# Escalator: An Autonomous Scheduling Scheme for Convergecast in TSCH
## 6 Evaluation
### Simulation Results  
Figure 11 shows the end-to-end delay per packet delivery hop counts in packet transmission in the simulation. In the simulation, the maximum number of packet delivery hop counts is five hops in the \(4\times 4\) grid and eight hops in the \(6\times 6\) grid. Figure 10(a),b shows the end-to-end delay when the interval of packet transmission is 20 s and 5 s on the \(4\times 4\) grid. 6 TiSCH-minimal and Orchestra increase the end-to-end delay as node traffic increases. In contrast, the end-to-end delay of Escalator can be seen to remain constant with increasing traffic of the node.  
Figure 10(c),d shows the end-to-end delay when the interval of packet transmission is 20 s and 5 s in the \(6\times 6\) grid. In Figure 10(c),d, we can see results similar to those of the testbed for the end-to-end delay. 6 TiSCH-minimal shows that the end-to-end delay increases as the node traffic increases due to contention. Orchestra provides a conflict-free schedule, but does not provide enough timeslots for the number of child nodes and traffic growth of the node since only one packet per slotframe cycle can be sent to the parent. As a result, Orchestra shows an increase in the end-to-end delay as the number of  
Figure 11: End-to-end delay per packet delivery hops in the simulation: (**a**) a packet transmission interval of 20 s on the \(4\times 4\) grid; (**b**) a packet transmission interval of 5 s on the \(4\times 4\) grid; (**c**) a packet transmission interval of 20 s on the \(6\times 6\) grid; (**d**) a packet transmission interval of 5 s on the \(6\times 6\) grid.  
network nodes and the traffic of nodes increase. Escalator shows that the end-to-end delay remains constant even as the number of nodes in the network increases and the traffic of the nodes increases.  
Figure 11(a) shows the PDR when the interval of packet transmission is 20 s and 5 s in the \(4\times 4\) grid. If the interval of packet transmission of the \(4\times 4\) grid is 20 s, the PDR of _Orchestra37_ and _Orchestra53_ is 100%. However, if the interval of packet transmission in the \(4\times 4\) grid is 5 s, the PDR of _Orchestra37_ and _Orchestra53_ is reduced to 74% and 76%, respectively. Orchestra cannot process the increased traffic of the nodes, resulting in packet loss due to the packets accumulating in the node's buffer.  
Figure 11(b) shows the PDR in the \(6\times 6\) grid. In this case, a packet drop occurs not only in Orchestra, but also in 6 TiSCH-minimal. In contrast, Escalator shows a PDR of 100% even when the number of nodes in the network and the traffic of the nodes increase. Escalator can transmit application traffic within a limited end-to-end delay regardless of the number of transmitted packets within the available bandwidth.  
Table 2 shows the average and maximum duty cycle of the nodes measured in the simulation. 6 TiSCH-minimal shows an average duty cycle of 2.4% under all simulation conditions. This is because all the nodes in 6 TiSCH-minimal use the same schedule of the shared communication method regardless of the network condition and the traffic requirement. The average duty cycle of Orchestra increased from 0.89%-1.31% depending on the number of nodes and packet transmission period. The average duty cycle of Escalator increased from 0.78%-1.54%. Although Escalator shows better performance in the packet delivery ratio and the end-to-end delay than Orchestra, the average duty cycle does not increase significantly.  
The maximum duty cycle of Escalator in the simulation increases to 6.85%. We can see in Figure 13 that the duty cycle increase for the number of routing entries in the Escalator node is greater than that of Orchestra. In Escalator, the amount of scheduled timeslot increases in proportion to the number of routing entries. Therefore, the number of routing entries increases with the node closer to the sink, which increases the use of the radio to transmit packets received from the child nodes to the sink.  
Figure 12: PDR per packet transmission interval in the simulation.