4. (13 pts) There are two hosts A and B that are connected by a path of Z links (and Z1 switches), each with a link capacity of B bps and a propagation delay of 2ms. There are no queuing delays. Assume that A wants to send a M-bit file to B, with a header of size h (Assume that the M-bit file could be contained in a single packet). Answer the following questions: a. (3pts) Derive an equation showing how long it takes A to send an M-bit file to B over this network, assuming the network is packet-switched with store-and-forward switches. b. (3pts) 'Cut through routing' is an alternative to store-and-forward where a switch waits for the first h bits of a packet to arrive, and then begins transmitting the packet on the next link immediately (even if the last bits of the packet haven't arrived yet). Derive an equation showing how long it takes A to send an M-bit file to B over this network, assuming the network is packet-switched with cut-through switches. c. (3pts) Lets assume our network uses circuit switching. When A wants to send a file to B, it first sends one 'setup' packet of exactly k bits (including both header and payload) to B (requesting as much capacity as possible) and all of the switches act like normal store-and-forward switches. After B receives the setup packet, a 'circuit' has been established and the switches no longer use store-and-forward: a bit coming in on a switch immediately moves to the output port at the switch. B sends the k bit packet back to A, and then A is free to begin transmitting her file with no headers attached. Derive an equation showing how long it takes A to sends an M-bit file to B over this network, which is circuit switched. d. (4 pts) Let k=100 bytes, Z = 8, B = 50 Mbps, and h= 50 bytes. (1) (2pts) Which of the above networks will transmit a 250-byte file fastest? (2) (2pts) Which of the above networks will transmit a 29.5-Mbyte file fastest? Note: 1 byte = 8 bits and 1 ms = 10-3s