I'm having a little bit of a hard time deciphering your question here, so perhaps you could rephrase it a little.
It sounds like you want to know how to find the latency in the Analysis Service, is that correct? For this information you can look at the Analysis Service statistics, which are described in KB01664. That being said, if the Analysis Service is unable to fetch data from the Data Archive altogether, I would suggest checking on the security settings for those points as well as how the Analysis Service is connecting to the Data Archive.
Why do you think the PI Analysis Service is unable to retrieve data from the PI Data Archive? Which version of Asset Analytics are you running? The logs are in different locations depending on the version.
Also, just a small note, the PI Analysis Service connects directly to the PI Data Archive. If it's having issues retrieving the data from PI Points, as long as the configuration strings are ok in AF, we don't need to worry about AF latency.
What's happens if you create a simple analysis that has the Sinusoid PI Point as input and simply outputs the value to another PI Point?