Otherwise, the math is pretty easy. The key questions are: how many requests per user per session, how many request per user per minute, and how many request per second can the hardware serve?

Supposing an even distribution of 180M visits per day and 1 requests per visit:

  125,000 visitors per minute

  125,000 http request per minute

  2,083 requests per second

That should be doable on a large vps of some sort, even for wordpress.

Now the question is, how complex is the workflow? Certainly a visit will consist of more than one request. Also, visitor frequency will most likely peak during certain periods of the day/week.