Question

I’m trying to calculate an appropriate timeout time for a real time simulator that I’m writing:

For p = probability of success, the time for a successful request = m, and the time for a failed attempt = f. What is the average time for 5 successful requests?

Answer 1

Let’s call the total number of tries x.

x = 5p + (x-5)(1-p)
x = 5 / p

The total time would be

t = 5m + (x-5)f

or

t = 5m + (5 / p - 5)f

If m=1, f=2, and p=0.1, the answer should be 5 * 1 + 45 * 2 = 95. This checks out.

There might be errors in here, but I did my best.