The initial estimate of 116,000 riders a day came from Parsons Brinckerhoff, the same people that projected 110,000 a day for Tren Urbano in San Juan, Puerto Rico.  "Data from the American Public Transportation Association (APTA) shows Tren Urbano carried an average of 31,400 passengers on weekdays in the third quarter of 2015"
https://ggwash.org/view/40846/check-out-the-metro-in-san-juan-puerto-rico

It should be noted that Tren Urbano started operations nearly 13 years ago, and San Juan has a population of 2.35 million vs just under a million for all of Oahu.