>point is I have all the things completed except background check which suggest I am in comprehensive check (No Military Background, No Government Background)
Get CBSA notes, that's the only way to know this. A lot of times, they work on a part of your BG check and they pause in between (priority changes, officer reassignment, etc) - which can lead to delays, movement in the application's position in a "queue" (not a real thing, just easier to explain). Unless you see Comprehensive security screening, no reason to assume it and put yourself through that torture
>I am wondering about when we should go for Writ of Mandamus?
You won't be successful with Mandamus. Any lawyer who pick your application will be doing so with the intention of leeching you. Writ of Mandamus isn't even something that you can involve with before 2 years have passed.
>based on applications tentative timeline or based on background check timeline.
They only promised a 6 month SLA processing time to 80% of applications, which they are doing quite well with right now. You could easily be 20% non-routine application that simply is going to take it's course. I'd suggest that you read through case notes of Mandamus on this forum where judges believed that there was a reasonable delay and check the nature of the delay that led them to believe it.
