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Consider the circuit-switched network in Figure 1.13. Recall that there are 4 circuits on each link. Label the four switches A, B, C and D, going in the clockwise direction.

a. What is the maximum number of simultaneous connections that can be in progress at any one time in this network?

b. Suppose that all connections are between switches A and C. What is the maximum number of simultaneous connections that can be in progress?

c. Suppose we want to make four connections between switches A and C, and another four connections between switches B and D. Can we route these calls through the four links to accommodate all eight connections?

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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.

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