Analytical Study on the Effects from Data Rate and Neighbor
4.2 Analytical Study on the Network Performance
The network performance will be analyzed in this section by employing both the analytical and the simulation results. The performance will be evaluated by considering the packet delivery ratio versus both the data rate and the neighbor interference. Table 4.1 summarizes the parameters adopted from the DSSS system for both the analytical and the simulation results. The packet delivery ratio R computed from (4.20) will be utilized as the analytical results; while the simulation results are conducted via the Network Simulator (ns-2, [21]).
Table 4.1: Analytical and Simulation Parameters Adopted from the DSSS System
Parameter Type Parameter Value
PHY header 128 bits
MAC header 272 bits
RTS Frame Size 160 bits + PHY header CTS Frame Size 112 bits + PHY header ACK Frame Size 112 bits + PHY header Payload Size of the Data Packet 1024×8 bits
Maximum Backoff Stages (m) 5 Minimum Contention Window (W ) 32
Channel Bit Rate 1 Mbit/s
Slot Time (σ) 20 µs
Propagation Delay (Tδ) 1 µs
TSIF S 10 µs
TDIF S 50 µs
In order to illustrate that one transmission pair is interfered by another α pairs of packet delivery, the simulations are performed with (α + 1) pairs of SNs for point-to-point packet delivery within the same transmission range.
Before exploring the performance on the packet delivery ratio R, an important parameter (i.e. the service time Tsv from (4.14)) will be investigated first. Figs. 4.2 and 4.3 show the comparison of Tsv versus the application layer data rate (λ) and the number of interfering neighbors (α). As shown in both plots with lower data rate and smaller number of interfering neighbors, the value of service time (i.e. Tsv ≈ 0.01 sec) is observed to be similar to the successful transmission time Ts = 0.0094 sec, which can be calculated from (4.11) via the data from Table I. The results indicate that there is almost no packet collision under these situations, which make Tsv similar to Ts without the necessity for considering the backoff time in (4.14). In most of the cases, the service time is perceived to significantly increase from a Critical Point (CP) either the data rate or the number of the interfering neighbors is augmented. The CP corresponds to the location of the channel capacity as C , 1/Tsv, which is defined as the maximum services of the packets per unit time. On the other hand, the total incoming packets per unit time obtained from the interfering neighbor SNs are computed as T = λ α. The reason for the drastic incline in both Figs. 4.2 and 4.3 is mainly caused by
2 4 6 8 10 12 14 0.005
0.01 0.015 0.02 0.025 0.03 0.035 0.04
λ (packets/sec) Tsv(sec)
α=6 α=9 α=12
Figure 4.2: Service Time (Tsv) vs. Data Rate (λ)
2 4 6 8 10 12 14 16
0.005 0.01 0.015 0.02 0.025 0.03 0.035
α Tsv (sec)
λ=5 λ=7.5 λ=10
Figure 4.3: Service Time (Tsv) vs. Number of Interfering Neighbors (α)
the cases that the total interfering effect T = λ α is around the same value or larger than the channel capacity C. Due to the system saturation, the service time will be significantly increased since the additional time is required for packet retransmission and collision. This assertion can also be validated by observing the CPs from both of Figs. 4.2 and 4.3. The CP for α = 12 and λ = 7.5 (such that T = λ α = 90) corresponds to the channel capacity calculated as C = 91.07; and the CP for α = 9 and λ = 10 (such that T = 90) corresponds to C = 91.87. It is noted that C = 1/Tsv, where the average service time Tsv is computed from (4.14). It can be perceived that both T and C share the similar values in these cases, which validate the existence of the CP where the system saturation occurs.
Fig. 4.4 shows the performance comparison for packet delivery ratio versus the application layer data rates under α = 6, 9, and 12; while Fig. 4.5 illustrates the comparison for packet delivery ratio versus different numbers of interfering neighbors with λ = 5, 7.5, and 10. From both plots, it can be observed that the analytical results is consistent with that acquired from the simulations, which validate the correctness of the derived analytical model. Similar to the observations from Figs. 4.2 and 4.3, the performance degradation is perceived from the location of the CP either the data rate or the number of the interfering neighbors is increased.
As T < C, comparably higher packet delivery ratio R can be achieved since most of the packets can be successfully delivered. On the other hand, as T reaches or exceeds the channel capacity C, some of the packets will not be transmitted due to the system saturation that causes the rapid decreases in the packet delivery ratio.
The above observations support the effectiveness of the proposed CNAR protocol with efficient usage of the system resources. The CNAR algorithm is designed to cognitively select the routing path, which inherently possesses smaller probability for packet collision. The total interfering effect from the neighbor SNs can be diminished such that the SNs within the route will not reach their channel capacities C. The proposed CNAR scheme can therefore conduct data delivery under better channel quality without wasting the limited system resources.
Moreover, the performance study in this chapter only consider the localized effect for packet transmission with infinite data queue in each SN. The system saturation problem can become
more severe by considering both (i) the hidden terminal problem and (ii) the finite queueing effect under the multi-hop data delivery. It is noted that the hidden terminal problem will further cause the interference from the tow-hop away neighbor SNs. The substantial benefits of using the proposed CNAR algorithm can become obvious under such realistic multi-hop environments. In the next chapter, the CNAR scheme will be compared with other existing protocols via simulations which emulate the environments of the WSNs.
2 4 6 8 10 12 14
Figure 4.4: Packet Delivery Ratio vs. Data Rate λ (Solid Lines: Analytical Results; Dashed Lines: Simulation Results)
Figure 4.5: Packet Delivery Ratio vs. Number of Interfering Neighbors α (Solid Lines: Ana-lytical Results; Dashed Lines: Simulation Results)