Validation and Analysis of the Model - Queuing Analysis of IEEE 802.11s for a Specific Rate Reg

5.2 Queuing Analysis of IEEE 802.11s for a Specific Rate Region

5.2.3 Validation and Analysis of the Model

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End-to-end Delay (ms)

Distance (feet) Theory, min, 6 Mbps Simulation, min, 6 Mbps Theory, max, 6 Mbps Simulation, max, 6 Mbps Simulation, Confidence Factor

Figure 5.3: Theory versus Simulation (6 Mbps)

Replacing the value of Λi using Lemma 5.3 and rearranging, Λ_e < ϕrB

L(1 +κ_rA)

This leads to equation (5.20).

For a data rate r, equation (5.19) shows the effect of the selected data rate on the end-to-end delay based on the number of hops and the interference information, according to the transmission ranges of the selected data rates. Similarly equation (5.20) shows the effect of the selected data rate on maximum achievable throughput. The rate- hop-interference trade-off has been shown in the next subsection using numerical results obtained from the theoretical analysis.

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End-to-end Delay (ms)

Distance (feet) Theory, min, 24 Mbps Simulation, min, 24 Mbps Theory, max, 24 Mbps Simulation, max, 24 Mbps Simulation, Confidence Factor

Figure 5.4: Theory versus Simulation (24 Mbps)

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End-to-end Delay (ms)

Distance (feet) Theory, min, 54 Mbps Simulation, min, 54 Mbps Theory, max, 54 Mbps Simulation, max, 54 Mbps Simulation, Confidence Factor

Figure 5.5: Theory versus Simulation (54 Mbps) Model Validation

To validate the proposed theoretical model, the results obtained from the theoretical analysis are compared with the simulation results from Qualnet 5.0.1 [71] network simulator framework. Qualnet-5.0.1 has in-built support for IEEE 802.11s mesh networking. 802.11g rate region is used for simulation purpose that supports eight different data rates as shown in Table 5.1. Two different network setups have been considered - first a network with

the maximum interference, and second a network with the minimum interference. For maximum interference network, 144 mesh STAs are placed in an approximate hexagonal structure (similar to the scenario considered in the theoretical analysis), where all the mesh STAs have data to transmit, and they content for reserving channels in the DTIM interval. The mesh gate is considered at one corner of the arena. The position of the originator mesh STA is shifted gradually through the diagonal of the arena to increase the Euclidean distance between the originator mesh STA and the mesh gate. The communication distance for different data rates are considered according to the CISCO white paper [121]. On the other hand, for minimum interference network, the communication is only between the packet originator and the mesh gate, and the interference is limited only among the mesh STAs in the data forwarding path. The data generation rate at the clients have been taken as 512 Kbps, and on average 10 clients are associated with every mesh STA. The DTIM interval is taken as 200 ms. Every simulation scenario is executed for 10 times with different seed values, and average is taken to plot the graphs.

The confidence factor, determines as the variance of the results obtained in different simulation trials with different seed values, have been shown in the figures using a vertical line.

Fig. 5.3 to Fig. 5.5 show the comparison between the theoretical results and the simulation results for three different data rates - the minimum data rate (6 Mbps), the maximum data rate (54 Mbps) and an intermediate data rate (24 Mbps). In the figures ‘max’ denotes the maximum interference scenario, and ‘min’ denotes the minimum interference scenario.

It can be seen from the figures that the results obtained from the theoretical model are similar with the simulation results for all the three data rates. It can be noted that the throughput value is not compared with the simulation results, as the theoretical analysis reveals the maximum achievable throughput based on the bound on end-to-end delay.

However, it has been observed from simulation traces that the actual network throughput for different data rates follows a similar pattern as obtained from the theoretical bound.

Nevertheless, the simulation values are less than their theoretical counterpart, as a result of compulsory physical and MAC layer signaling overhead.

Model Analysis

Similar scenarios, as described earlier, have been used to analyze the results obtained from the theoretical model. Fig. 5.6 shows the end-to-end delay for different 802.11g data rates in the minimum interference scenario of IEEE 802.11s mesh networking technology.

Similarly, Fig. 5.7 shows the end-to-end delay for different data rates in the maximum interference scenario. In the minimum interference scenario, 54 Mbps and 48 Mbps perform

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End-to-end Delay (ms)

Distance (feet) Data Rate = 6 Mbps Data Rate = 9 Mbps Data Rate = 12 Mbps Data Rate = 18 Mbps Data Rate = 24 Mbps Data Rate = 36 Mbps Data Rate = 48 Mbps Data Rate = 54 Mbps

Figure 5.6: Delay at minimum interference

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End-to-end Delay (ms)

Figure 5.7: Delay at maximum interference

better than other data rates when the distance between the originator mesh STA and the mesh gate is less than 100 feet. At 100 feet distance, 36 Mbps provides less end-to-end delay. The trend changes again after 100 feet distance. This time 24 Mbps achieves better result than other data rates. Proceeding this way, it can be observed that 6 Mbps performs better than all other high data rates when the distance is 300 feet. This variation of end- to-end delay is the result of the different number of hops between the end pair for different

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Average Number of Hops

Figure 5.8: Data rate vs number of hops

data rates. Fig. 5.8 shows the average number of hops between the originator mesh STA and the mesh gate for different data rates. When the distance is less that 100 feet, the mesh gate can be reached from the originator mesh STA using single hop only. Therefore 54 Mbps performs better than all other rates. However, at 100 feet distance, 54 Mbps and 48 Mbps require two hops to transmit the packet, whereas the packet can be forwarded using single hop if 36 Mbps data rate is used. As per-hop processing delay increases with the increase in number of hops, 36 Mbps achieves less end-to-end delay than other rates in this case. Similarly at 300 feet distance, 6 Mbps requires only single hop to transmit the packets, whereas 54 Mbps requires four hops. At this stage 6 Mbps performs better because the originator mesh STA can directly communicate with the mesh gate, whereas 9 Mbps and 12 Mbps require two hops and rest other high rates require even more number of hops.

The minimum interference scenario clearly shows the effect of the selected data rate on network performance based on number of hops required to transmit the packets. However, the interference is limited only among the previous hop and the next hop forwarder mesh STAs for this scenario. Fig. 5.7 shows the effect of interference over the performance for different data rates, using the maximum interference scenario. In this scenario, all the mesh STAs in the 12×12 grid topology have data to transmit. It can be seen from the figure that at maximum interference scenario, 54 Mbps functions better than all other low rates, irrespective of the hop distance. Fig. 5.9 shows average number of active neighbors

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Number of Interfering Neighbors

Data Rate (Mbps)

Figure 5.9: Data rate vs interfering neighbors

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Figure 5.10: Throughput at minimum interference

at different data rates that interfere with the transmission of a mesh STA. The figure shows that the average number of interfering mesh STAs increases exponentially as the data rate decreases. High interference reduces the chance of obtaining MCCAOPs in the DTIM interval during the channel reservation procedure. Therefore, average channel reservation delay increases significantly, that suppresses the advantages obtained by reducing number of hops using low data rates.

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Throughput (bps)

Figure 5.11: Throughput at maximum interference

Fig. 5.10 shows average throughput for the minimum interference scenario. In the minimum interference scenario, the rate-hop-interference trade-off significantly impacts maximum achievable throughput at the mesh STAs. Similar to the earlier cases, the data rate that provides maximum throughput changes with the change in the distance between the originator mesh STA and the mesh gate. Nevertheless, 54 Mbps data rate always provides maximum throughput in case of maximum interference scenario, as shown in Fig. 5.11.

In the real life community and commodity wireless mesh networks, the number of interfering neighbors changes with time, based on the number of associated clients and their individual traffic demands. Low data rates may be selected when number of active mesh STAs in the neighborhood is less, to reduce the number of hops between end-to- end communication pairs. On the contrary, high data rates should be selected when interference level is more. This rate-hop-interference trade-off is explored in this chapter to enhance the basic IEEE 802.11s mesh protocols to support multi-rate functionality, as discussed in the next section.

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