If the agent is reporting, it posts a value of 1 to its Availability metric (shown below in the metric browser for a node called WEB1_NODE in the ECommerce-Services tier of the ECommerce application)
You can build health rules and alert on this at the node level, to get notification when a node is not reporting, or a the tier level to ensure each tier always has a certain minimum number of nodes.
so if you see a 1 posted in that metric, you know the agent reported.
For your cases 1 and 3, this wil be 0.
For case 2, it is extremely unlikely that this metric would be 1 and absolutely no other data would be reported from the agent. That said, if it is 1 but you do not see Business Transaction activity that you expect within the instrumented node, then it is likely you are missing necessary entry points because your application is not running within a framework for which there is out of the box configuration.
Warm regards,
Peter
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