**Consider the following data,**

Number of switches in the circuit switched network = 4.

Number of links used in the circuit switched network = 4.

Number of circuits on each link = 4.

The routers are connected in clock wise direction.

**The maximum number of simultaneous connections between the switches in a network is as follows:**

• The number of circuits on each link is the maximum number of simultaneous connections in a network.

• When there are n connections between each of the four pairs of adjacent switches, it gives a maximum of 4 n connections.

• The number of connections on each link between the adjacent switches is 4.

• Thus, the maximum number of simultaneous connections in the circuit switched network is 44 =16 connections.

**Therefore, the maximum number of simultaneous connections is 16.**

**When all the connections are between the switches A and C, the maximum number of simultaneous connections is as follows:**

• When both switches have n connections the maximum number of simultaneous connections is also n.

• From the host A to host C, when each link has n circuits the number of simultaneous connections possible is n for each host. This gives a total of 2n connections.

• Thus, the maximum number of possibilities from A to C, with 4 circuits on each link is 24=8 connections (represented in 2 different colors).

• The green colored lines are actively used.

• The path can only occur because the switches are connected in clockwise direction.

**Therefore, the number of simultaneous connections possible from A to C is 8.**

**The condition for the network is represented by the following diagram:**

• Yes, it possible to make four connections between A and C and other four connections between B and D.

• Of the four connections on a link, two connections can in the clockwise path from A to B and another two connections can be in clockwise from B and C. Similarly, two connections can be in the counter-clockwise path from A to B and another two connections can be in counter-clockwise from B to C.

• The same procedure is implemented to the paths from B to D.

• The green colored lines represent the path in clockwise direction.

• The blue colored lines represent the path in counter-clockwise direction.