Consider the sliding window flow-control protocol operating between a sender…
2021
Consider the sliding window flow-control protocol operating between a sender and a receiver over a full-duplex error-free link. Assume the following:
The time taken for processing the data frame by the receiver is negligible.
The time taken for processing the acknowledgement frame by the sender is negligible.
The sender has infinite number of frames available for transmission.
The size of the data frame is 2,000 bits and the size of the acknowledgement frame is 10 bits.
The link data rate in each direction is 1 Mbps (= 106 bits per second).
One way propagation delay of the link is 100 milliseconds.
The minimum value of the sender's window size in terms of the number of frames, (rounded to the nearest integer) needed to achieve a link utilization of 50% is_____________.
Attempted by 42 students.
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Correct answer: 51
Given values:
Data frame size = 2000 bits
Acknowledgement frame size = 10 bits
Link data rate (each direction) = 1,000,000 bits/s
One-way propagation delay = 100 ms = 0.1 s
Compute transmission times and RTT:
Data frame transmission time t_data = 2000 / 1,000,000 = 0.002 s
ACK transmission time t_ack = 10 / 1,000,000 = 0.00001 s
Round-trip time RTT = t_data + 2 * propagation + t_ack = 0.002 + 0.2 + 0.00001 = 0.20201 s
Relation between window size and utilization:
When the sender transmits a window of W frames back-to-back, the sender is busy transmitting for W * t_data every RTT. Therefore utilization U = (W * t_data) / RTT.
Solve for W to achieve 50% utilization (U = 0.5):
W = U * RTT / t_data = 0.5 * 0.20201 / 0.002 = 50.5025
Round to nearest integer: 51 frames (more precise calculation).
Comment on common approximation:
If transmission times (data and ACK) are treated as negligible inside the RTT and RTT is approximated by two-way propagation only (RTT ≈ 0.2 s), then W = 0.5 * 0.2 / 0.002 = 50 exactly. This is the value given by the question's answer.
Final answer (as per the question's approximation and rounding): 50 frames.
Note: Using the fully precise RTT including frame transmission and ACK transmission gives 51 frames when rounded to the nearest integer.
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