7.4 Analysis
7.5.2 Performances of Alternative Radio Resource Partitions
In Fig. 7.5, we investigate the effects of various numbers of sub-channels r and time slots m on the efficiency of the reserved radio resources based on the multi-channel random access MAC protocol in the considered OFDMA system with 100 stations.
We have the following two observations:
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 0
25 50 75 100 125 150 175 200 225 250
# of stations
Access latency (msec.)
To=10ms,r=1 (anl.) To=10ms,r=1 (sim.) To=200ms,r=1 (anl.) To=200ms,r=1 (sim.) To=10ms,r=6 (anl.) To=10ms,r=6 (sim.) To=200ms,r=6 (anl.) To=200ms,r=6 (sim.) single channel
six channels
Fig. 7.4: Average latency of the reserved radio resources based on the multi-channel random
access MAC protocol with three time slots per frame and one/six sub-channels to send bandwidth/ranging requests in an OFDMA system by simulation and analysis.
10 0 30 20
50 40
0 10
20 30
40 50
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Reserved time slots Reserved sub−channels
Efficiency
Fig. 7.5: Effects of various sub-channels and time slots on the efficiency of the reserved radio resources based on the multi-channel random access MAC protocol in an OFDMA system with 100 stations.
• As shown in the figure, the efficiency of the reserved radio resources is monotonously decreasing as the number of the reserved time slots or sub-channels in a frame grows. This is because too many reserved radio resources may cause them stay-ing idle. For example, when the number of reserved slots m = 3, the efficiency η for the number of reserved sub-channels r = 1 ∼ 50 decreases from 0.37 to 0.15. Similarly, as r = 6, η = 0.35 ∼ 0.3 for m = 1 ∼ 48. The phenomenon of monotonously decreasing efficiency with the increasing number of reserved sub-channels represents that the maximization of efficiency performance is also to optimize the reserved resources left for the data transmissions for the given access latency requirement. Thus, although we aim to maxize the efficiency by adjusting the numbers of reserved sub-channels and time slots, this prob-lem is also an optimization probprob-lem for the reserved resource left for the data transmission.
• Furthermore, as shown in the figure, the efficiency of the reserved radio resources seems to be more sensitive to the changes of the number of reserved sub-channels in the frequency domain than that of the number of reserved time-slots in the time domain. We will try to explain this situation by investigating the effect of the reserved radio resources in the frequency and time domains on the collision probability of the multi-channel random access MAC protocol next.
By means of (7.8), Fig. 7.6 shows the effects of various reserved sub-channels and time slots on the collision probability of the multi-channel random access MAC protocol in the considered OFDMA system with 100 stations. Clearly, reserving more radio resources for random access can yield a lower collision probability. However, it is interesting to investigate in which domain of the OFDMA system, frequency domain or time domain, is more effective in improving the efficiency and latency performances for the system adopting the multi-channel random access MAC protocol. As shown in the figure, increasing the number of the reserved sub-channels r can reduce the collision probability more effectively than changing the number of reserved time slots
10 0 30 20
50 40
0 10
20 30
40 50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Reserved time slots Reserved sub−channels
Collision probability
Fig. 7.6: Effects of various reserved sub-channels and time slots on the collision probability of the multi-channel random access MAC protocol in the considered OFDMA system with 100 stations.
m. For m = 6, changing r = 6 to 48 can lower the collision probability pc from 0.64 to 0.17. By contrast, the collision probability pc decreases from 0.49 to only 0.4 when m changes from 2 to 48 for r = 6. By comparing (7.8) and (7.10), one can easily see that a lower collision probability leads to a higher efficiency for the reserved random access radio resources. Hence, from Fig. 7.6, one can explain why in Fig. 7.5 changing the amount of reserved radio resource for random access in the frequency domain of the OFDMA system can more significantly affect the efficiency than in the time domain of the OFDMA system.
Figure 7.7 illustrates the effects of various reserved sub-channels and time slots on the average latency of the multi-channel random access MAC protocol in the OFDMA system with 100 stations. In contrast to the phenomenon observed in Fig.
7.5, the number of the reserved time slots dominates the latency performance com-pared to that of the reserved sub-channels. For example, the access latency for r = 6 decreases from 95 msec to 10 msec as m changes from 2 to 48. On the contrary, when r increases from 2 to 50 , the latency for m = 6 is reduced only from 95 msec to 20 msec. Intuitively, the more reserved time slots help stations to resolve the contentions earlier and to send the request in the prior frame. Although, from (7.11), increasing the number of reserved sub-channels can lower the collision probability, it is not as effective as increasing the time slots from the aspect of reducing the access latency because the station waits more frames to count down the backoff slots in the case of few reserved slots. Notably, it is important to combine Figs. 7.5 and 7.7 to determine a set of (r, m) with the maximum efficiency and satisfactory delay performance. For the case k = 100 and To = 10 msec, (r, m) = (2, 29) can achieve the highest efficiency under the constraint of Dmax = 25 msec.