Duty Cycling MAC [3p] In this exercise, you will further learn how duty-cycle MAC based on pream- bles work, and what is its average delay to successfully deliver packets. Consider a duty-cycled WSN, where nodes are in sleep state to save energy. We suppose that they wakeup at random once in a range of [0,T] seconds. According to the duty cycling protocol, when a sender node wants to send a packet to a particular destination ove a single hop, it sends a long preamble message (of length T) to hit the receiver whenever it wakes up. When the receiver wakes up and sees the preamble, it sends an ACK packet (containing the number 1) immediately to the sender to indicate that the receiver is available to receive. After receiving the ACK, sender transmits the data packet. If the packet is received correctly by the receiver, it will send an ACK packet with number > 0, otherwise it will send another ACK packet with number -1. The same scenario repeats until the packet gets through. Now consider a channel allowing a data rate R and assume the lengths of data and ACK packets are L and Lack, respectively, and the propagation delay along the channel is tas. Neglect the turn-around time at the sender and the receiver. Suppose that the probability the data packet is dropped is Pe and suppose that ACK packets are always correctly received. The average delay a packet experiences is defined as the time interval between the moment the sender starts sending preambles until the end of the correct data packet reception (note that it does not include the transmission of the last ACK packet). (a) [0.5p] Discuss how this duty-cycle MAC can be implemented together with the mechanisms of IEEE 802.15.4 MAC in the beacon-enabled modal- ity. Use less than half a page, A4 format, 12 pt size characters. (b) [2.5p] The average delay to transmit a message can be defined as T = Tw+Td where Tw is the average wake up time plus the time to receive the ACK, and Ta is the average time to send the data packet. Compute the average delay to transmit a message in the above summarised duty cycling protocol. [Hint: It can be useful to recall that, if p is the probability of packet losses, the formula to approximate the average number of transmissions before a packet is successfully received can be approximated (to start with) as o npn, where pn is the succesfull transmission probability at attempt n and obviously function of p.]