To simulate Flow-based routing using MATLAB which is a kind of routing algorithm in which routes are selected according to the traffic flows or demand among nodes. In this replication, we will configure a network in which each link has a specific capacity, and data flows are delivered reducing congestion. We will be replicated flow-based routing by resolving from a source to a destination for the least congested paths provided the link capacities and demands.
Here is a series of steps to simulating Flow-Based Routing in MATLAB.
Steps to Simulate Flow-Based Routing in MATLAB
- Define the Network Topology, Link Capacities, and Flow Demands:
- Signify the network in which each entry shows the capacity of the link among nodes using an adjacency matrix. A 0 entry denotes no direct link.
- Describe a matrix or a list of traffic demands among node pairs.
% Number of nodes
numNodes = 5;
% Define adjacency matrix for link capacities (in units of bandwidth)
linkCapacities = [0 10 0 20 0;
10 0 15 0 25;
0 15 0 30 10;
20 0 30 0 40;
0 25 10 40 0];
% Define flow demands (in units of bandwidth) between node pairs
% Rows represent source-destination pairs: [source, destination, demand]
flowDemands = [
1 5 5; % Demand from Node 1 to Node 5 with 5 units of flow
2 4 10; % Demand from Node 2 to Node 4 with 10 units of flow
3 5 7 % Demand from Node 3 to Node 5 with 7 units of flow
];
% Display the network link capacities
disp(‘Network Link Capacities:’);
disp(linkCapacities);
- Implement a Shortest Path Algorithm with Capacity Constraints:
- Compute the shortest path depends on the current load on each link using Dijkstra’s algorithm or a same technique. Adapt the path selection according to the available capacity.
function [distances, previous] = dijkstraWithCapacity(linkCapacities, sourceNode, currentLoad)
numNodes = size(linkCapacities, 1);
distances = inf(1, numNodes); % Initialize distances to infinity
distances(sourceNode) = 0; % Distance to itself is zero
previous = zeros(1, numNodes); % Track 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);
visited(u) = true;
% Update distances for neighboring nodes with capacity constraint
for v = 1:numNodes
if ~visited(v) && linkCapacities(u, v) > 0 && (currentLoad(u, v) < linkCapacities(u, v))
% Effective cost considers current load on the link
cost = 1 / (linkCapacities(u, v) – currentLoad(u, v)); % Less congested links have lower cost
newDist = distances(u) + cost;
if newDist < distances(v)
distances(v) = newDist;
previous(v) = u;
end
end
end
end
end
- Simulate Flow Assignment for Each Demand Pair:
- For each demand, determine the least congested path utilizing dijkstraWithCapacity. Rely on the flow demand, modernize the load on each link along the path.
% Initialize load matrix to track current load on each link
currentLoad = zeros(numNodes, numNodes);
% Process each flow demand
for i = 1:size(flowDemands, 1)
sourceNode = flowDemands(i, 1);
destinationNode = flowDemands(i, 2);
demand = flowDemands(i, 3);
% Find the least congested path from source to destination
[distances, previous] = dijkstraWithCapacity(linkCapacities, sourceNode, currentLoad);
% Reconstruct the path from source to destination
path = destinationNode;
while path(1) ~= sourceNode
path = [previous(path(1)), path];
end
disp([‘Path for demand ‘, num2str(demand), ‘ from Node ‘, num2str(sourceNode), ‘ to Node ‘, num2str(destinationNode), ‘: ‘, num2str(path)]);
% Update link load based on the selected path
for j = 1:length(path)-1
u = path(j);
v = path(j+1);
currentLoad(u, v) = currentLoad(u, v) + demand;
currentLoad(v, u) = currentLoad(v, u) + demand; % Symmetric update
end
end
% Display final link loads
disp(‘Final Link Loads after Flow Assignment:’);
disp(currentLoad);
- Check Link Utilization and Congestion:
- Estimate and indicate the link utilization as a percentage of capacity. Detect any links, which are congested (load exceeds capacity).
% Calculate utilization as a percentage
utilization = (currentLoad ./ linkCapacities) * 100;
utilization(isnan(utilization)) = 0; % Handle divide-by-zero for non-links
% Display utilization
disp(‘Link Utilization (% of Capacity):’);
disp(utilization);
% Check for congestion
congestedLinks = utilization > 100;
if any(congestedLinks, ‘all’)
disp(‘Warning: Some links are congested (load exceeds capacity).’);
[row, col] = find(congestedLinks);
for k = 1:length(row)
fprintf(‘Link from Node %d to Node %d is congested.\n’, row(k), col(k));
end
else
disp(‘No congestion detected.’);
end
- Visualize the Network and Link Utilization (Optional):
- Envision the network that highlighting the link capacities and current load on each link using MATLAB’s plotting functions.
% Define node positions for visualization
nodePositions = [10 10; 20 10; 20 20; 10 20; 15 25];
figure;
hold on;
% Plot links with utilization as color intensity
for i = 1:numNodes
for j = i+1:numNodes
if linkCapacities(i, j) > 0
% Scale color based on utilization
colorIntensity = min(utilization(i, j) / 100, 1);
plot([nodePositions(i, 1), nodePositions(j, 1)], [nodePositions(i, 2), nodePositions(j, 2)], …
‘Color’, [1 – colorIntensity, 0, colorIntensity], ‘LineWidth’, 2);
midPoint = (nodePositions(i, 🙂 + nodePositions(j, :)) / 2;
text(midPoint(1), midPoint(2), [num2str(currentLoad(i, j)), ‘/’, num2str(linkCapacities(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’);
end
title(‘Network Link Utilization (Red = High Load)’);
hold off;
Explanation of Key Components
- Dijkstra’s Algorithm with Capacity Constraints: A changed Dijkstra’s algorithm computes the shortest path depends on effective cost that deliberates both link capacity and current load.
- Load Assignment: Load is allocated to the chosen path that modernizing the load matrix to reflect current usage, for each flow demand.
- Link Utilization Check: Utilization is estimated as a percentage of capacity, which emphasizing overloaded (congested) links in which utilization surpasses 100%.
- Visualization: The network visualization utilizes color intensity to indicate the link utilization that offering an intuitive view of congestion within the network.
Possible Extensions
- Dynamic Re-routing: If a link turns out to be congested then actively reroute future flows to prevent the congestion.
- Multi-Commodity Flow Optimization: Resolve for optimal flow allocation to reduce congestion and balance traffic loads.
- Adaptive Link Weights: Dynamically adapt link weights rely on congestion to steer traffic via less-utilized paths.
We had thoroughly understood the concepts and simple steps for Flow Based Routing projects, which were simulated using MATLAB platform. We are furnished to present more advanced insights and detailed explanation according to your needs.
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