CHAPTER 5 Simulation Results
5.1. Delay Time
The formula (17) is our proposed scheme to evaluate the delay time of one certain node transmitting its scheduling information MSH-DSCH. The MATLAB 7.0 is applied to calculate this complex operation in our numeric validations. Following parameters are applied:
Exponent = 2
Node ID: random number between 1~4095
Probability: Pc= 0.5
And the result is shown as Figure 5.1. The “sim” denotes a curve by simulation;
“math” denotes a curve by mathematics. With this figure, it shows our mathematical model approaches the simulation result. By the way, the error rate is analyzed by the statistic method, as Figure 5.2, presents the difference in distance between the method by behavior simulation and by our proposed mathematic formula. The error is under 10% while the nodes of number between 2 to 20. Except for the exponent x=2, we are also interested in x=3 and x=4. These simulation results are shown from Figure 5.3 to Figure 5.6. The errors are under 10% throughout the above simulations. The stable accuracy is performed all over these simulation results; even the different exponents are applied.
2~20 Nodes, x=2
0 20 40 60 80 100 120
2 4 6 8 10 12 14 16 18 20
Number of nodes
opportunities(time slot)
sim math
Figure 5.1: The delay time of opportunities between simulation and mathematic model-1
2~20 Nodes Error Rate
0 10 20 30 40 50 60 70 80 90 100
2 4 6 8 10 12 14 16 18 20
Number of nodes
Error rate (100%)
x=2
Figure 5.2: The error rate between simulation and mathematic model-1
2~20 Nodes, x=3
0 50 100 150 200 250
2 4 6 8 10 12 14 16 18 20
Number of nodes
opportunities(time slot)
sim math
Figure 5.3: The delay time of opportunities between simulation and mathematic model-2
2~20 Nodes Error Rate
0 10 20 30 40 50 60 70 80 90 100
2 4 6 8 10 12 14 16 18 20
Number of nodes
Error rate (100%)
x=3
Figure 5.4: The delay time of opportunities between simulation and mathematic model-2
2~20 Nodes, x=4
Number of nodes
opportunities(time slot)
sim math
Figure 5.5: The delay time of opportunities between simulation and mathematic model-3
2~20 Nodes Error Rate
0
Number of nodes
Error rate (100%)
x=4
Figure 5.6: The delay time of opportunities between simulation and mathematic model-3
Besides, as shown in the Table 5.1 and Figure 5.7, there is an error rate comparison
between the [9] and proposed evaluation. In order to compare with original analysis, Table 5.1 follows the original table format in the [9], that’s why the exponent x is list here without regular order.
Table 5.1: Comparison between original and proposed evaluation Numbers of Nodes X Original (100%) Proposed (100%)
2 2 2.47 0.75
3 3 3.12 1.97
4 3 2.81 1.39
5 1 0.85 0.36
6 0 0.36 0.38
7 2 2.28 2.2
8 2 3.85 0.9
9 1 0.86 0.65
10 0 0.42 0.1
Compare between Original and Proposed Evaluation
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
2 3 4 5 6 7 8 9 10
Number of nodes
Error rate (100%)
original proposed
Figure 5.7: Comparison between original and proposed evaluation
The Figure 5.7 shows that the values predicted by our model have a smaller degree of error than the values generated by [9]’s model do.
5.2. The Success Probability of MSH-DSCH Transmission
The formula (18) is a recursive function, so the initial value should be assumed for the recursive calculation. The initial value of π is assumed as follows,
...) 0, 0, 0,
(0)
= (1, π
If we are interested in the exponent x=2, the probability of success is evaluated as Figure
5.8. The inverse ratio depicted in this figure shows that as the number of nodes increases, the probability of success decreases.
Success Probability of MSH-DSCH transmission
0 0.1 0.2 0.3 0.4 0.5 0.6
2 3 4 5 6 7 8 9 10
Number of Nodes
Probability
x=2
Figure 5.8: The mean of success probability that a node transmit MSH-DSCH
The Figure 5.9 shows the probabilities of success which three different exponents are compared. This figure shows that as the number of exponent increases, the probability decreases. So there is a concept that the small exponent can speed-up the MSH-DSCH transmission. This is useful in the future as a mechanism of QoS or call admission control.
For example, a node which has the small exponent may have the more probabilities to transmit its scheduling information MSH-DSCH. The time for transmitting the MSH-DSCH
may image as a call setup time at beginning of a link connection. Thus the higher
probability for transmitting scheduling information MSH-DSCH implies the higher chance or priority it will be to initialize a connection.
Success Probability of MSH-DSCH transmission
0 0.1 0.2 0.3 0.4 0.5 0.6
2 3 4 5
Number of Nodes
Probability x=2
x=3 x=4
Figure 5.9: The mean of success probability when x is non-identical
CHAPTER 6
Conclusions and Future Works
In this thesis, we have proposed a Markov Chain model which can be used to simulate MSH-DSCH transmission behavior in 802.16 mesh mode. This model considers the competing probability and back behavior of transmitting MSH-DSCH. It also helps us to realize the competing behavior more clearly. In the future, there will be more possibilities to design the WiMax mesh mode based on this model.
Based on this model, we derived a formula to evaluate an average delay time of MSH-DSCH transmission. Furthermore, this delay time may impact the starting time of a link connection. Thus the higher probability for transmitting scheduling information
MSH-DSCH implies the higher chance or priority it will be to initialize a connection. More important, the processing time of the following three-way handshaking is also influenced by MSH-DSCH transmission delay. By this model, we separate out the factors that affect the delay time. These factors are possibly useful for future researches.
Our scheme also evaluates the success probability of MSH-DSCH transmission. That is useful for QoS negotiation and adaptation. A conclusion is obtained that the success probability is inversely proportionate to the number of nodes. We may get a threshold to guarantee the connection is more stable by applying this probability in the future.
Finally, we have a simulation. It appears that results calculated from our mathematic model closely resemble the results from simulation. In other words, the theoretical model fits the experimental data well.
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