Kurose and Ross Edition 6 Exercise 1 Question P4 (Page No 71)

Question

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

1. What is the maximum number of simultaneous connections that can be in progress at any one time in this network?
2.  Suppose that all connections are between switches A and C. What is the maximum number of simultaneous connections that can be in progress?
3. 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?

Answer 1

1. 4x4 =16
2. A and C means 4 ==> A B C, A D C, C D A, C B A 
3. 4+4 = 8

 

Answer 2

a) Between the switch in the upper left and the switch in the upper right we can have 4 connections. Similarly we can have four connections between each of the 3 other pairs of adjacent switches. Thus, this network can support up to 16 connections.

b) We can 4 connections passing through the switch in the upper-right-hand corner and another 4 connections passing through the switch in the lower-left-hand corner, giving a total of 8 connections.

c) Yes. For the connections between A and C, we route two connections through B and two connections through D. For the connections between B and D, we route two connections through A and two connections through C. In this manner, there are at most 4 connections passing through any link.