# Parent and PHY Selection in Slot Bonding IEEE 802.15.4e TSCH Networks
## 5 Evaluation
### Testbed Results
#### 5.3.1 \(\delta\) Selection  
First, the optimal \(\delta\) values for the heuristic were determined, using the monitored link reliability values of the testbed. The expected number of delivered packets calculation was used, as described in the slot bonding problem formulation, to calculate the expected PDR values [7]. Figure 11 shows the comparison between different \(\delta\) values, for the two network scenarios as discussed in Section 5.1.2, each for the two different slotframe lengths, 261 ms and 423 ms. It is clear from the results that the 261 ms slotframe was saturated, with all average PDR values being below 1. For scenario 1, with both the 261 ms and the 423 ms slotframes, the best performing \(\delta\) was 0.6 with the PDRs being 0.86 and 0.97, while the PDRs of the GA were 0.91 and 0.99. Similar to the simulator results, the heuristic found the best trade-off between using fast PHYs with shorter bonded slots and lower reliability values when \(\delta=0.6\). When \(\delta>0.6\), the lower reliability actually started deteriorating the overall PDR. The average observed deviation in PDR values between the heuristic and its near-optimal counterpart was 0.05 and the maximum of all deviations was 0.37 in scenario 1, when including both slotframe sizes and all \(\delta\) values. When only taking into account \(\delta=0.6\), the average observed difference was 0.04 and the maximum was 0.11. For scenario 2, the heuristic actually performs best when \(\delta=0.8\) with the average PDRs being 0.93 and 0.98 compared to the 0.96 and 1.0 PDRs of the GA. So again, the performance of the heuristic is very close to that of the centralized GA scheduler. For this scenario, the average deviation in PDR values between the heuristic and its near-optimal counterpart was 0.03 and the maximum of all deviations was 0.18, when including both slotframe sizes and all \(\delta\) values. When only looking at \(\delta=0.8\), the average observed difference was 0.02 and the maximum was 0.09. The results show that the optimal \(\delta\) was different for scenario 1 (i.e., \(\delta=0.6\)) and scenario 2 (i.e., \(\delta=0.8\)) (although the differences between the PDR results were small for both \(\delta\) values in both scenarios). This is explained by the fact that the enabled 1000 kbps PHY links in scenario 1 showed lower link reliability values, when compared to the values of the enabled links in scenario 2 (as explained in Section 5.1.2, a random subset of the 1000 kbps links was disabled in each scenario). Therefore, in scenario 1, a \(\delta>0.6\) affects the PDR results more severely than in scenario 2 as it introduces less reliable links in the topology. Figure 12 shows the average number of times per iteration each PHY was used for a link for the GA scheduler and the heuristic with increasing \(\delta\) values for scenario 2 for both slotframe lengths. The PHY allocations of scenario 1 are not shown as these were similar to those of scenario 2. Only links of nodes for which a packet could reach the root (i.e., there is at least one allocated slot for every link along the path towards the root) are shown. While the heuristic clearly prefers the faster 1000 kbps PHY (i.e., if the link is reliable enough, as defined in Algorithm 1), the GA also seems to focus on allocating 50 kbps PHYs. In the case of the heuristic, when \(\delta\) increases, the number of 1000 kbps PHYs also increases and the number of used 50 kbps PHYs decreases. When comparing both slotframes, it is clear that for the longer slotframe length of 423 ms, it is possible to allocate more 50 kbps PHYs because there is more free space, leading to higher PDR values, as observed in Figure 11.  
The PHY allocation and theoretical PDR results show that the heuristic generally performs well in terms of PDR but that the optimal \(\delta\) value is dependent on the specific environment.