EWMA for calculating Estimated RTT

[alman9898]

Homework Statement

For a given TCP connection, suppose 4 acknowledgments have been returned with RTTs: SampleRTT(4), SampleRTT(3), SampleRTT(2), SampleRTT(1). SampleRTT(1) is the most recent, SampleRTT(2) is the second most recent, etc.

Calculate EstimatedRTT...

Homework Equations

Initialize EstimatedRTT to SampleRTT(4), the first sample.

EstimatedRTT = $$(1-\alpha)\times EstimatedRTT$$ + $$\alpha\times SampleRTT$$

The Attempt at a Solution

Plugging in I get...

$$(1-\alpha)^{3}\times SampleRTT(4) + \alpha\times(1-\alpha)^{2}\times SampleRTT(3) + \alpha\times(1-\alpha)\times SampleRTT(2) + \alpha\times SampleRTT(1)$$

But, EWMA is supposed to put less emphasis on older values...this seems to work for SampleRTT(3) and SampleRTT(2) but SampleRTT(4) will have a larger coefficient. I believe it's supposed to be multiplied by a factor of alpha as well, but I can't seem to find any arithmetic error and it's very annoying...am I doing it wrong or what?

For reference, alpha = .1 in this problem, but that's not exactly important, the calculations should be the same.

 

[KataKoniK]

Your attempt at a solution is correct, but there is a small error in your equation. The correct equation for calculating EstimatedRTT using EWMA is:

EstimatedRTT = (1-α) * EstimatedRTT + α * SampleRTT

Where α is the smoothing factor, typically set to a value between 0 and 1. So in your case, the correct equation would be:

EstimatedRTT = (1-0.1)^3 * SampleRTT(4) + 0.1 * (1-0.1)^2 * SampleRTT(3) + 0.1 * (1-0.1) * SampleRTT(2) + 0.1 * SampleRTT(1)

This will give you the correct value for EstimatedRTT, taking into account the smoothing factor α.

 

[Mene]

Your calculation for EstimatedRTT is correct. However, it is important to note that the value of alpha will affect the weight given to each SampleRTT. A larger value of alpha will put more weight on the most recent SampleRTT, while a smaller value of alpha will put more weight on the older SampleRTTs. So, in this case, since alpha = 0.1, the most recent SampleRTT(1) will have a weight of 0.1, while the oldest SampleRTT(4) will have a weight of 0.1^3 = 0.001. This shows that the EWMA method does indeed put less emphasis on older values.