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My question is about the maximum bandwidth a switch\router can support for an entire network (not just 1 machine to another).

These pieces of equipment are often rated at 100 MBit, 1 GBit, etc. However they often have at least 4 ports if not more.

Quoting from Wikipedia:

An Ethernet switch operates at the data link layer of the OSI model to create a separate collision domain for each switch port. With four computers (e.g., A, B, C and D) on four switch ports, any pair (e.g. A and B) can transfer data back and forth while the other pair (e.g. C and D) also do so simultaneously, and the two conversations will not interfere with one another. In full duplex mode, these pairs can also overlap (e.g. A transmits to B, simultaneously B to C, and so on)

So if A is talking to B and C is talking to D at the same time through a 1 GBit switch, will each pair receive a 0.5 GBit connection or will each pair receive a 1 GBit connection? If each pair is receiving a 1 GBit connection, then the total network bandwidth at that time is 2 GBit and then seems dependent on the number of ports available on the router as well as the number of machine pairs on the network.

3

Vendor's will label this as the fabric or backplane of the switch and is something you can generally find in the documentation/specs. If you are bored you can go read a history of the term on etheralmind.

Router's will often have other limitations such as packets per second and processing power when using things like ACLs.

Also keep in mind Ethernet is generally full-duplex, meaning it is 1G in and 1G out at the same time (they are independent).

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