Question

Suppose that the five measured SampleRTT values are
130 ms, 106 ms, 150 ms, 140 ms, and 115 ms.

1) 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 120 ms just before the first of these five samples were obtained.

2) Compute also the DevRTT after each sample is obtained, assuming a value of β = 0.25 and assuming the value of DevRTT was 10 ms just before the first of these five samples was obtained.

3) Last, compute the TCP TimeoutInterval after each of these samples is obtained.

4) Will there be a timeout event for any of the packages? Explain. (hint you can use Excel in this one like we did in class)

Answer 1

Answer:

Given,

Sample RTT's = 130 ms, 106 ms, 150 ms, 140 ms, 115 ms

EstimatedRTT (old) = 120 ms,

DevRTT (old) = 10 ms,

α = 0.125,

β = 0.25

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

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

TimeoutInterval = EstimatedRTT + 4* DevRTT

EstimatedRTT(new) in the wake of getting the principal test RTT = 130ms,

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

substitute values

EstimatedRTT = 0.125 * 130 + (1-0.125) * 120

= 0.125* 130 + 0.875 * 120

= 16.25 + 105

= 121.25ms

DevRTT in the wake of acquiring the primary example RTT:

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

substitute values

= 0.25 * |130-121.25| + (1 - 0.25) *10

= 0.25 *8.75 + 0.75 * 10

= 2.1875 + 7.5

= 9.6875ms

Break Interval in the wake of acquiring the primary example RTT:

TimeoutInterval = EstimatedRTT + 4* DevRTT

= 121.25 + 4 *9.6875

= 160ms

EstimatedRTT in the wake of getting the second example RTT = 106ms,

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

EstimatedRTT = 0.125 * 106 + (1-0.125) * 121.25

= 0.125*106+0.875*121.25

= 13.25+106.09375

= 119.34375ms

DevRTT in the wake of getting the second example RTT:

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

= 0.25 * |106-119.34375| + (1-0.25) *9.6875

= 0.25 *13.34375 + 0.75 * 9.6875

= 3.3359375 + 7.265625

= 10.6ms

Break Interval in the wake of getting the second example RTT:

TimeoutInterval = EstimatedRTT + 4* DevRTT

= 119.34375 + 4 * 10.6

= 161.74ms

EstimatedRTT in the wake of getting the third example RTT = 150ms:

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

EstimatedRTT = 0.125 * 150 + (1-0.125) *119.34

= 0.125* 150 + 0.875 * 119.34

= 18.75 + 104.42

= 123.17ms

DevRTT subsequent to acquiring the third example RTT:

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

= 0.25 * |150-123.17| + (1-0.25) *10.6

= 0.25 *26.83 + 0.75 * 10.6

= 6.7 + 7.95

= 14.65ms

Break Interval subsequent to acquiring the third example RTT:

TimeoutInterval = EstimatedRTT + 4* DevRTT

substitute values

= 123.17 + 4 *14.65

= 181.77ms

EstimatedRTT subsequent to acquiring the fourth example RTT=140ms:

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

substitute values

EstimatedRTT = 0.125 * 140 + (1-0.125) * 123.17

= 0.125* 140 + 0.875 * 123.17

= 17.5 +107.77

= 125.27ms

DevRTT subsequent to acquiring the fourth example RTT:

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

substitute values

= 0.25 * |140-125.27| + (1-0.25) *14.65

= 0.25 *14.73 + 0.75 * 14.65

= 3.68 + 10.99

= 14.67ms

Break Interval subsequent to acquiring the fourth example RTT:

TimeoutInterval = EstimatedRTT + 4* DevRTT

substitute values

= 125.27 + 4 *14.67

= 183.94ms

EstimatedRTT subsequent to acquiring the fifth example RTT = 115ms:

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

EstimatedRTT = 0.125 * 115 + (1-0.125) * 125.27

= 0.125* 115 + 0.875 * 125.27

= 14.375 +109.61

= 123.985ms

DevRTT subsequent to acquiring the fifth example RTT:

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

= 0.25 * |115-123.985| + (1-0.25) *14.67

= 0.25 *8.985 + 0.75 * 14.67

= 2.25 + 11

= 13.25ms

Break Interval subsequent to acquiring the fifth example RTT:

TimeoutInterval = EstimatedRTT + 4* DevRTT

substitute values

= 123.985 + 4 *13.25

= 176.985 ms