# 2 CA-R2: A Hybrid MAC Protocol for Machine-Type Communications
## 6 Simulation Experiments and Results
### Experiments with Poisson Traffic  
A final set of measurements was taken to compare 2 CA-R\({}^{2}\) and DCF under saturation-free channel conditions. To this end, each station in the simulation generated packets according to a Poisson process with parameter \(\lambda=2.5\) packets per second. This value was selected to maintain the total network traffic below the channel data rate, even in the case with the largest number of stations in the system. At the same time, this value allowed us to observe the system response under a wide range of conditions of channel utilization when the number of stations in the network was varied. In addition, each station was configured with a maximum queue size of five packets, which proved to be large enough to reduce buffer overflow to negligible levels. In this set of experiments, an error-free channel was assumed. The performance of the mechanisms was measured as indicated by (9), that is, in terms of the delay that a packet experiences measured from its generation time to the instant when the transmitter obtains a notification about the successful reception. Note that with greedy traffic generation, this delay is only due to channel access since a new packet is generated only if the previous one has been delivered so that there is no queue buildup at the transmitter. In contrast, with Poisson traffic, the packet generation and transmission are independent processes. Therefore, a new packet can be generated even if the previous one has not been delivered, thus leading to possible queue buildup. Therefore, in this case, part of the access delay is due to queuing delay. Figure 14: Mean delivery time of a complete set of packets  
As in the previous simulation experiments, each case was simulated 10 times in order to obtain mean values and provide their confidence intervals with a 95% confidence level. Figure 15 shows the corresponding results for access delay. It can be seen in the figure that under the described conditions, the performance of the 2 CA-R\({}^{2}\) mechanism is superior to the one achieved by DCF, a situation that becomes more noticeable when the number of stations is increased. In order to explain this result, it is convenient to consider the queuing delay for each protocol. Figure 16 shows that the queuing delay when using DCF increases as the number of devices increases. In fact, in the worst case, i.e., when there are 256 devices in the scenario, there is on average about 3 ms of queuing delay. In turn, the queuing delay when using the 2 CA-R\({}^{2}\) protocol is very close to 0 regardless of the increase in the number of devices. Thus, it is noticeable that the mean access delay for 2 CA-R\({}^{2}\) is entirely due to the collision resolution time, unlike DCF where this delay has a significant contribution to the mean access delay, a situation that is exacerbated by increasing the number of devices. Figure 16: Queuing delay comparison between 2 CA-R\({}^{2}\) and DCF with Poisson traffic. Figure 15: Access delay comparison between 2 CA-R\({}^{2}\) and DCF with Poisson traffic. It is important to emphasize that under these traffic conditions, not all stations participated in the initial collision of each CRI of 2 CA-R\({}^{2}\). This is due to the fact that the number of active stations in different CRIs varied due to the bursty nature of the source. Thus, one may think that estimating the value of \(N\) in the same way as before would not be adequate (i.e., making it equal to the number of successful transmissions in the previous CRI). However, Table 6 summarizes some results that can be used to assess the suitability of this strategy. These results are the average fraction of CRIs starting with one, two, and more than two contending devices. The last column in Table 6 shows the channel utilization achieved by the network in each case. As can be seen, in this scenario, a high percentage of CRIs of the 2 CA-R\({}^{2}\) started with only one device trying to transmit (therefore, they were granted immediate access).