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# Computer Networking : A Top-down Approach

 Authors: James F. Kurose, Keith W. Ross ISBN: 9780132856201 Edition: 6
 Chapter: Transport Layer Exercise: Problems Question: 31

### Question

Suppose that the five measured SampleRTT values (see Section 3.5.3) are 106 ms, 120 ms, 140 ms, 90 ms, and 115 ms. Compute the EstimatedRTT after each of these SampleRTT values is obtained, using a value of α = 0.125 and assuming that the value of EstimatedRTT was 100 ms just before the first of these five samples were obtained. Compute also the DevRTT after each sample is obtained, assuming a value of β = 0.25 and assuming the value of DevRTT was 5 ms just before the first of these five samples was obtained. Last, compute the TCP TimeoutInterval after each of these samples is obtained.

### Answer

Calculate the EstimatedRTT after obtaining the first sample RTT=106ms,

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

EstimatedRTT =0.125 * 106 + (1-0.125) * 100

=0.125* 106 + 0.875 * 100

=13.25 + 87.5

=100.75ms

Calculate the DevRTT after obtaining the first sample RTT:

DevRTT = β * | SampleRTT- EstimatedRTT|+(1- β)* DevRTT

=0.25 * |106-100.75| + (1-0.25) *5

=0.25 *5.25 + 0.75 * 5

=1.3125 + 3.75

=5.0625ms

Calculate the Timeout Interval after obtaining the first sample RTT:

TimeoutInterval = EstimatedRTT +4* DevRTT

= 100.75 + 4 *5.0625

=121ms

Calculate the EstimatedRTT after obtaining the second sample RTT=120ms,

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

EstimatedRTT =0.125 * 120 + (1-0.125) * 100.75

=0.125* 120 + 0.875 * 100.75

=15 + 88.15625

=103.15625ms

Calculate the DevRTT after obtaining the second sample RTT:

DevRTT = β * | SampleRTT- EstimatedRTT|+(1- β)* DevRTT

=0.25 * |120-103.15625| + (1-0.25) *5.0625

=0.25 *16.84 + 0.75 * 5.0625

=4.21 + 3.79

=8ms

Calculate the Timeout Interval after obtaining the second sample RTT:

TimeoutInterval = EstimatedRTT +4* DevRTT

= 103.15 + 4 *8

=135.15ms

Calculate the EstimatedRTT after obtaining the third sample RTT=140ms:

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

EstimatedRTT =0.125 * 140 + (1-0.125) * 103.15

=0.125* 140 + 0.875 * 103.15

=17.5 +90.26

=107.75ms

Calculate the DevRTT after obtaining the third sample RTT:

DevRTT = β * | SampleRTT- EstimatedRTT|+(1- β)* DevRTT

=0.25 * |140-107.75| + (1-0.25) *8

=0.25 *32.25 + 0.75 * 8

=8.06 + 6

=14.06ms

Calculate the Timeout Interval after obtaining the third sample RTT:

TimeoutInterval = EstimatedRTT +4* DevRTT

= 107.75 + 4 *14.06

=164ms

Calculate the EstimatedRTT after obtaining the fourth sample RTT=90ms:

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

EstimatedRTT =0.125 * 90 + (1-0.125) * 107.75

=0.125* 90 + 0.875 * 107.75

=11.25 +94.28

=105.53ms

Calculate the DevRTT after obtaining the fourth sample RTT:

DevRTT = β * | SampleRTT- EstimatedRTT|+(1- β)* DevRTT

=0.25 * |90-105.53| + (1-0.25) *14.06

=0.25 *15.53 + 0.75 * 14.06

=3.88 + 10.545

=14.42ms

Calculate the Timeout Interval after obtaining the fourth sample RTT:

TimeoutInterval = EstimatedRTT +4* DevRTT

= 105.53 + 4 *14.42

=163.21ms

Calculate the EstimatedRTT after obtaining the fifth sample RTT=115ms:

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

EstimatedRTT =0.125 * 115 + (1-0.125) * 105.53

=0.125* 115 + 0.875 * 105.53

=14.375 +92.34

=106.715ms

Calculate the DevRTT after obtaining the fifth sample RTT:

DevRTT = β * | SampleRTT- EstimatedRTT|+(1- β)* DevRTT

=0.25 * |115-106.715| + (1-0.25) *14.42

=0.25 *8.285 + 0.75 * 14.42

=2.07 + 10.815

=12.885ms

Calculate the Timeout Interval after obtaining the fifth sample RTT:

TimeoutInterval = EstimatedRTT +4* DevRTT

= 106.715 + 4 *12.885

=158.255ms

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