In this thesis, we present the simulation results to show the performance comparisons of our proposed 2L-DMA algorithm with that of eOCSA algorithm.
Furthermore, we will also present the performance comparisons of our proposed 2L-DMA algorithm with a modified version of our proposed 2L-2L-DMA algorithm, (2L-DMA mv). In our simulations, we assume that either all requests have the same MUST proportions or all requests have random MUST proportions from in a range. We also assume that the request for each MS is randomly generated; with the constraint that the sum of all requests is 12×30 slots. We consider one burst for each MS.
As mention before, for those unmapped requests after our 2L-DMA algorithm first phase, which can contain MUST part and WISH part; in our 2L-DMA algorithm second phase we consider that there burst can consist of only the MUST part or the MUST part with some WISH slots only; the burst does not consist of the complete request size, due to the objective of the second phase, which is to map as much possible MUST part, for this reason we do not consider the burst having the total amount of the request size.
The number of MSs is randomly chosen from 1 to 40. The over allocated slots, unused slots and efficiency are average over 1000 trials. For our simulation, the physical bandwidth is 10 MHz and the frame duration is 5 ms. The duplexing techniques is TDD, and the permutation mode is PUSC, which is the most commonly
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used mode. Also as mentioned before, the selected algorithm to compare our 2L-DMA algorithm with is that of eOCSA. We couldn’t compare 2L-DMA with other published algorithms for various reasons.
Our proposed 2L-DMA algorithm first phase consist of a modified eOCSA algorithm, which make eOCSA the main comparison algorithm. After the first phase, when mapping the remaining unmapped MUST part we consider vertical blocks; with others algorithm we can’t obtain what we denotes vertical blocks.
To compare our proposed 2L-DMA algorithm with that of eOCSA algorithm, we assume that all requests have the same MUST proportions. We start by evaluating the impact of the unused slots overhead, which is define as the fraction of the downlink sub-frame taken by the slots that are left unused in a certain frame.
Figure 6. Unused Slots Overhead for 10 Mobile
Stations (MSs)
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Figure 6, illustrate that under the low traffic load (10 MSs) the eOCSA algorithm generate much more unused slots than our 2L-DMA algorithm. Our algorithm reduces the unused slots, since it start mapping the unmapped MUST part into the vertical block by filling the unused slots. However, after mapping into the vertical block, this can still contain unused slots, so our algorithms fill this space with unmapped WISH part partially in order to minimize the unused slots generated by eOCSA. Furthermore, in figure 6 it is shown that when the MUST proportions is 0.7 our proposed algorithm increase the unused slots, due that there are not much unmapped WISH part to fill into the unused slots; and when the MUST proportions is 0.8 our proposed algorithm increase the unused slots, due that the unmapped MUST part is too large and sometime can’t be mapped. On average, the unused slots of eOCSA are 23.931 and 7.257 with our 2L-DMA algorithm.
Figure 7. Over Allocated Slots Overhead for 10
Mobile Stations (MSs)
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In figure 7, we compare the over allocated slots of eOCSA algorithm with our proposed algorithm. The over allocated slots overhead is define as the fraction of the downlink sub-frame taken by the portions of the burst that are not actually being utilized for sending data. Fig. 7 shows that our proposed 2L-DMA algorithm is generating less over allocated slots when the MUST proportions are increasing, this is because after filling the unused slots our algorithm will fill some over allocated slots while also removing some mapped WISH part in this row so it can also be filled.
Figure 8. System Efficiency for 10 Mobile
Stations (MSs)
eOCSA is shown. As shown, eOCSA is not properly performing mainly because of its problem with the unused slots; and due to the amount of unused slots generated by eOCSA, it leads to a low performance. Fig. 8 illustrates how our proposed 2L-DMA algorithm outperforms eOCSA.30
Our proposed algorithm has the best performance because it actually reduces the problem with the unused slots generated by eCOSA. However, we can also observe from the result given in fig. 8 that our proposed algorithm is very steady when the MUST proportions is from 0.2 to 0.6, and starting from 0.7 the efficiency began to decrease, due to the size of the MUST proportions. When the MUST proportions is too large, the unmapped MUST part can’t be mapped, since there are not enough space in order to map these.
For example, the sum of the unused slots and the mapped WISH part that can be partially removed is not enough in order to map the unmapped MUST part. Our proposed 2L-DMA algorithm perform better when the MUST proportions is 0.6; at this proportion the efficiency of our proposed algorithm is 96.313% with over allocated slots and unused slots counted as waste.
So far, we have seen in Fig. 6, 7 and 8 the results of the over allocated slots, the unused slots and the efficiency under 10 MSs (or 10 requests). Furthermore, since our proposed algorithm performs better when the MUST proportions is 0.6, we will illustrate it’s results of the over allocated slots, the unused slots and the efficiency when increasing the amount of MSs.
Fig. 9, 10 and 11; show the results of eOCSA algorithm again compared to our proposed algorithm when we increase the network traffic and with MUST proportions 0.6; note that as we increase the network traffic our algorithm perform differently.
Under heavy traffic load (40 MSs) our proposed algorithm perform almost similar to eOCSA, this is because eOCSA is at its best performance, so there are not much unmapped request to deal with in our proposed algorithm second phase.
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Figure 9. Unused Slots Overhead with MUST proportions 0.6
Figure 10. Over Allocated Slots Overhead with
MUST proportions 0.6
32 modified version of our proposed 2L-DMA algorithm, (2L-DMA mv). We assume that all requests have random MUST proportions from in a range. As mentioned before, in the modified version of our proposed 2L-DMA algorithm all requests are mapped according to the size of the MUST parts in the descending order (largest MUST part first) in “eOCSA mapping”. Fig. 12 shows the results of the unused slots overhead between the two comparative algorithms when the MUST proportions are from 0.2 to 0.8. The fig. 12 illustrates that the modified version of our proposed 2L-DMA algorithm is generating more unused slots overhead when compare to our proposed 2L-DMA algorithm, due that 2L-DMA mv map all request according to the size of the MUST parts, it results in more unused slots when compare to 2L-DMA.
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Figure 12. Unused Slots Overhead with MUST proportions from 0.2~0.8
Figure 13. Over Allocated Slots Overhead with
MUST proportions from 0.2~0.8
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In figure 13, we can observe the over allocated slots overhead generated with MUST proportions from 0.2 to 0.8. This fig. illustrate that 2L-DMA mv generate more over allocated slots overhead compare to our 2L-DMA algorithm, due to the fact that when mapping all the request in the descending order of the MUST part size, the mapping is more disorderly, resulting in more over allocated slots.
Fig. 14 describes the efficiency of the two comparative algorithms. Note that our proposed 2L-DMA algorithm performs better when compare to the modified version of our proposed algorithm, this is because 2L-DMA mv generate much more over allocated slots and unused slots by mapping the requests in the descending order of the MUST part size. On average, the efficiency of 2L-DMA mv are 95.142% and 96.267% with our 2L-DMA algorithm for 10 MSs.
Figure 14. System Efficiency with MUST
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Chapter 5
Conclusion
In this thesis, the resource allocation problem which is also known as the bin packing problem in WiMAX system is concerned. First, the resource allocation problem in WiMAX system is briefly introduced. Then we introduce our proposed data mapping algorithm for two-level request called 2L-DMA algorithm. The basic idea of our proposed algorithm is to apply a two-level request; MUST part, for urgent data and WISH part for non-urgent data; and to return as less possible MUST part to the scheduler.
In chapter 3, our proposed 2L-DMA is described. Our proposed 2L-DMA algorithm is divided into two phases. The first phase, called “eOCSA mapping”, consists of mapping all requests according to a modified eOCSA algorithm which takes into account that all request can consist of two parts (or two levels): MUST part and WISH part. The second phase, called “Unmapped MUST part mapping”, consists of mapping as much unmapped MUST part as possible for those unmapped requests.
The objective is to improve the resources allocation by utilizing our 2L-DMA algorithm. The simulation results are presented in chapter 4. From the simulation results we conclude that our proposed 2L-DMA algorithm can improve the performance compared to that of eOCSA, due to the fact that it minimizes the unused slots generated in “eOCSA mapping” by first filling this waste space with unmapped
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MUST part and then with unmapped WISH partially. On average, the efficiency of eOCSA is 91.443% and 96.267% with our 2L-DMA algorithm for 10 MSs.
In addition, we present a modified version of our proposed 2L-DMA algorithm (2L-DMA mv) which consist of mapping all the requests in the descending order of the MUST part size (largest MUST part first) and starts by mapping the largest one regardless the size of the request in the “eOCSA mapping ”.
In conclusion when compared to our 2L-DMA algorithm the simulations results show that our 2L-DMA algorithm outperform 2L-DMA mv, due to the fact that when mapping all requests according to the size of the MUST part in the “eOCSA mapping ” it maximize the unused slots. On average, the efficiency of 2L-DMA mv are 95.142% with different MUST proportions and 96.267% for our 2L-DMA algorithm also with different MUST proportions, under 10 MSs for both algorithms.
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References
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Autobiography
My name is Arleth Soleiy Garth Campbell, I was born in Nicaragua, in 1987. Am bilingual, I speak both Spanish and English very fluently. I received my B.S. degree in Computer System from the Universidad Cristiana Autónoma de Nicaragua, in 2008. After I graduated from my college I decided to come to Taiwan for further education. I have been living here in Taiwan for almost 3 years now. Upon the first year, I studied Mandarin Chinese language at National Taiwan Normal University; then I enrolled at this prestigious university named National Chiao Tung University, where I received my M.S degree in Telecommunication & Networking from EECS department in the year 2011.