For people who sleep at work to be on call I hear it is usual to pay them a lower than usual rate (40% ish) for every hour of availability which (depending on the time) will change into a [much] higher than usual rate if they have to do anything. It seems fine to be paid 40% for the other 16 hours and 2 times 24 in the weekend. At 40% these 128 hours would be 99.2 hours. I would jump out of bed at 3 am to do whatever you want. (well almost)