What's the best way to calculate remaining download time?

Question

Let\'s say you want to calculate the remaining download time, and you have all the information needed, that is: File size, dl\'ed size, size left, time elapsed, momentary dl

Answer 1

You could use an averaging algorithm where the old values decay linearly. If S_n is the speed at time n and A_{n-1} is the average at time n-1, then define your average speed as follows.

A_1 = S_1
A_2 = (S_1 + S_2)/2
A_n = S_n/(n-1) + A_{n-1}(1-1/(n-1))

In English, this means that the longer in the past a measurement occurred, the less it matters because its importance has decayed.

Compare this to the normal averaging algorithm: A_n = S_n/n + A_{n-1}(1-1/n)

You could also have it geometrically decay, which would weight the most recent speeds very heavily: A_n = S_n/2 + A_{n-1}/2

If the speeds are 4,3,5,6 then A_4 = 4.5 (simple average)
A_4 = 4.75 (linear decay)
A_4 = 5.125 (geometric decay)

Example in PHP

Beware that $n+1 (not $n) is the number of current data points due to PHP's arrays being zero-indexed. To match the above example set n == $n+1 or n-1 == $n

Output

array (size=4)
  0 => int 4
  1 => float 3.5
  2 => float 4
  3 => float 4.5

array (size=4)
  0 => int 4
  1 => float 3.5
  2 => float 4.25
  3 => float 4.8333333333333

array (size=4)
  0 => int 4
  1 => float 3.5
  2 => float 4.25
  3 => float 5.125