An FTP server running at host A must transmit a file of length F bytes to host B over a network path consisting of N links (N1 routers in the path). Assume the links all have the same transmission speed of R bits/second and that processing, queuing, and propagation delays are all negligible relative to the transmission delays.

(a) Suppose the network operates as a message-switched datagram network and that a header of h bytes (combined headers for all protocol layers) is added to the entire message when it is being transmitted. How long does it take to send the file from A to B?

(b) Suppose the network operates as a packet-switched datagram network, the F bytes are segmented into M packets of P bytes each, and a header of h bytes is added to each packet when it is being transmitted. How long does it take to send the file from A to B?

(c) Suppose the network operates as a packet-switched virtual-circuit network, the F bytes are segmented into M packets of P bytes each, and a header of h/2 bytes is added to each packet when it is being transmitted. The virtual circuit set-up time is Ts. How long does it take to send the file from A to B?

(d) Suppose the network operates as a pure circuit-switched network with an end-to-end transmission speed of R bits/second once the circuit has been established. A header of h/2bytes is added to the entire file when it is transmitted and the circuit set-up time is Ts. How long does it take to send the file from A to B?

(e) Under what conditions (what values of Ts) does the packet-switched datagram network provide a faster transfer of file F from A to B than the circuit-switched network?