# Combined Access Barring Scheme for IoT Devices Using Bayesian Estimation
## 4 Performance Evaluation and Discussion  
The performance evaluation of the proposed technique is verified by performing extensive simulations in Matlab. System model is programmed in Matlab and the results are plotted that are shown and explained in this section. The general parameter setting for the simulations is mentioned in Table 1. The number of devices is \(U\) = 10,000, 30,000 and it affects the overall TST because more number of devices means larger TST. Since all the devices arrive in the system within very short time \(T_{A}=500\) ms, the access delay also depends on the total number of devices. The simulation runs until all the \(U\) devices get served. The number of preambles are varied from \(R=5\rightarrow~{}50\) and the selection also affects TST and access delay. Larger the number of preambles, larger is the choice for the devices to choose a preamble from a given pool. Then the probability of collision decreases, and consequently the probability of success (or idle) increases and hence TST and access delay is reduced. The periodicity of bitmap \(T_{P}\) is also an important factor as the eNodeB changes the class access based on this parameter. Larger the value of \(T_{P}\), larger is the waiting time of devices belonging to this class and vice versa, and its value is taken to be 320 ms as it can have value of \(160,320,640,1280\) ms [23]. To analyze the performance of the proposed scheme, we take Beta distribution as arrival distribution which can be written as follows:  
\[f_{T}(t)=\frac{t^{\alpha-1}(T_{A}-t)^{\beta-1}}{T_{A}^{\alpha+\beta-1}B(\alpha,\beta)}, \tag{26}\]  
where \(B(\alpha,\beta)\) denotes the Beta function \(\int_{0}^{1}t^{\alpha-1}(1-t)^{\beta-1}dt\), \(\alpha=3\), and \(\beta=4\)[16]. \(T_{A}\) is the time in which all the devices arrive in the system, and its value is assumed to be 500 ms. The number of devices arriving in one time slot can be written as:  
\[\lambda_{i}=U\int_{t_{i-1}}^{t_{i}}f_{T}(t)dt,~{}~{}~{}~{}~{}i=1,2,\cdots,T_{A} \tag{27}\]  
This distribution is considered to imitate the bursty nature of the arrival pattern which is normally the situation for IoT devices. In Figure 4, we plot TST versus number of preambles for \(U\) = 10,000 using ACB, EAB and proposed CAB schemes. For the proposed CAB scheme, we have plotted the scenarios depicted in Algorithms 1 and 2. Generally we can foresee that TST increases with increase in \(U\) and decreases with increase in \(R\) which is obvious because large \(R\) means large pool of choices for the devices. We see that ACB exhibits the least TST while EAB shows the largest value of TST. The proposed CAB shows less TST than EAB because it does not uses DTX whereas it shows more TST than ACB because the devices need to wait for their classes to be declared unbarred. Moreover, we see that the CAB plot shown by Algorithms 1 and 2 are quite close to each other. This shows that our estimation for the backlog closely follows the actual number of backlogged devices. We also included the simulations of the techniques previously presented in [11; 12; 13]. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Total Number of Devices (\(U\)) & 10,000, 30,000 \\ No. of Preambles (\(R\)) & 5 to 50 \\ Periodicity of bitmap broadcast (\(T_{P}\)) & 320 ms \\ Performance Metrics & Access Delay, Total Service Time \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance Parameters. In Figure 5, we plot the transmission probability for CAB in case of Algorithms 1 and 2. For ACB, at the start, the number of devices are less and the corresponding transmission probability is close to 1. As the number of devices starts increasing, the transmission probability starts decreasing. After the devices get success, the number of devices decreases again thus increasing the transmission probability. But for CAB, the transmission probability decreases after sometime and then starts increasing before coming down again.