit/log onto your website at the same time?
In my experience we've generally refer to a spike in traffic to differentiate an unexpected or irregular increase from regular/daily peak periods. For example, a website may have peak periods around opening and closing time, but a spike might result from an advertising campaign or news article.
In this example, the "spike" is pretty distinctive compared to the rest of the day and remains unexplained.
If it is caused by users all visiting from a news site, it is called the Slashdot effect or Slashdotting.
Slashdot is one of the first internet news aggregators. When they posted a news article, it often crashed the sites they linked to because so many Slashdot users would visit simultaneously.
Today the term "slashdotting" can be applied when any site suddenly sends many visitors to another site simultaneously.
I would call it a Peak in visitors. This indicates that we're not having a usual amount of visitors, but more. The peak could be a small peak, or a large peak (a spike of visitors).
As a unit of time, you could go for Peak Hour/day/period.
peaked, peak·ing, peaks
1. Nautical To raise (a gaff) above the horizontal.
2. To bring to a maximum of development, value, or intensity.
If you have a sudden influx of users that happens to result in your site being taken down, your site has been given what a Redditor would call a hug of death.
ADDOS: Accidental Distributed Denial of Service
You wanted all those folks to visit, just... not at the same time.
I've known this as a "spike in traffic". I find such spikes are more caused by robots that try to hack into the server by trying to request specific URLs in a super short time frame (I say about 20 to 25 requests per second). I find when users visit my site, I see no huge spikes at all since most requests total no more than 50 KB to 500 KB each depending on photo size and when google crawls my site like crazy, I still don't get spikes. It only happens when bots try to hack my server.
I think the proper term is Digital Bulge.
It's bottleneck or rush hour or even road rage. You can call any from the above or even a custom word based on what amount your website/app gets hit by.
Only thing I could think about:
like in traffic
If it happens once in a while, I'd add the word oscillation with peak and/or spike.
Also, if it happens periodically, I'd add the word redundancy.
Yes, it is called DDOS attack.