In this problem you will derive the efficiency of a CSMA/CD like multiple access protocol. In this protocol the time is slotted and all nodes are synchronised to the slot times. The length of a slot in this case is much less the than the actual time to transmit one frame Let the slot length be S seconds Let the frame length be L bits Let the transmission rate be R bps Let the number of nodes be Nand assume that each node has an infinite amount of packets to send Assume the propagation delay is much less than S, so that all nodes can detect * * . a collision before the end of the slot. The protocol operates as below: If a node has not acquired the channel, all nodes contend with probability p. If exactly 1 user transmit in that slot, then that user keep possession of the channel for the next k slots, transmitting an entire frame. o If a node has the possession of the channel, other nodes refrain from transmitting until that node finish transmitting the frame. Once the transmission completes all nodes again compete for the channel a) If a frame takes k slots to transmit find a relationship between L and S. b) What is the average number of consecutive unproductive (collision) slots in this protocol? Hint: Think about the probability of having m consecutive unproductive slots The following geometric series may be helpful in determining this for la1 c) What is the overall efficiency of this system? d) Show that the efficiency approaches 1 as the frame length becomes large