# No Free Lunch--Characterizing the Performance of 6 TiSCH When Using Different Physical Layers
## 6 Experimental Results
### Network Formation Time  
The network formation time is measured between the moment the DAG root is selected, and the moment the DAG root has received a data packet from each more. The network formation process encompasses the time it takes for a motes to synchronize to the network, the time it takes for it to complete a security handshake and the time it takes for it to acquire a rank. It is the time a user would have to wait for their network to be fully functional.  
This is a worst case setup, as we turn on all the motes first, and the gateway last. Per the 6 TiSCH standard, traffic generated by the motes during their secure handshake uses shared cells. All motes trying to join approximately at the same time will cause a lot of contention of these shared cells, increasing the network formation time.  
Figure 4 shows that the FSK 868 MHz OFDM 868 MHz, and O-QPSK 2.4 GHz network is 90%-formed in 7, 9, and 11 min, respectively. The higher the link budget (i.e., the longer the range), the faster the network forms.  
To understand the impact of PHY on network formation time, we plotted in Figure 5 the number of neighbors evolving over time. Because of its long range, a mote using FSK 868 MHz tends to discover more nodes, faster than a node using O-QPSK 2.4 GHz. This observation exactly follows the link budget from Table 1. Discovering many neighbors is helpful in two ways. First, it allows a mote to quickly hear a node that is already part of the network, hence to synchronize quickly. Second, it gives a mote a higher probability of joining through a neighbor closer to the root; this decreases the number of hops necessary for joining.  
However, having a longer range increases the risk of neighbor table overflow. For example, if the neighbor table can hold up to 10 entries, what is the appropriate behavior when a mote hears 15 other motes? The challenge is that, without having another mote in its neighbor table, a mote cannot keep statistics to elect the \"best\" neighbors, and has to to make decisions on partial data, such as  
Figure 4: The network tends to form faster when using a longer-range PHY.  
a single RSSI value. We note that none of the standards makes clear recommendation for neighbor table grooming.  
Figure 6 gives some insights into the network formation itself. It plots how the rank reported by the motes evolves over time. Per the RPL and Minimal Scheduling Function standards [17; 31], a mote's rank is computed using Equation (1), where \(numTx\) and \(numAck\) are counters of the number of transmission attempts and transmission successes to a neighbor, respectively. \(minHopIncrease=256\) is the rank increase if the link to the mote's routing parent is ideal. If that link becomes lossy (i.e., \(numTx/numAck>1\)), the \"cost\" associated with the link increases, and the mote's rank increases accordingly.  
\[rank=\left((3\cdot\frac{numTx}{numAck})-2\right)-minHopIncrease. \tag{1}\]  
The first portion of Figure 6 (\(t<50\) min) shows that the nodes start by having a very high rank. This is caused by two phenomena, combined. First, a mote may not discover its neighbor with the lowest rank immediately, and instead join with a artificially high rank; this resolves over time as the network stabilizes by becoming shallower. Second, all motes attempting to join create contention on the minimal cell, causing transmissions to fail, \(numTx/numAck\) to increase, and the motes' rank to increase. This, again, resolves as the network stabilizes by having less contention on the shared cells. These two phenomena compete--the longer the PHY range, the shallower the initial network, but the higher the contention. Figure 6 shows that, once the network has stabilized, it tends to be shallower (smaller DAG rank) when using a longer-range PHY.  
Figure 5: Motes discover more neighbors faster when using a longer-range PHY.