**How to Calculate Network Aggregate utility in NS2**

To calculate the Network Aggregate utility in NS2 means that the total of the utilities of all users in the network. The utility functions are commonly used in networking to indicate the fulfilment or advantage a user derives from the network’s resources (for instance: bandwidth, throughput). Usually, it is developed to make sure fair resource distribution, where each user’s utility is increased without sacrificing the entire network performance. The below guide will guide you to measure the aggregate utility in ns2:

**Common Utility Functions in Networks**

**Logarithmic Utility**:

U(x)=log(x)U(x) = \log(x)U(x)=log(x)

This is frequently used in **proportional fairness**, where the utility rises as throughput increases, yet with diminishing returns.

**Linear Utility**:

U(x)=xU(x) = xU(x)=x

This is a basic model where utility maximizes linearly with the resource (like throughput).

**Exponential Utility**:

U(x)=1−e−xU(x) = 1 – e^{-x}U(x)=1−e−x

This utility grows fast initially however saturates, making it useful in some congestion control issues.

**Steps to Calculate Network Aggregate Utility in NS2**

The **aggregate utility** is the total of the utilities of all users in the network. To calculate it, you need to:

- Compute the
**throughput**or resource allocation for each user. - Apply a
**utility function**to the throughput of each user. - Sum the utilities to get the
**aggregate utility**.

**Model the Network in NS2**

First, configure your network model in NS2. Let’s assume a basic wireless or wired network where numerous users are linked to a base station or router, and we are interested in computing the utility according to their throughput.

**Example Setup:**

# Define base station and user nodes

set bs [$ns node] ;# Base station

set ue1 [$ns node] ;# User 1

set ue2 [$ns node] ;# User 2

# Set up links (wired or wireless)

$ns duplex-link $ue1 $bs 10Mb 10ms DropTail

$ns duplex-link $ue2 $bs 10Mb 10ms DropTail

**Generate the Trace File**

Allow tracing to log the packet transmissions, which will permit you to estimate the throughput of each user. This throughput will be used as input for the utility calculation.

# Enable tracing

set tracefile [open out.tr w]

$ns trace-all $tracefile

**Calculate the Throughput for Each User**

Compute the throughput by counting the total number of bytes obtained by each user and divide by the total simulation time.

**AWK Script to Calculate Throughput:**

awk ‘{

if ($1 == “r” && $4 == “tcp”) { # Only consider received TCP packets

if ($3 == 1) { # Packets received by User 1

ue1_total_bytes += $6; # $6 is the packet size in bytes

}

if ($3 == 2) { # Packets received by User 2

ue2_total_bytes += $6;

}

}

} END {

simulation_time = 100.0; # Replace with actual simulation time in seconds

# Convert total bytes to bits and calculate throughput for each user

ue1_throughput_bps = ue1_total_bytes * 8 / simulation_time; # Throughput in bps for UE1

ue2_throughput_bps = ue2_total_bytes * 8 / simulation_time; # Throughput in bps for UE2

print “Throughput for User 1: ” ue1_throughput_bps ” bps”;

print “Throughput for User 2: ” ue2_throughput_bps ” bps”;

}’ out.tr

**Apply the Utility Function**

Next, apply a utility function to the throughput of each user. For simplicity, let’s use a **logarithmic utility function** U(x)=log(x)U(x) = \log(x)U(x)=log(x), which is often used in network utility maximization.

**AWK Script to Apply Utility Function:**

You can compute the utility of each user in terms of their throughput by modifying the throughput calculation script:

awk ‘{

if ($1 == “r” && $4 == “tcp”) { # Only consider received TCP packets

if ($3 == 1) { # Packets received by User 1

ue1_total_bytes += $6; # $6 is the packet size in bytes

}

if ($3 == 2) { # Packets received by User 2

ue2_total_bytes += $6;

}

}

} END {

simulation_time = 100.0; # Replace with actual simulation time in seconds

# Convert total bytes to bits and calculate throughput for each user

ue1_throughput_bps = ue1_total_bytes * 8 / simulation_time; # Throughput in bps for UE1

ue2_throughput_bps = ue2_total_bytes * 8 / simulation_time; # Throughput in bps for UE2

# Calculate the utility for each user (logarithmic utility function)

ue1_utility = log(ue1_throughput_bps);

ue2_utility = log(ue2_throughput_bps);

# Calculate the aggregate utility

aggregate_utility = ue1_utility + ue2_utility;

print “Utility for User 1: ” ue1_utility;

print “Utility for User 2: ” ue2_utility;

print “Aggregate Utility: ” aggregate_utility;

}’ out.tr

This script:

- Estimates the throughput for each user.
- Establishes the logarithmic utility function U(x)=log(x)U(x) = \log(x)U(x)=log(x).
- Sums the utilities to calculate the
**aggregate utility**of the network.

**Modify the Utility Function**

You can easily use various kinds of utility functions by altering the utility function in the script. For instance:

**Linear Utility**: U(x)=xU(x) = xU(x)=x

ue1_utility = ue1_throughput_bps;

ue2_utility = ue2_throughput_bps;

**Exponential Utility**: U(x)=1−e−xU(x) = 1 – e^{-x}U(x)=1−e−x

ue1_utility = 1 – exp(-ue1_throughput_bps);

ue2_utility = 1 – exp(-ue2_throughput_bps);

**Log Aggregate Utility Over Time**

If you want to measure the **aggregate utility** at various time intervals (like every 1 second), fine-tune the script to log the utility occasionally.

**AWK Script for Time-Windowed Aggregate Utility:**

awk ‘{

if ($1 == “r” && $4 == “tcp”) {

interval = int($2); # Group events by time intervals (in seconds)

if ($3 == 1) {

ue1_total_bytes[interval] += $6; # Sum packet sizes for UE1

}

if ($3 == 2) {

ue2_total_bytes[interval] += $6; # Sum packet sizes for UE2

}

}

} END {

for (interval in ue1_total_bytes) {

ue1_throughput_bps = ue1_total_bytes[interval] * 8; # Throughput for UE1 in bits

ue2_throughput_bps = ue2_total_bytes[interval] * 8; # Throughput for UE2 in bits

# Apply the utility function (logarithmic in this case)

ue1_utility = log(ue1_throughput_bps);

ue2_utility = log(ue2_throughput_bps);

# Aggregate utility for the interval

aggregate_utility = ue1_utility + ue2_utility;

print “Time Interval: ” interval ” s, Aggregate Utility: ” aggregate_utility;

}

}’ out.tr

This script estimates the **aggregate utility** for each time interval (e.g., per second), permitting you to monitor how the network utility changes over time.

The above procedure will walk you through the detailed structure of Network aggregate utility and how to calculate it in the ns2 environment with the help of the provided techniques and examples. We will offer anything regarding this network aggregation or when to use the utility functions, if needed.

To compute the Network Aggregate utility using the NS2 tool, we are prepared to assist you in achieving optimal results. Kindly provide us with the details of your parameters, and we will conduct a comparative analysis of your project’s networking performance and share the findings with you.