Even though it's not related to verifying the correctness of software, a performance test suite is part of the testing strategy for many applications. Usually, they are expected to assess the performance of the software in terms of how fast it can do its job and how many concurrent users it can handle.
Due to their nature, performance tests are usually very expensive as they have to repeat an operation multiple times to get a benchmark that is able to provide a fairly stable report and absorb outliers that could have taken too long to run just because the system was busy doing something else.
For this reason, the performance test suite is usually only executed after all other suites are passed (also, it doesn't make much sense to assess how fast it can test the software when we haven't checked that it actually does the right thing).
For our chat example, we could write a benchmark suite that verifies how many messages per second we are able...