Question

Suppose we run the Stop and Wait ARQ protocol on a link, with 50% line utilization. The link is now replaced with a new one that has half the round trip delay and six times the bit rate. If we do not change the frame length, how much will be the new line utilization?

a. It remains the same.

b. If it does not remain the same, then it can only grow, since now we have a better link, with shorter delay and higher bit rate.

c. It will be 75%.

d. It will be 25%.

Answer 1

Option (d) is the correct answer.

Line utilization = 50%

We know, line utilization = 1 / (1 + 2a)

Where, T_p / T_t = a

T_p = Propagation time

T_t = Transmission time = (size of frame) / (bit rate)

We have, line utilization = 50%

or, 1 / (1 + 2a) = 1/2

or, 1 / (1 + 2(T_p/T_t)) = 1/2

or, 1 + 2(T_p/T_t) = 2

or, 2(T_p/T_t) = 2 - 1

or, 2(T_p/T_t) = 1

or, (T_p/T_t) = 1/2

or, 2T_p = T_t

New transmission time = T_tn = (size of frame) / (6 * bit rate) = T_t / 6

New propagation time = T_pn = T_p / 2 [As the round-trip delay is half now]

New utilization, 1 / (1 + 2(T_pn/T_tn))

= 1 / (1 + 2((T_p/2)/(T_t/6)))

= 1 / (1 + 2(3(T_p/T_t)))

= 1 / (1 + 2(3(1/2)))

= 1 / (1 + 3) = 1/4 = 25%

Option (a) is incorrect as it will not remain the same.

Option (b) is incorrect as it will be 25%.

Option (c) is incorrect as it will not be 75% (correct answer is 25%).

Please comment in case of any doubt.
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