Consider a modification to TCP's congestion control algorithm. Instead of additive increase, we can use multiplicative increase. A TCP sender increases its window size by a small positive constant α (0 < a < 1) whenever receives a valid ACK. Find the functional relationship between loss rate L and maximum congestion window W. Argue that for this modified TCP, regardless TCP's average throughput, a TCP connection always spends the same amount of time to increase its congestion window size from W/2 to W.