initialize : double credit = N
At every request :
penalty = (elapsedTime / window_size) - (1/N)
gain = N* (elapsedTime / window_size)
credit = min( credit + gain - (penalty<0) , N)
if( credit < 0 ) throw exception
gain = N * (elapsedTime / window_size);
credit = min(credit + gain, N);
if (credit >= 1) {
credit--;
log(...);
} else {
return; /* not enough credits */
}
But I'm not really sure of the value it adds over simply taking a cost of 1 as you suggest. When time beween requests are spreaded more than window_size/N they don't cost credit. This mean you have a smaller number of "hot" clients (clients who are not full credit) to monitor.
The second idea that often occurs in problems with sliding windows is the telescoping sum which is hiding implicitly in the sum of elapsed Times.