IRTT = 10ms (Given)
ID = 5ms (Given)
$\alpha$ = 0.5
Given these information, we calculate the Timeout (The time within which the acknowledgement should reach te sender to avoid retransmission).
According to Jacobson's Algorithm, TO = 4 * ID + IRTT
So, TO = 4 * 5 + 10 = 30ms
Now, ARTT = 20ms (The acknowledgement reached after 20ms which is less than te TO time, so we can proceed without Karn's modification)
Actual Deviation, AD = | IRTT - ARTT | = 10ms
New RTT = $\alpha$ IRTT + (1 - $\alpha$)ARTT = 0.5 * 10 + (1 - 0.5) * 20 = 15ms
New Deviation, ND = $\alpha$ ID + (1 - $\alpha$)AD = 0.5 * 5 + (1 - 0.5 ) * 10 = 7.5ms
Thus, we calculate the RTT and Deviation for the next transmission. We proceed as above with the subsequent transmissions.
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IRTT = 15ms
ID = 7.5ms
TO = 4 * 7.5 + 15 = 45ms
ARTT = 30ms (The acknowledgement reached after 30ms which is less than TO time)
Actual Deviation, AD = | IRTT - ARTT | = 15ms
New RTT = $\alpha$ IRTT + (1 - $\alpha$ )ARTT = 0.5 * 15 + (1 - 0.5) * 30 = 22.5ms
New Deviation, ND = $\alpha$ ID + (1 - $\alpha$ )AD = 0.5 * 7.5 + (1 - 0.5) * 15 = 11.25ms
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IRTT = 22.5ms
ID = 11.25ms
So, TO = 4 * 11.25 + 22.5 = 67.5ms
Now, ARTT = 40ms (The acknowledgement reached after 40ms which is less than TO time)
Actual Deviation, AD = | IRTT - ARTT | = 17.5ms
New RTT = $\alpha$ IRTT + (1 - $\alpha$)ARTT = 0.5 * 22.5 + (1 - 0.5) * 40 = 31.25ms
New Deviation, ND = $\alpha$ ID + (1 - $\alpha$ )AD = 0.5 * 11.25 + (1 - 0.5) * 17.5 = 14.375ms
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IRTT = 31.25ms
ID = 14.375
TO = 4 * 14.375 + 31.25 = 88.75ms
