Repeat Parts a and b in Question P7 for the

Authors:

James F. Kurose, Keith W. Ross

Chapter:

Multimedia Networking

Exercise:

Problems

Question:8 | ISBN:9780132856201 | Edition: 6

Question

Repeat Parts a and b in Question P7 for the estimate of average delay deviation.

Answer

Refer the previous question 7( sub parts a and b):

To express the estimate of delay d in terms of the four sample delays, we can use the formula described in Section 7.3:

$d=(1-u)*d+u*(r-t)$

Using this formula for each sample delay, we have:

$\large d = (1 - u) * ((1 - u) * ((1 - u) * d + u * (r4 - t4)) + u * (r3 - t3)) + u * (r2 - t2) + u * (r1 - t1)$

To generalize the formula for n sample delays, we can use a recursive approach:

$\large d = (1 - u) * d + u * (r - t)$

Expanding this formula for n sample delays, we have:

$\large d = (1 - u)^{n} * d + u * (1 - (1 - u)^{n}) / u * (r1 - t1) + u * (1 - (1 - u)^{n}) / u * (r2 - t2) + ... + u * (1 - (1 - u)^{n}) / u * (rn - tn)$

Simplifying further, we can express the general formula as:

$\large d = (1 - u)^{n} * d + (1 - (1 - u)^{n}) / u * ((r1 - t1) + (r2 - t2) + ... + (rn - tn))$

d = (1 - u)^n * d + (1 - (1 - u)^n) / u * ((r1 - t1) + (r2 - t2) + ... + (rn - tn))

This formula provides the estimate of average delay deviation based on n sample delays.

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