The distance between two stations M and N is L kilometers. All frames are K…

2007

The distance between two stations M and N is L kilometers. All frames are K bits long. The propagation delay per kilometer is t seconds. Let R bits/second be the channel capacity. Assuming that processing delay is negligible, the minimum number of bits for the sequence number field in a frame for maximum utilization, when the sliding window protocolis used, is:

GATECS200770

  1. A.

    A

  2. B.

    B

  3. C.

    C

  4. D.

    D

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Show answer & explanation

Correct answer: C

Goal: find the minimum number of sequence-number bits n so that the sliding-window sender can achieve full utilization.

  • One-way propagation delay = L·t, so round-trip propagation delay = 2Lt.

  • Transmission time per frame = K/R.

  • To keep the sender busy (utilization = 1), the sender must be able to send W frames in the time between sending a frame and receiving its ACK. Therefore:

    W · (K/R) ≥ (K/R) + 2Lt

  • Rearrange to get the required window size:

    W ≥ 1 + 2LtR / K

    So the minimum integer window is Wmin = ceil(1 + 2LtR / K).

  • The sequence-number field of n bits provides 2^n distinct sequence numbers, so we need

    2^n ≥ Wmin = 1 + 2LtR / K

    Hence

    n = ceil(log2(1 + 2LtR / K)) = ceil(log2((2LtR + K)/K)).

Therefore the minimum number of bits in the sequence-number field is ceil(log2((2LtR + K)/K)).

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