In this question, you will compare delays in packet switching (i.e. in IP networks), in circuit switching (i.e. in PSTN telephony) and in virtual circuit packet switching (i.e. in FR networks). Assume that the following parameters are defined for the switching networks:                   

N: number of hops between two end points

L: message length in bits

B: data rate in bits per second (same on all links)

P: fixed packet size in bits

H: overhead (header) bits per packet

S: call setup time (in circuit switching and in virtual circuit) in seconds

D: propagation delay per hop in seconds

F: processing delay per packet per hop in packet switching.

Assume the processing delay per packet per hop in virtual circuit packet switching is F/3 (packets are usually referred to as frames in virtual circuit packet switching). Do the following:

6.1 Using the defined parameters above, derive a mathematical expression showing under what condition the packet switching delay is equal or less than circuit switching delay.

6.2 Using the defined parameters above, derive a mathematical expression showing under what condition the virtual circuit packet switching delay is equal or less than packet switching delay.

Assume that there are no acknowledgements. Show your steps in deriving your equations/expressions.

Notes:

• In circuit switching, a circuit is established first, followed by data transfer and circuit teardown.
• In packet switching, no circuit is established. The message is divided into packets and for each packet a header is added. Each packet is independently routed to the destination.
• Virtual circuit packet switching is similar to circuit switching in the sense that a connection is established before data transfer, and the connection is released after data transfer. Virtual circuit packet switching is similar to packet switching in data transfer. Processing delay is smaller compared to packet switching. In this question, it is 1/3 of the processing delay of the packet switching.
• In order to answer part (6.1) of this question, you need to find packet switching delay (Tps) and circuit switching delay (Tcs) in terms of the defined parameters. Then simplify the expression Tps<= Tcs .Similarly for part (6.2).