Question

In: Computer Science

Five values of SampleRTT are 10 ms, 5 ms, 15 ms, 25 ms, and 30 ms....

Five values of SampleRTT are 10 ms, 5 ms, 15 ms, 25 ms, and 30 ms.

Compute the EstimatedRTT, DevRTT, and Timeoutinterval after each of these SampleRTT values is obtained.

Assume α = 0.125 and β = 0.25.

Initial value of EstimatedRTT was 15 ms and initial value of DevRTT was 10 ms just before the first of these five samples was obtained.

Solutions

Expert Solution

Initial stage

Estimated RTT= 15 ms

DevRTT = 10 ms

α = 0.125

ß = 0.25

First Stage

Sample RTT = 10 ms

Estimated RTT = (1-α)*Estimated RTT prev + α*sample RTT

= (1-0.125)*15 + 0.125*10

= 0.875 * 15 + 1.25

= 13.125 + 1.25

= 14.375 ms

DevRTT= (1-ß)*DevRTT prev + ß*|sample RTT - EstimatedRTT|

= (1-0.25)*10 + 0.25*|10-14.375|

= 0.75*10 + 0.25*|-4.375|

= 7.5 + 0.25*4.375

= 7.5 + 1.093

= 8.593 ms

Timeout = EstimatedRTT + 4*DevRTT

= 14.375 + 4*8.593

= 14.375 + 34.372

= 48.747 ms

Second Stage

Sample RTT = 5 ms

Estimated RTT = (1-α)*Estimated RTT prev + α*sample RTT

= (1-0.125)*14.375 + 0.125*5

= 0.875 * 14.375 + 0.625

= 12.578 + 1.25

= 13.828 ms

DevRTT= (1-ß)*DevRTT prev + ß*|sample RTT - EstimatedRTT|

= (1-0.25)*8.593 + 0.25*|5-13.828|

= 0.75*8.593 + 0.25*|-8.828|

= 6.444 + 0.25*8.828

= 6.444 + 2.207

= 8.651 ms

Timeout = EstimatedRTT + 4*DevRTT

= 13.828 + 4*8.651

= 13.828 + 34.604

= 48.432 ms

Third Stage

Sample RTT = 15 ms

Estimated RTT = (1-α)*Estimated RTT prev + α*sample RTT

= (1-0.125)*13.828 + 0.125*15

= 0.875 * 13.828 + 1.875

= 12.099 + 1.875

= 13.974 ms

DevRTT= (1-ß)*DevRTT prev + ß*|sample RTT - EstimatedRTT|

= (1-0.25)*8.651 + 0.25*|15-13.974|

= 0.75*8.651 + 0.25*|1.026|

= 6.488 + 0.25*1.026

= 6.488 + 0.2562

= 6.7445 ms

Timeout = EstimatedRTT + 4*DevRTT

= 13.974 + 4*6.7445

= 13.974 + 26.978

= 40.952 ms

Fourth Stage

Sample RTT = 25 ms

Estimated RTT = (1-α)*Estimated RTT prev + α*sample RTT

= (1-0.125)*13.974 + 0.125*25

= 0.875 * 13.974 + 3.125

= 12.227 + 3.125

= 15.352 ms

DevRTT= (1-ß)*DevRTT prev + ß*|sample RTT - EstimatedRTT|

= (1-0.25)*6.744 + 0.25*|25-15.352|

= 0.75*6.744 + 0.25*|9.648|

= 5.058 + 0.25*9.648

= 5.058 + 2.412

= 7.47 ms

Timeout = EstimatedRTT + 4*DevRTT

= 15.352 + 4*7.47

= 15.352 + 29.88

= 45.232 ms

Fifth Stage

Sample RTT = 30 ms

Estimated RTT = (1-α)*Estimated RTT prev + α*sample RTT

= (1-0.125)*15.352 + 0.125*30

= 0.875 * 15.352 + 3.75

= 13.433 + 3.75

= 17.183 ms

DevRTT= (1-ß)*DevRTT prev + ß*|sample RTT - EstimatedRTT|

= (1-0.25)*7.47 + 0.25*|30-17.183|

= 0.75*7.47 + 0.25*|12.817|

= 5.602 + 0.25*12.817

= 5.058 + 3.204

= 8.262 ms

Timeout = EstimatedRTT + 4*DevRTT

= 17.183 + 4*8.262

= 17.183 + 33.049

= 50.232 ms

venereology answered 1 week ago

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