Question: Consider a stop-and-wait system with two-way traffic between nodes A and B. Assume that data frames are all of the same length and require D seconds for transmission. Acknowledgment frames require R seconds for transmission and there is a propagation delay P on the link. Assume that A and B both have an unending sequence of packets to send, assume that no transmission errors occur, and assume that the time-out interval at which a node resends a previously transmitted packet is very large. Finally, assume that each node sends new data packets and acknowledgments as fast as possible, subject to the rules of the stop-and-wait protocol.

(a) Show that the rate at which packets are transmitted in each direction is (D +R +2P)- 1. Show that this is true whether or not the starting time between A and B is synchronized.

(b) Assume, in addition, that whenever a node has both an acknowledgment and a data packet to send, the acknowledgment is piggybacked onto the data frame (which still requires D seconds). Assume that node B does not start transmitting data until the instant that it receives the first frame from A (i.e., B's first frame contains a piggybacked ack). Show that all subsequent frames in each direction are data frames with a piggybacked ack. Show that the rate in each direction is now (2D + 2P)-1. Note that if D > R, this rate is less than that in part (a).