Thanks for your response!
Could it be the case that some users are logged on to multiple systems at the same time? That wouldn't necessarily result in having multiple log files like this, but let's try to figure out what's going on.
Yes, this user has two pools
BTW, the fact that your log files are called logs, logs1, etc, indicates a minor configuration issue: the Path and name of log file setting of the Flexengine logging policy setting should be just that – the path and the file name of the log file. I assume you have it configured as something like \\server\share\%username%\logs, where it should be something like \\server\share\%username%\logs\FlexEngine.log.
Note that this is unrelated to the symptoms you're seeing; just wanted to point it out.
I think you are right, we may configured like this "\\server\share\%username%\logs"