James Serra gives us a few options to monitor different aspects of Power BI:
Performance analyzer: Find out how each of your report elements, such as visuals and DAX formulas, are performing. Using the Performance Analyzer, you can see and record logs that measure how each of your report elements performs when users interact with them, and which aspects of their performance are most (or least) resource intensive. This is accomplished by clicking a “Start recording” button and interacting with the elements you want to test. More info at Use Performance Analyzer to examine report element performance.
Click through for several other tools, which you can combine to get a better feel for how your environment is doing.