Hey there.
Thanks for kicking off the conversation @cwata!
SonarQube analysis happens in two parts – when the scanner is executed (typically in a CI context, like in Jenkins) and when the report is received by the SonarQube server.
At the scanner-level, there should be nothing to worry about. The analyses will happen independently of each other. The analyses aren’t even aware the other is occuring.
At the server-level… there’s also nothing to worry about. SonarQube will process reports in the order that they are received. While the Enterprise Edition will also up to 10 reports to be processed simultaneously, it still won’t let two analyses of the same project process concurrently.