Simulation Analysis
4.4 The Impact of Buer Size
Table 4.8: Simulation parameters in 500000 time slot.
Parameter type Parameter value
Width of grid network × Height of grid network 10 × 10
Packet generating rate per node 0.0167, 0.0333, 0.00833 packet/time slot
Ran-MAC probability 0.1 packet/time slot
Buer size 10 ∼ 60 packets
Information pool size 100 ∼ 600 packets
Maximal retransmission time 5times
Maximal packet alive time 10time slots
Simulation duration 500000 time slots
Table 4.8 describes the simulation parameters in detail. Each experiment also runs on 50 tasks, and the results are averaged. In the section 4.4, each experiment with variable buer sizes runs at the packet generating rates. We analysis the impact of variable buer sizes on throughput and packet loss. To clearly know the impact of variable buer size, packet generating rates of 0.0167, 0.0333 and 0.00833 are selected to represent respectively the rise of throughput, the maximal throughput and the decline of throughput, each in turn representing high tra c load, middle tra c load, and low tra c load.
4.4.1 Packet Loss
Figure 4.7: Buer size v.s. Packet loss (at arrival 0.0333 packet/time slot)
0 20 40 60 80
Figure 4.8: Buer size v.s. Packet loss (at arrival 0.0167 packet/time slot)
0 20 40 60 80 0
5 10 15
x 104
Buffer size
Packet loss
XOR Unicast
Figure 4.9: Buer size v.s. Packet loss (at arrival 0.0083 packet/time slot).
Table 4.9: Decrease of packet loss by increase of per buer size.
Packet generating rate Buer size 10 ∼ 30 Buer size 30 ∼ 80
0.0083 - XOR 1241.2 19.38
0.0167 - XOR 2080.55 193.02
0.0333 - XOR 468.8 72.62
0.0083 - Unicast 1033.75 81.32
0.0167- Unicast 314.7 84.76
0.0333- Unicast −61.65 30.38
Figures 4.7, 4.8 and 4.9 show that packet loss decreases as buer size increases. Table 4.9 shows that using Unicast, the increase of per buer size from 10 ∼ 30 averagely reduces packet loss by 1033.75 and 314.7, respectively at packet generating rates of 0.0083 and 0.0167.
However, the buer size increased from 30 ∼ 80 averagely reduces packet loss by 81.32 and 84.76, respectively at packet generating rates of 0.0083 and 0.0167. We know that packet loss is improved by the increase of per buer size, much more by the increase from 10 ∼ 30 than by that from 30 ∼ 80 at packet generating rates of 0.0083 and 0.01667. Using the
XOR coding algorithm, Table 4.9 shows that the impact of the packet loss improved by increasing the buer size from10 ∼ 30 is more obvious than that improved by the increase from 30 ∼ 80. As the buer size exceeds 30, the decrease trend of packet loss slows down and ceases rapidly. Overall, no matter whether the XOR coding algorithm is utilized or not, this result suggests that the optimal buer size is 30, and it is concluded that packet loss is decreased by the increase of buer size.
4.4.2 Throughput
0 20 40 60 80
0 0.002 0.004 0.006 0.008 0.01 0.012
Buffer Size
Throughput
XOR Unicast
Figure 4.10: Buer size v.s. Throughput (with packet generating rate 0.0333)
Figures 4.10, 4.11 and 4.12 demonstrate that the throughput of the grid network increases along with buer size and increases faster from the buer size 10 ∼ 30 than that from the buer size 30 ∼ 80. With or without the XOR coding algorithm, as the previous subsection 4.4.1 mentioned, packet loss decreases faster from the buer size 10 ∼ 30 than that from the buer size 30 ∼ 80 (see Figures 4.7, 4.8 and 4.9). Thus, the throughput increases faster with the increase of per buer size from 10 ∼ 30 than with the increase of per buer size from 30 ∼ 80. Table 4.10 shows that, in the XOR coding algorithm, the increase of per buer size
0 20 40 60 80 0
0.002 0.004 0.006 0.008 0.01 0.012 0.014
Buffer Size
Throughput
XOR Unicast
Figure 4.11: Buer size v.s. Throughput (with packet generating rate 0.0167)
generating rates of 0.0083, 0.01667 and 0.0333. Moreover, with the increase of per buer size from 30 ∼ 80, throughput is improved by about 0.68%, 1.60%, and 0.79%, respectively at packet generating rates of 0.0083, 0.01667 and 0.0333. Although the buer size increases little from 10 ∼ 30, it enables the throughput to increase faster. Hence, throughput is also improved by the increase of per buer size from 10 ∼ 30 much more than by that from 30 ∼ 80. Overall, the throughput increases because of increase of the buer size with limited storage resource.
0 20 40 60 80 0
0.002 0.004 0.006 0.008 0.01
Buffer Size
Throughput
XOR Unicast
Figure 4.12: Buer size v.s. Throughput (with packet generating rate 0.0083)
Table 4.10: Ratio of throughput increase in buer size 30 (or 80) to that in buer size 10 (or 30).
Packet generating rate Buer size 30 to 10 Buer size 80 to 30
0.0083 - XOR 1.071839 1.006863
0.0167 - XOR 1.127344 1.016077
0.0333 - XOR 1.096358 1.007988
0.0083 - Unicast 1.101762 1.010305
0.0167 - Unicast 1.045612 1.005792
0.0333 - Unicast 1.016299 1.002703
Chapter 5 Conclusion
In this thesis, we explore the network coding technique, the XOR coding algorithm, to improve the throughput of the grid network, and to examine how packet generating rate and buer size impact the network throughput, packet loss and end-to-end delay. In our simulation, the XOR coding algorithm, being built on greedy grid unicast routing, namely U nicast, is evaluated with Unicast. Under the light tra c load, 500000 to be exact trans-mitted, which are generated randomly with their source and destination pairs distributed uniformly over the 20 × 20 grid network, the distribution of the tra c load of each grid in the XOR coding algorithm or in Unicast is like a hill, the results of which are similar to , but atter than those of a previous paper [6] due to collisions and retransmissions. In the 10 × 10 grid network, which is in a stable state and runs with the same number of time slots, namely 500000 time slots, at packet generating rates of 0.005 0.1, the XOR coding algorithm improves the throughput and end-to-end delay by about 74.7% and 55.7% on average as compared with Unicast. With respect to variable buer size, the throughput increases along with the buer size, and increases faster when the buer size is between 10 30. On the contrary, packet loss decreases along with the buer size, and decreases faster when the buer size is between 10 30. However, as the buer size exceeds 30, the increase of
the throughput and the decrease of packet loss slows down and ceases rapidly. Thus, with limited resources, this result suggests that 30 is the optimal buer size. As a summary of the series of simulation analyses, it can be concluded that the network coding can both in-crease network throughput and reduce end-to-end delay for the grid network under dierent network environments.
In the future, we will perform several theoretical analyses, such as those on throughput, end-to-end delay, packet loss, with queuing model, and try to nd the theoretical tra c load of each grid cell in the collisions and retransmissions network model. Moreover, we will extend the network coding to delauney network and hexagonal network, to know how network topology impacts throughput, end-to-end delay, packet loss, and nd the relationship between the network topology and the network coding. Finally, the random linear network coding algorithm will also be implemented between MAC layer and IP layer in the realistic environment.
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