## 6 Performance Evaluation
### Network Throughput  
In this section, we compare the communication schedule and network throughput of D-MSR with those of WirelessHART. Figures 21 and 22 show samples of constructed schedules for 29 end-to-end connections with a publishing period of two seconds in WirelessHART and D-MSR respectively. In these matrices, the communication schedule reserved for transmitting either management traffic or sensor data are shown. Through different colors in each cell in the matrix, the number of edges re-using that particular timeslot-channel cell are shown. Figure 21 shows the global matrix (the combination of superframes with a size of 25, 200, 400 and 800 timeslots) of the allocated timeslot-channel cells by the WirelessHART network manager. In this scenario, the network manager  
Figure 19: End-to-end connection between nodes 37 and 45 in WirelessHART (**a**) and D-MSR (**b**).  
Figure 20: Average end-to-end hop distance (**a**) and delay (**b**) (D-MSR _vs._ WirelessHART).  
schedules each communication in an interference-free cell and avoids the spatial reuse of any cell between different edges, except for during the advertisement period. Figure 22 shows the combination of all schedule-matrices in each node in the network, which represents the global schedule-matrix (the combination of superframes with a size of 25 and 200 timeslots) in D-MSR. The D-MSR matrix looks more dense with more unused cells. There are two reasons for this. Firstly, in D-MSR the nodes just keep track of current cell usage in their own two-hop neighborhood. This means that reuse of the same cell in different two-hop neighborhoods could occur. As is shown in Figure 22, a given cell may be reused by 10 edges in different neighborhoods. Secondly, since more edges are considered in the uplink and downlink graph, more communication schedules are constructed in the WirelessHART network.  
In addition, we evaluate the network throughput of both D-MSR and WirelessHART in different network densities. We gradually increase the transmission range of nodes in five steps from 15 to 25 meters to provide a different network density from seven to 21 neighbors in the one-hop neighborhood. For each network density, to evaluate the reachable network throughput, we try to establish the maximum number of end-to-end connections between field devices. As the network density increases, more bottlenecks are observed and less end-to-end connections can be established. In D-MSR more end-to-end connections can be established thanks to the RPL in the routing layer which does not need to route the traffic through the access points. On the other hand, the implemented WirelessHART passes all the traffic through the gateway. Figure 23 shows the network throughput: the number of transmitted packets in the whole network per second. As the network density is increased, the network throughput for both D-MSR and WirelessHART decreases, but less severely so for WirelessHART.  
The spatial reuse of communication resources provides more network throughput for D-MSR than WirelessHART in the case of a sparse network. For example, when the number of neighbors in the one-hop neighborhood is seven, the network throughput is around 150% higher for D-MSR than WirelessHART. However, as the network becomes more dense, less disjoint two-hop neighborhoods can be observed. Consequently, less communication resources can be reused, which results in less network throughput difference. The communication schedule of D-MSR and WirelessHART for each of those five densities are shown in the Appendix. In the case of D-MSR, the communication schedules become more sparse and more channels are allocated to the communication schedules, as network density increases. In summary, the spatial reuse of communication resources in D-MSR improves the throughput in the large-scale network.  
Figure 23: Network throughput (D-MSR _vs._ WirelessHART).  
Figure 22: The combination of schedule-matrix of the current slot/channel usage for the sample D-MSR network.