Consider a path with k+ 1 nodes: a source host, a destination host andk-1 intermediate routers, linked by k transmission links of bandwidth W bits/second each. The propagation delay over each link is seconds. Processing and queueing delays at intermediate nodes are all negligible, no errors happen and no packets are ever lost. The source has an infinite queue of messages to be transmitted to the destination. Each message consists of L bits of user data We are interested in two performance metrics End-to-end throughput is defined as the number of useful bits per sec sent by the source. (From the point of view of the user, useful are considered only the bits in the message, but not the headers or signaling messages.) End-to-end delay is defined as the time elapsed from when the sender is ready to transmit the message until the message is entirely received by the destination. We wish to compare these two metrics in each of the following switching methods Message Switching: The message is sent from node to node in a store-and-forward manner: each node receives the whole message and then sends it on the next link to the following node, using the full transmission speed. Each message requires to add a header of length H bits. As soon as the entire first message is fully received at the destination, the destination sends back an acknowledgment packet of size H bits, also in a store-and-forward manner. Upon reception of the acknowledgement, the sender can start the transmission of the next message.1 Packet Switching: A message is broken up into packets of size P(assume that L/P is an integer) and a header of H bits is added in front of every packet. Packets are forwarded from node to node in a store-and-forward manner, using the full transmission speed. As soon as the last packet of the message is fully received at the destination, the destination node sends an acknowledgement for the whole message, of size H bits, and forwarded in a store-and-forward manner back to the sender. Upon reception of the acknowledgement, the sender can start the transmission of the second message Questions: 1. Give a formula for the throughput and delay in Message Switching, as a function of the parameters (L,H,k,W,t) 2. Give a formula for the throughput and delay in Packet Switching, as a function of the parameters (L,P ,H,k,W,t) 3. Which one achieves lower end-to-end delay: Message Switching to Packet Switching? You can assume the following values of the parameters : = 0,H& P and k is very large 4. Consider Packet Switching again. You are free to choose the size of the packets (P), while all other parameters (L, H, k, W, ) are fixed, known and out of your control. How would you choose the packet size P to so as to minimize the end-to-end delay