Example U problem for GBN with errors                              KJC (8/29/03)
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The situation is:

  - 1.544-Mbps link of length 3000 km
  - Propagation of 5 nanosec/m
  - Mean frame length of 250 bytes
  - Pr[bit error] = 1.0e-4 (bit errors are iid)
  - GBN ARQ with N = 30 (N is the window size)

The requirement is:

  - Compute U

Solution:

  We first compute p = Pr[frame error]...

    p = 1 - (1 - 1.0e-4)^(250 * 8) = 0.1813

  Then, we compute t_fr an t_pr...

    t_fr = (250 * 8) / 1.544e6 = 0.001295 sec

    t_pr = 5.0e-9 * 3000000 = 0.015 sec

  Is N * t_fr less than or greater than 2 * t_pr + t_fr?

    N * t_fr = 30 * 0.001295 = 0.03885 sec

    2 * t_pr + t_fr = 2 * 0.015 + 0.001295 = 0.031295 sec

    So, we have N * t_fr > 2 * t_pr + t_fr

  Computing U...

    U = (t_fr * (1 - p)) / (t_fr + 2 * t_pr * p)

      = (0.001295 * (1 - 0.1813)) / (0.001295 + 2 * 0.015 * 0.1813) = 15.74%

    which is a very poor utilization of the link

Notes:

  If we had N * t_fr < 2 * t_pr + t_fr we would have used:

    U = (N * t_fr * (1 - p)) / ((1 - p + N * p) * (2 * t_pr + t_fr))

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