# On the Evaluation of the NB-IoT Random Access Procedure in Monitoring Infrastructures
## 4 Performance Assessment  
Cross-validation was conducted to evaluate the accuracy of the implemented simulation platform. According to all the different monitoring systems detailed in Section 2.3, it is reasonable to assume a periodic reporting traffic. Conducted tests consider a 3 GPP reference scenario [49], which suitably models highly dense sensor networks. Specifically, transmission requests arrival is modeled according to the uniform distribution in the interval \((0,60)\) s, which is in line with the requirements of a number of smart monitoring applications. In addition, \(M=5000\) or \(M=10{,}000\) motionless devices are uniformlydistributed within a cell with a radius of 1.5 km. Consequently, every second there are, on average, \(M/60\) different mobile terminals that want to transmit a preamble. The base station uses a single NB-IoT carrier of 180 kHz and the uplink is configured in _Single-Tone_ mode with a subcarrier spacing of 15 kHz. The chosen uplink scheduling strategy is First In First Out. The simulation environment is summarized in Table 3.  
The details related to the considered NPRACH resource configurations are summarized in Tables 4 and 5.  
Note that for Configuration 1 only the _Normal_ class is considered, while Configuration 2 contemplates all three coverage classes. It is worth mentioning that, to increase the statistical significance of reported results, each simulation was repeated 150 times with different seeds.  
System performance was evaluated in terms of the number of devices involved in the random access procedure, as well as collision and success probabilities. In addition, the analysis of the percentage error between the estimated success probability, i.e., \(\mathcal{S}_{N,s}\), and the simulated success probability, i.e., \(\overline{\mathcal{S}_{N,s}}\), was conducted for each set of simulations. The end-to-end delay was statistically analyzed for additional completeness of the performance evaluation. Finally, to provide further performance insights, the impact of RAO periodicity was investigated with a third resource configuration.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(\alpha\) [\#] & 10 \\ \(n\) [\#] & 1 \\ \(c\) & _Normal_ \\ \(\mathrm{z}a_{c}\) [\#] & 6 \\ \(\alpha\) [\#] & 10 \\ periodicity [ms] & 80 \\ \(s\) [\#] & 36 \\ \(B\) [ms] & 512 \\ \(W\) [ms] & 24 \\ \hline \hline \end{tabular}
\end{table}
Table 4: NPRACH Configuration 1 [50].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Traffic model & Uniform Distribution—(0, 60) s \\ Number of sensors (\(M\)) [\#] & 5000, 10,000 \\ Sensors spatial distribution & Uniform \\ Cell radius [km] & 1.5 \\ NB-IoT bandwidth [kHz] & 180 \\ Transmission mode & Single-Tone \\ Subcarrier spacing [kHz] & 15 \\ Uplink scheduler & FIFO \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of the simulation environment.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(\alpha\) [\#] & 10 \\ \(n\) [\#] & 1 \\ \(c\) & _Normal_ \\ \(\mathrm{z}a_{c}\) [\#] & 6 \\ \(\mathrm{z}a\) [\#] & 10 \\ periodicity [ms] & 80 \\ \(s\) [\#] & 36 \\ \(B\) [ms] & 512 \\ \(W\) [ms] & 24 \\ \hline \hline \end{tabular}
\end{table}
Table 5: NPRACH Configuration 2 [50].