Exercise We derived in the lecture the expression of the efficiency of the Stop- And-Protocol as a function of the bit rate b, the propagation time T, and the bit error rate ber: Suppose the bit rate by, the propagation time T, and the bit error rate ber are given (known). 1) (80 points) Derive the expression of the optimal packet size Smax that maximizes the efficiency. Express Smax as a function of the bit rate by the propagation time T,, and the bit error rate ber. (Hint: a function f(x) is optimal for some value x, if and only if f(x)=. In other words, derive the function f(x) and solve f(x) = 0. 2) (2.5 points) Suppose br = 1.5 Mbps, Tp = 50ms, and ber = 5.10-6. What is the optimal packet size Smax? 3) (15 points) Suppose br = 1.5 Mbps, Tp = 50ms, and ber = 5.10-6. Plot the efficiency as a function of the packet size S from 0 to 180,000 bits. 4) (2.5 points) Using the plot, check the value of the packet size S you found in Question 3). Exercise We derived in the lecture the expression of the efficiency of the Stop- And-Protocol as a function of the bit rate b, the propagation time T, and the bit error rate ber: Suppose the bit rate by, the propagation time T, and the bit error rate ber are given (known). 1) (80 points) Derive the expression of the optimal packet size Smax that maximizes the efficiency. Express Smax as a function of the bit rate by the propagation time T,, and the bit error rate ber. (Hint: a function f(x) is optimal for some value x, if and only if f(x)=. In other words, derive the function f(x) and solve f(x) = 0. 2) (2.5 points) Suppose br = 1.5 Mbps, Tp = 50ms, and ber = 5.10-6. What is the optimal packet size Smax? 3) (15 points) Suppose br = 1.5 Mbps, Tp = 50ms, and ber = 5.10-6. Plot the efficiency as a function of the packet size S from 0 to 180,000 bits. 4) (2.5 points) Using the plot, check the value of the packet size S you found in Question 3)