How to calculate the Jain’s fairness index in routing?

I have network structure G = (V,E) with vertex set V, edge set E. The vertices are representing nodes and an edge connects two nodes. The edge values are positive and there is no self loops. I have differnt routing paths. how to calculate the each routing path jain index?

Answer 1

[Simran]

Hello @kuna Venkateswararao,

To calculate the “Jain’s fairness index” of a network, you can follow these steps:

1.) First you should know the resources (bandwidth) allocated to each path of your network. For my example sample network, I took these paths:

% Define the resources (bandwidths) for each edge in the paths 
resources_path1 = [10, 15, 20, 25];  % Path 1: A -> B -> C -> D -> E 
resources_path2 = [30, 25];         % Path 2: A -> D -> E 

2.) Then you calculate the “Jain’s fairness index” using the below formula, where (n) is the number of resources and (x_i) is the resource value of each segment.

% Function to calculate Jain's fairness index 
function fairness_index = calculate_jains_index(resources) 
n = length(resources); 
sum_resources = sum(resources); 
sum_squares = sum(resources.^2); 
fairness_index = (sum_resources^2) / (n * sum_squares); 
end 

3.) Then using the above function, calculate “Jain’s fairness index” for each path.

After following the above steps, I got the “Jain’s fairness index” values for both to be:

You can refer to these documentation links for more help:

for creating “user-defined functions” like "jain's fairness index" - https://www.mathworks.com/help/releases/R2021a/matlab/matlab_prog/create-functions-in-files.html

“array indexing”: https://www.mathworks.com/help/releases/R2021a/matlab/math/array-indexing.html