# A MAP Overhead Aware Two-Dimensional OFDMA Burst Construction Algorithm
## 5 Simulations Results and Discussion
### Simulation Results  
The effect of the average requested bandwidth on total throughput were also investigated. The arrival data rate varied from 100 Kbps to 1.3 Mbps with the same number of connections, 20 (SSs). Figure 8 shows the total throughputs achieved by EHA, enhanced One Column Striping with non-increasing Area first mapping (eOCSA) [8], Weighted Less Flexibility First (WLFF) [7], and Hungary Algorithm (HA) [11]. Each burst adopts only one MCS based on the worst SNR of all assigned subchannels. The WLFF and eOCSA constructed the burst that may occupy more than one subchanel to fully utilize the bandwidth. However, they did not consider subchannel diversity and often constructed bursts with poor MCS. Even when the traffic was light, WLFF and eOCSA could not satisfy the requested bandwidth (300 kbps \(\times\) 20 connections = 6 Mbps). The reason is that WLFF and eOCSA constructed bursts without considering subchannel diversity, and therefore the allocated bandwidth for each connection is placed on the unsuitable subchannel.  
The EHA and HA considered the characteristic of subchannel diversity. When the traffic was light, they constructed bursts in good subchannel quality. The number of available slots, \(BWA_{i}\), was sufficient to satisfy the requested bandwidth. However, when the requested bandwidth increased, EHA provided at most two times the throughput that HA provides. The reason is that EHA shrink occupied slots of the burst if the requested bandwidth was satisfied. Thus, unused slots in this subchannel can be used by other bursts. Further, HA did not consider the requested bandwidth of each connection. The connection may only require a few subchannel to transmit its data, but it was allocated too many subchannels that could not be used by other connections.  
Figure 8: The effect of different average requested bandwidths.  
Figure 9 illustrates the total throughput of EHA, eOCSA, WLFF, and HA in different numbers of connections, Mbps means mega bit per second. The number of connections increased gradually from 5 to 35 with the same overall data arrival rates, 20 Mbps. The total throughputs of EHA, eOCSA, WLFF, and HA increased when the number of bursts increased. The EHA and HA gave each connection multi-bursts to construct its bursts in good subchannel quality. However, EHA constructed the burst by reducing the number of occupied slots to considered internal fragmentation and it left the unused free slots to other bursts. The WLFF and eOCSA gave each connection one burst to construct its bursts and did not consider subchannel diversity. Thus, they had more opportunities to construct a burst in bad quality subchannels.  
Figure 10 illustrates the total throughput of EHA, eOCSA, WLFF, and HA in variation of the channel quality between subchannels. As the standard deviation of the SNR increased, the numbers of subchannels with good SNR increased, and the numbers of subchannels with poor SNR increased, too. The EHA always constructed bursts in good channel quality and reserved unused slots to other bursts. The subchannel allocated to the connection could redistribute to others if the connection did not use it. However, HA did not consider the requested bandwidth of each connection. The connection with a better channel condition might get more subchannels to transmit data. The unused subchannels could not reassign to other connections. The WLFF and eOCSA constructed bursts in the subchannels with worse SNRs as the standard deviation of the SNR increased since they did not consider subchannel diversity.  
Figure 9: The effect of different number of connections.