**How to Calculate Network Connectivity Robustness in NS2**

To calculate the Network Connectivity Robustness in NS2, we have to uphold the connectivity of the network amongst nodes, even in the presence of failures, interruptions or dynamic variations like node mobility. It can be assessed by verifying parameters like the percentage of linked nodes over time, the size of linked elements and how the network acts when particular nodes or links fail.

Here’s how to calculate network connectivity robustness in NS2:

**Key Metrics for Network Connectivity Robustness**

**Connected Components**: The total of groups of nodes that can interact directly or indirectly. In a fully linked network, all nodes belong to a distinct connected element.**Average Path Length**: The average number of hops amongst any two nodes in the network.**Node/Link Failure Analysis**: Inspecting how the network connectivity is impacted when specific nodes or links fail.**Node Degree**: The amount of direct neighbors a node has. Higher average node degree means better resilience to failure.**Packet Delivery Ratio (PDR)**: A drop in PDR could represent a loss in connectivity amidst nodes.

**Steps to Calculate Network Connectivity Robustness in NS2**

**Generate the Trace File**

First, make certain that your simulation is creating a trace file that logs all the packet transmission and reception events:

set tracefile [open out.tr w]

$ns trace-all $tracefile

This trace file will help you analyze how packets move amongst nodes and how connectivity is upholde or lost over time.

**Calculate the Number of Connected Components**

Estimate the number of **connected components** by validating how many distinct groups of nodes can interact with one another. If your network is divided into numerous elements because of failures or node mobility, the network connectivity robustness minimizes.

You can write an AWK or Python script to assess the trace file and record the count of distinct linked components at various time intervals.

Here’s an approach to measure linked components:

- Parse the trace file to develop an adjacency list of the network, denoting which nodes can directly communicate with one another.
- Use a graph traversal algorithm like BFS (Breadth-First Search) or DFS (Depth-First Search) to find connected components.

**Python Example for Finding Connected Components:**

You can parse the trace file and design the adjacency list for each timestamp and use a Python script to compute the linked elements.

from collections import defaultdict, deque

# Build adjacency list from trace file (simplified)

def build_adjacency_list(tracefile):

adj_list = defaultdict(set)

with open(tracefile, ‘r’) as f:

for line in f:

if line.startswith(‘r’): # Look at received packets

data = line.split()

src_node = int(data[2]) # Source node

dst_node = int(data[3]) # Destination node

adj_list[src_node].add(dst_node)

adj_list[dst_node].add(src_node)

return adj_list

# Find connected components using BFS

def find_connected_components(adj_list):

visited = set()

components = []

for node in adj_list:

if node not in visited:

queue = deque([node])

component = []

while queue:

current = queue.popleft()

if current not in visited:

visited.add(current)

component.append(current)

queue.extend(adj_list[current] – visited)

components.append(component)

return components

# Example usage:

adj_list = build_adjacency_list(“out.tr”)

components = find_connected_components(adj_list)

print(f”Number of connected components: {len(components)}”)

In this code:

**build_adjacency_list()**creates a graph (adjacency list) from the trace file, where each node can interact with its neighbors.**find_connected_components()**uses BFS to find all linked components in the graph.

If the sum of connected components rises significantly over time, it signifies that the network is fragmenting and the connectivity robustness is reducing.

**Analyze Average Path Length**

The **average path length** is the average number of hops amongst any two nodes in the network. A robust network upholds shorter path lengths, even as nodes or links fail.

Quantify the average path length by fine-tuning the adjacency list created above and compute the shortest path amongst every pair of nodes using algorithms like **Floyd-Warshall** or **Dijkstra**. Here’s a basic approach using **Floyd-Warshall** for an undirected graph:

def floyd_warshall(adj_matrix):

n = len(adj_matrix)

for k in range(n):

for i in range(n):

for j in range(n):

if adj_matrix[i][k] + adj_matrix[k][j] < adj_matrix[i][j]:

adj_matrix[i][j] = adj_matrix[i][k] + adj_matrix[k][j]

return adj_matrix

def calculate_average_path_length(adj_list, num_nodes):

inf = float(‘inf’)

adj_matrix = [[inf]*num_nodes for _ in range(num_nodes)]

# Initialize adjacency matrix

for node, neighbors in adj_list.items():

for neighbor in neighbors:

adj_matrix[node][neighbor] = 1

adj_matrix[neighbor][node] = 1

# Distance from each node to itself is zero

for i in range(num_nodes):

adj_matrix[i][i] = 0

# Compute shortest paths

dist_matrix = floyd_warshall(adj_matrix)

# Calculate the average path length

total_length = 0

count = 0

for i in range(num_nodes):

for j in range(num_nodes):

if dist_matrix[i][j] != inf and i != j:

total_length += dist_matrix[i][j]

count += 1

if count > 0:

return total_length / count

return inf

**floyd_warshall()**estimates the shortest paths amongst all node pairs.**calculate_average_path_length()**uses the adjacency list to measure the average count of hops amongst nodes.

A lower average path length represents better network robustness, while the maximizing path length suggests decreased connectivity.

**Simulate Node or Link Failures**

You can replicate **node or link failures** to monitor how the network acts under stress. By imitating failures and assessing the connectivity after failures, you can evaluate the robustness of the network.

To simulate node failures in NS2:

# Example of node failure at a specific time

$ns at 50.0 “$node(2) set energy 0”

After simulating failures, you can re-analyze the total of connected components, PDR, or average path length to monitor the effect on connectivity robustness.

**Calculate Packet Delivery Ratio (PDR)**

PDR can give you an idea of network connectivity robustness, as a drop in PDR represents that packets are being lost because of connectivity issues (like nodes going offline or paths being broken).

Here’s how to measure PDR using an AWK script:

awk ‘{

if ($1 == “+” && $4 == “tcp”) {

sent_packets++;

}

if ($1 == “r” && $4 == “tcp”) {

received_packets++;

}

} END {

if (sent_packets > 0) {

pdr = (received_packets / sent_packets) * 100;

print “Packet Delivery Ratio (PDR): ” pdr “%”;

} else {

print “No packets were sent.”;

}

}’ out.tr

High PDR values signify good connectivity robustness, while a drop in PDR advises that the network is losing connectivity.

**Monitor Node Degree Distribution**

Nodes with a higher degree (i.e., more direct neighbors) are more resilient to failure. You can compute the **node degree distribution** to evaluate how well-connected the network is.

To measure the degree of each node:

def calculate_node_degree(adj_list):

degrees = {node: len(neighbors) for node, neighbors in adj_list.items()}

return degrees

Nodes with higher degrees have better redundancy, making the network stronger. If node degrees drop significantly after node or link failures, the network may lose connectivity robustness.

The delivered process contains the entire instructions and examples with snippet codes to help you obtain the knowledge of network connectivity robustness and how to measure it in ns2 to maintain the connectivity under extreme conditions.

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