You are asked to design a land-line network for a new residential area. The netw
ID: 3859475 • Letter: Y
Question
You are asked to design a land-line network for a new residential area. The network is circuit switched. Since it is a new area, traffic statistics are not available. There are three approximations of the traffic rate:
• 30 calls/minute,
• 20 calls/minute,
• and 50 calls/minute.
Each of theapproximations has a probability of 0.3, 0.2 and 0.5, respectively. The duration of calls has an average of 3 minutes.
using matlab solve the following:
1. For the given , show a plot of the blocking probability as the number of circuits increase.
2. Design the number of circuits such that the blocking probability is 0.02 or less ?
3. 10% of the circuits fail each year. Redesign the number of circuits such that the blocking
probability would not exceed 0.03 even with circuits failure.
please need a step by step solution, I only have few hours to submit it :(
Explanation / Answer
Here is the matlab code as per the given criteria:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Here is the main file:
close all
clear all
Lambda=0:0.0001:0.0065; % mean arrival rate (calls per second)
d=200; % mean duration (seconds per call)
a = Lambda.*d; % traffic intensity in Erlangs
n = 1;
b = erlangb(n, a); % n channels/servers
II=find(b<0.1);
plot(a(II), b(II), 'b')
hold on
n = 2;
b = erlangb(n, a); % n channels/servers
II=find(b<0.1);
plot(a(II), b(II), 'g')
n = 3;
b = erlangb(n, a); % n channels/servers
plot(a, b, 'r')
n = 4;
b = erlangb(n, a); % n channels/servers
plot(a, b, 'k')
legend('1', '2', '3', '4 channels', 0)
xlabel('Traffic Intensity (Erlangs)');
ylabel('Blocking Probability');
title('Erlang B formula');
plot(a, 0.02, ':k') % 2% line
erlangb file:
function B = erlangb(N, A)
if (length(N)~=1) | (fix(N) ~= N) | (N < 0)
error('N must be a scalar positive integer');
end
% Here we test that elements of A are real and positive ?
esum = zeros(size(A));
for II=0:N
esum = esum + A .^ II ./ factorial(II);
end
B = A .^ N ./ (factorial(N) .* esum);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Please run these codes into your matlab window and check out the output.
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