To simulate Least Cost Routing using MATLAB that can be replicated by determining the minimum-cost paths amongst nodes within a network utilizing an algorithm like Dijkstra’s Algorithm or Bellman-Ford. Least cost routing, from a source to every other node that detects the best path with the lowest cumulative cost. Share all your project details to phdprime.com we will provide you with detailed guidance.
Below, we compute least-cost paths in a static network using Dijkstra’s Algorithm.
Steps to Simulate Least Cost Routing in MATLAB
- Define the Network Topology and Link Costs:
- Signify the network in which each entry shows the cost of traveling among nodes using an adjacency matrix. A cost of inf intends no direct connection exists.
% Number of nodes
numNodes = 5;
infCost = inf; % Define infinity to represent no direct connection
% Define adjacency matrix for link costs
linkCosts = [0 2 infCost 6 infCost;
2 0 3 8 5;
infCost 3 0 infCost 7;
6 8 infCost 0 9;
infCost 5 7 9 0];
% Display the network topology
disp(‘Network Link Costs:’);
disp(linkCosts);
- Implement Dijkstra’s Algorithm for Least Cost Path Calculation:
- To determine the shortest path from the source node to every other node according to the cumulative costs with the help of Dijkstra’s algorithm.
function [distances, previous] = dijkstra(linkCosts, sourceNode)
numNodes = size(linkCosts, 1);
distances = inf(1, numNodes); % Initialize distances to infinity
distances(sourceNode) = 0; % Distance to source is zero
previous = zeros(1, numNodes); % Store previous nodes for path reconstruction
visited = false(1, numNodes); % Track visited nodes
for i = 1:numNodes
% Find the unvisited node with the smallest distance
[~, u] = min(distances + inf * visited); % Exclude already visited nodes
visited(u) = true;
% Update distances for neighboring nodes
for v = 1:numNodes
if ~visited(v) && linkCosts(u, v) < inf
newDist = distances(u) + linkCosts(u, v);
if newDist < distances(v)
distances(v) = newDist;
previous(v) = u;
end
end
end
end
end
- Run the Least Cost Routing Calculation from a Source Node:
- Place a source node, then computing the least cost path from the source to each other node utilizing Dijkstra’s algorithm.
sourceNode = 1; % Choose the source node
[distances, previous] = dijkstra(linkCosts, sourceNode);
% Display the shortest path cost to each node
disp([‘Least Cost Paths from Node ‘, num2str(sourceNode), ‘:’]);
disp(distances);
- Reconstruct and Display the Least Cost Paths:
- We need to use the previous array to backtrack and from the source to each destination rebuild the path.
% Function to reconstruct the path from source to a destination
function path = reconstructPath(previous, sourceNode, destNode)
path = destNode;
while path(1) ~= sourceNode
path = [previous(path(1)), path];
end
end
% Display the least cost path from the source node to each destination
for destNode = 1:numNodes
if destNode ~= sourceNode
path = reconstructPath(previous, sourceNode, destNode);
disp([‘Path from Node ‘, num2str(sourceNode), ‘ to Node ‘, num2str(destNode), ‘: ‘, num2str(path)]);
disp([‘Cost: ‘, num2str(distances(destNode))]);
end
end
- Visualize the Network Topology and Least Cost Paths (Optional):
- Envision the network topology and emphasize least-cost paths from the source node to other nodes utilizing MATLAB’s plotting functions.
% Define node positions for visualization
nodePositions = [10 10; 20 10; 20 20; 10 20; 15 25];
% Plot the network topology
figure;
hold on;
for i = 1:numNodes
for j = i+1:numNodes
if linkCosts(i, j) < inf
plot([nodePositions(i, 1), nodePositions(j, 1)], …
[nodePositions(i, 2), nodePositions(j, 2)], ‘k–‘);
midPoint = (nodePositions(i, 🙂 + nodePositions(j, :)) / 2;
text(midPoint(1), midPoint(2), num2str(linkCosts(i, j)), …
‘HorizontalAlignment’, ‘center’, ‘BackgroundColor’, ‘white’);
end
end
plot(nodePositions(i, 1), nodePositions(i, 2), ‘bo’); % Plot nodes
text(nodePositions(i, 1), nodePositions(i, 2), num2str(i), …
‘VerticalAlignment’, ‘bottom’, ‘HorizontalAlignment’, ‘center’);
end
title(‘Network Topology with Link Costs’);
% Highlight the least cost path from the source node to each destination
for destNode = 2:numNodes
path = reconstructPath(previous, sourceNode, destNode);
for k = 1:length(path)-1
plot([nodePositions(path(k), 1), nodePositions(path(k+1), 1)], …
[nodePositions(path(k), 2), nodePositions(path(k+1), 2)], ‘r-‘, ‘LineWidth’, 2);
end
end
hold off;
- Analyze Path Efficiency (Optional):
- Monitor the total cost of each path and compute the efficiency parameters such as average path cost.
% Calculate the average path cost from the source node
avgPathCost = mean(distances(distances < inf));
disp([‘Average Path Cost from Node ‘, num2str(sourceNode), ‘: ‘, num2str(avgPathCost)]);
Explanation of Key Components
- Adjacency Matrix: The adjacency matrix describes the network topology in which each element denotes the cost among nodes. An inf entry intends no direct link.
- Dijkstra’s Algorithm: Dijkstra’s algorithm iteratively discovers the shortest path from the source to each node by choosing the node with the least cumulative distance at every single step.
- Path Reconstruction: With the support of previous array, paths from the source node to any other node can be rebuilt that enabling us to track the least-cost route.
- Visualization: Emphasizing the least-cost paths from the source node supports explain the computed paths and envisioning the network topology.
Possible Extensions
- Dynamic Cost Changes: Replicate a dynamic network by modifying the link costs and then monitoring how least-cost paths are recomputed.
- Multiple Source Nodes: Compute the least-cost paths for several source nodes which replicating the impact of distributed routing.
- Realistic Weight Metrics: Utilize realistic weights depends on the parameters such as latency, bandwidth, or reliability rather than arbitrary costs.
In these projects, we successfully computed the minimum-cost paths in a static network with the help of Dijkstra’s Algorithm through the simulation steps using MATLAB environment. If necessary, we can deliver more in-depth simulation and information on this subject.
