Question

4. A network has N subscribers. Each subscriber is connected directly to all other subscribers.
(a) What is the total number of lines L in the network?
(b) What is the value of L for N = 2, 10, 100, and 1,000?
(c) How many lines must be built to each subscriber?
(d) Is this kind of network structure suitable for a public telecommunications network? Explain

Answer 1

Answer:

a) Here, Total No. of subscribers=N

So, the total number of lines in the network, L = $\frac{N(N-1)}{2}$

b) If N=2, then L=1;

If N=10, then L=45;

If N=100, then L= 4950;

If N=1000, then L= 499500.

c) In a mesh topology network with N subscribers, (N–1) lines must be built to each subscriber.

d) No it is not suitable for a public telecommunications network.

Because it is costly and complex to implement. Needs more power to active all nodes. The nodes will face redundant connection problem etc.

Explanation:

a) Because each subscriber is directly connected to all other subscribers, the network follows a mesh topology.

b) If N=2,

L=$\frac{2*(2-1)}{2}$ = 1.

If N=10,

L= $\frac{10*(10-1)}{2}$ = 45.

If N=100,

L= $\frac{100*(100-1)}{2}$ = 4950

If N=1000,  

L= $\frac{1000*(1000-1)}{2}$ = 499500.