How to Calculate Network Normalized MSE in omnet++

To calculate the network normalized mean squared error in OMNeT++ has comparing the predefined or computed network performance with the actual or preferred performance over a simulation execution. The NMSE is a parameter that normalizes the Mean Squared Error (MSE) to offer a relative evaluation of the error in relation to the network’s estimated performance. The below is the procedure to calculate the NMSE in OMNeT++:

Step-by-Step Implementation:

Collecting Data

During simulation, we need to gather two sets of data:
- Predicted/Estimated Values: These are the values of model or techniques to predict.
- Actual/Desired Values: These are the actual values monitored in the network or the preferred target values.

Make sure we have these data points at each relevant time step or event.

Calculate the Mean Squared Error (MSE)

The MSE is estimated as the average of the squared differences among the predicted values (y^i\hat{y}_iy^i) and the actual values (yiy_iyi).

MSE=1n∑i=1n(y^i−yi)2\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (\hat{y}_i – y_i)^2MSE=n1i=1∑n(y^i−yi)2

Where:

nnn is the number of observations or data points.
y^i\hat{y}_iy^i is the predicted or estimated value.
yiy_iyi is the actual or desired value.

Calculate the Normalization Factor

The normalization factor is normally based on the variance of the actual values or the range of the actual values and it supports to scale the MSE relative to the network’s expected performance. A communal method is to use the variance of the actual values:

Variance=1n∑i=1n(yi−yˉ)2\text{Variance} = \frac{1}{n} \sum_{i=1}^{n} (y_i – \bar{y})^2Variance=n1i=1∑n(yi−yˉ)2

Where yˉ\bar{y}yˉ is the mean of the actual values.

Calculate the Normalized MSE (NMSE)

Normalize the MSE by dividing it by the variance (or another suitable normalization factor):

NMSE=MSEVariance\text{NMSE} = \frac{\text{MSE}}{\text{Variance}}NMSE=VarianceMSE

Implementing in OMNeT++

In OMNeT++, we would usually estimate these metrics within the simulation model or using a post-processing script. Here’s an instance of how we might implement this:

double predicted_value;

double actual_value;

double mse = 0.0;

double variance = 0.0;

double nmse = 0.0;

int num_samples = 1000; // Assume 1000 samples

std::vector<double> predicted_values; // Store your predicted values

std::vector<double> actual_values; // Store your actual values

// Calculate MSE

for (int i = 0; i < num_samples; i++) {

mse += pow(predicted_values[i] – actual_values[i], 2);

}

mse = mse / num_samples;

// Calculate Variance

double mean_actual = std::accumulate(actual_values.begin(), actual_values.end(), 0.0) / num_samples;

for (int i = 0; i < num_samples; i++) {

variance += pow(actual_values[i] – mean_actual, 2);

}

variance = variance / num_samples;

// Calculate NMSE

nmse = mse / variance;

EV << “Network Normalized MSE: ” << nmse << endl;

Interpretation

The NNMSE value offers an indication of how well model or procedure is performing relative to the variability in the actual network data.
A lower NNMSE signifies better performance, while a higher NNMSE recommends that the model’s predictions deviate meaningfully from the actual data.

Overall, we had understood the basic concepts on how to compute the NMSE in OMNeT++ tool that has includes gathering the data then estimated the MSE after that estimate the normalized factors and NMSE. If you have any query about the NMSE we will support and provide it.

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How to Calculate Network Normalized MSE in omnet++

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