## 5 Performance Evaluation
### Performance Analysis
However, a significant disadvantage of fixed preamble allocation with dynamic \(p_{ACB}\) scheme is that when the arrival rate of devices is relatively small, there will be a lot of idle preambles, i.e., preambles that are selected by no devices. As has been clearly shown in Figure 10, the redundancy of allocated preambles will obviously reduce the preamble utilization rate. With a larger value of the arrival rate, more devices will attempt to access the network, leading to an increase of average preamble utilization rate. When the number of available preamble resources are insufficient for active devices, the utilization rate remains at peak value. Average access delays for DS devices obtained by scheme A and scheme C are relatively longer. In the operations of scheme A and scheme C, as \(p_{ACB}\) is set to a fixed value 0.2, more devices will be blocked despite insufficient amount of RA resources. The improper access barring leads to an increase of average access delay. As the number of allocated preambles in scheme A is fixed as 54, active devices in scheme A have more preambles to consume than devices in scheme C. Therefore, average access delay of scheme A is shorter than that of scheme C. In these two schemes, when the number of active devices exceeds the maximum amount of available preamble resources, i.e., when the arrival rate of DS devices is larger than \(1.8\times 10^{3}\), the fixed \(p_{ACB}\) will lead to a longer access delay and a drop of preamble utilization rate due to the neglect of load variation. Compared with scheme A, the advantage of scheme C lies in it can dynamically adjust \(L_{DS}\) based on load situation. Thus, it can maintain high preamble utilization rate when there are sufficient preamble resources. Similar as scheme B, the preamble utilization rate will gradually increase with the increase of arrival rate. The performance curves of the D-ACB scheme is the most similar to that of our proposed scheme. Among pre-existing methods, D-ACB has the best delay performance. When comparing our proposed scheme with D-ACB scheme, the delay performance of our scheme is approximately 5 ms, i.e., 23%, better than D-ACB scheme. By comparing with the straight line of 22 ms, we can find that our scheme can effectively meet the delay requirement in a wide range of arrival rate. From the perspective of preamble utilization rate, our scheme is about one percentage point less than D-ACB scheme. Nevertheless, compared to the promotion of delay performance, the little drop of preamble utilization rate of our scheme is insignificant. It is worth noting that the comprehensive performances of our scheme and D-ACB scheme are better than most other schemes. Figure 11 presents the number of preambles remained for DT devices, i.e., for Pool 2. We can observe that with the increase of the arrival rate of DS devices, average number of preambles remained for DT devices of scheme C, scheme D and our proposed scheme will gradually drop to a minimum value 10, as we have set the maximum number of available preambles for DS devices \(L_{avail\_DS}\) to 54. The number of preambles remained for DT devices of scheme A and scheme B both maintain the value 10 for the reason that the number of preambles allocated to DS devices is set to a fixed value 54. From  
the curves of this figure, we can derive that our proposed scheme can save as much preambles as possible for DT devices for the reason that our scheme has considered the preamble utilization rate for DS devices. The analytical results present that our proposed scheme is better than scheme A and B in terms of the number of preambles remained for DT devices. When compared with D-ACB, our scheme exhibits almost the same performance with it for the reason that D-ACB has also paid attention to increase the preamble utilization rate. Our proposed scheme is slightly better than dynamic \(L_{DS}\) with fixed \(p_{ACB}\) scheme in terms of preambles remained for DT devices.