Consider a CSMA/CD network, running at 10Mbps, interconnecting 5 computers (A to E) as in Figure 1. In Region 1, three computers (A, B, C) are connected to the hub R1 with a cable of length 1Km (one way) as shown in the figure, while in Region 2, two computers (D and E) are connected to R2 with a cable of length 1Km (one way) as well. R1 and R2 are connected with a cable of length 2Km. Assume that propagation speed along a cable is v = 2 108 m/s and ignore the requirement of repeater due to signal degradation. A B 1 Km R1: hub 1 Km 1 Km Region 1 10Mbps Ethernet 2 Km R2: hub or switch 1 Km 1 Km + D E Region 2 10Mbps Ethernet Figure 1: Network for CSMA/CD Problem (a) (5 points) Assume that R2 is a switch. Compute the shortest packet length P (in bits) for the computer in Region 1 so that CSMA/CD protocol will function correctly. For all the remaining questions, assume that R2 is a hub. (b) (5 points) Compute the shortest packet length P' (in bits) so that CSMA/CD protocol will function correctly for the network in Figure 1. Assume that time is divided into a series of slots, where the length of each slot is set to be equal to transmission delay of P' (your answer to (b)) over this 10Mbps Ethernet. This way, if there are at least two computers or more in the same collision domain transmitting packets in the same time slot, there will be a collision. In each time slot, each computer transmits one packet with probability p independently of one another. (c) (5 points) What is the probability a of having a packet being successfully transmitted without collision in one time slot? (d) (15 points) Assume that all packets are of length nP' (n times larger than your answer to (b)). What is the channel efficiency n (efficiency of the CSMA/CD)? Show your reasoning and write your answer in terms of a in (c), n, and other given parameters or numbers. (e) (5 points) How does the efficiency n (your answer to (d)) change as n increases to infinity? Is it always better to choose larger n in this CSMA/CD network? Briefly show your reasoning. You can answer to this question even if you can't solve (d) above.