The need for switching

• Clearly, the idea to connect each pair of users by a separate wire is absurd.
  • Most of the wires would go unused as you are unlikely to call every number in the world or connect to every WWW server on the Internet.
  • Even if you did, the wires would go unused most of the time.
  • Further, the number of wires coming out of your phone or computer would have to be equal to the number of phones in the world or the number of WWW servers on the Internet.
  • The phone company would have to come back very often to add cables.
• Question: If there are N users in a network, how many wires do you need to run to connect each pair of users by a separate wire.
• Answer: $N+(N-1)+(N-2)+\ldots+2+1=\frac{N*(N+1)}{2}$, i.e., the number of wires grows quadratically with the number of users.
• Question: How do we overcome these difficulties and still ensure that every desired connection is possible?