In: Computer Science
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.
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