## 4 Performance Evaluation
### Simulation Results
In addition, there is no difference on the control overhead between streams because control message in the proposed scheme consists of path search and reporting. This implies that the performance gap between two protocols is observed by effectiveness of the adaptive path selection and traffic shaping. Specially, traffic shaping plays a great role in strict requirement by providing several alternative path and (_m,k_)-firm set. We evaluated the performance when the network is congested by measuring the SDSR of the application as a function of the amount of background traffic. The results are plotted in Figures 5 and 6 for different (_m,k_)-firm sessions and applied schemes. For instance, 56 AG represents (5,6)-firm stream session supported by MK-AG. The results of this evaluation exhibited a similar pattern as a function of different requirements. In all cases, the SDSR decreases as the amount of background traffic increases. The increased background traffic caused the network to become congested; therefore, more packets missed the deadline or were discarded. As compared to the MK-AG protocol, the proposed scheme is robust against congestion; consequently, adaptive path selection and traffic adjustment contribute to  
Figure 4: SDSR for (2,5)-firm application. finding alternative paths. On the other hand, even though MK-AG takes congestion into account by considering the link delivery ratio, it does not compensate for lost packets as a result of congestion. Moreover, the static comparison matrix does not allow the source to change the path accordingly. As compared to light background traffic condition in Figures 3 and 4, the high impact of control overhead is observed in Figures 5 and 6. This is caused by the delay of control message at intermediate node as well as packet loss. These two features can lead to prevent establishing multiple paths and deliver the DBP values in early time. As a result, path selection and traffic shaping can be perform later than previous case, that is, light traffic condition. Thus, more packets missed deadline so lower SDSR is measured. This negative effect is observed in strict (_m,k_)-firm requirement more frequently. In addition to conducting a comparative study with the existing scheme, we conducted the simulation by varying the network environment and parameters in the proposed scheme. Figure 5: SDSR in (2,3)-firm application. Figure 6: SDSR in (2,5)-firm application. Figure 7 shows the SDSR of the (2,3)-firm application as a function of the number of nodes. These results show that an increase in the number of nodes contributes to improving the SDSR. Because the node density is related to the number of paths, a large number of nodes enable more paths to be established between nodes. This means that the options of load balancing to prevent congestion and increased opportunities to change the path become available. Based on this analysis, great improvement is observed when using a more strict requirement such as a (5,6)-firm stream. The last simulation result in Figure 8 shows the impact of the number of (\(m\),\(k\))-firm sets on each session. We measured the SDSR by varying the number of sets from 2 to 4 in the adaptive traffic handling procedure in Algorithm 2. Higher SDSR is observed for a larger number of sets whereas the lowest values are measured for two sets. Because the larger number of levels provides a greater possibility to maintain a positive DBP value, enhanced SDSR values are obtained in all cases. In particular, a stricter (\(m\),\(k\))-firm streams benefits from a large number of sets. Figure 8: SDSR in (2,3)-firm application as a function of (\(m\),\(k\))-firm sets. Figure 7: SDSR in (2,3)-firm application as a function of node density. We measure the network lifetime of the proposed and existing scheme in two separate (\(m\),\(k\))-firm applications in Figures 9 and 10. In this paper, network lifetime is defined as elapsed time until the first sensor node or group of sensor nodes in the network runs out of energy.