5.7 Numerical Results and Discussion
5.7.2 Performance of Different Adaptive Scheduling/
Transmission Schemes
For each class of adaptive scheduling/transmission policies, i.e., Opt, MP, MG, and RR, the performance metric we are interested in is the average packet loss rate (due to buffer overflow) versus the average transmit power. Here, the average packet loss rate is summed over all users and normalized by the total packet arrival rate. Note that the normalized system throughput is equal to one minus the normalized packet loss rate. The average transmit power is calculated per user and in each of the policies considered, all users consume the same average transmit power.
In Figs. 5.2, 5.3, 5.4, 5.5, we plot the performance, in terms of normalized packet loss rate versus average transmit power, of Opt, MP, MG, and RR for
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0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Average transmit power (dB)
Normalized packet loss rate
RR MG MP Opt
Figure 5.2: Performance, in terms of the normalized packet loss rate versus the average transmit power for different adaptive scheduling/transmission policies:
Opt, MP, MG, RR. Number of users N = 2, data packets arrive at rate λ = 0.5 packets/time slot with Poisson distribution, buffer length B = 12 packets, channel model is described in Tab. 5.1.
N = 2 and different values for other system parameters. This allows us to observe the general trends in the performance of the proposed classes of adaptive scheduling/transmission policies.
The first observation is that Opt always performs best. This is expected as in this class of policies, the scheduling and transmission decisions are jointly optimized. In general, the performance of MP varies considerably across the power range. At the high power range, the performance of MP is relatively close to that of Opt. However, at mid-range of average transmit power, MP performs quite far from optimal. MP does not offer a stable performance due to the inflexibility of the transmission scheme.
The performance of MG and RR follows opposite trends. At low power, MG outperforms RR and gets closer to the performance of Opt. On the other
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0 0.05 0.1 0.15 0.2 0.25
Average transmit power (dB)
Normalized packet loss rate
RR MG MP Opt
Figure 5.3: Performance, in terms of the normalized packet loss rate versus the average transmit power for different adaptive scheduling/transmission policies:
Opt, MP, MG, RR. Number of users N = 2, data packets arrive at rate λ = 0.5 packets/time slot with Poisson distribution, buffer length B = 8 packets, channel model is described in Tab. 5.1.
hand, in the high power range, RR performs much better than MG and closely approaches the performance of Opt. These trends in performance can be ex- plained as follows. Max-gain scheduling is good for achieving power efficiency, as it allows a user with the best channel condition to transmit. As a result, the max-gain scheduling policies perform well at low range of transmit power, where the need for power efficiency is high. However, by favoring users with the best channel condition, max-gain scheduling is (short term) unfair to others. When transmission can be carried out at high power level, instead of power efficiency, what important is every user is allowed to transmit frequently. This is what RR does. Therefore, RR approaches optimal performance when average transmit power is increased.
To see how the relative performance of Opt, MG, and RR depend on dif-
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0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Average transmit power (dB)
Normalized packet loss rate
RR MG MP Opt
Figure 5.4: Performance, in terms of the normalized packet loss rate versus the average transmit power for different adaptive scheduling/transmission policies:
Opt, MP, MG, RR. Number of users N = 2, data packets arrive at rate λ = 0.5 packets/time slot with Poisson distribution, buffer length B = 12 packets, channel model is the same as in Tab. 5.1 except that the gains for states γ0, γ1, γ2 are set to 0, 0.5, 0.9 respectively.
ferent system scenario, we vary the system parameters and again compare the performance of these schemes in Fig. 5.3, 5.4, 5.5. First, in Fig. 5.3, we reduce the buffer size from 12 packets to 8 packets. As can be seen, all schemes perform worse. However, it seems that MG suffers more from the reduction in buffer length than RR does. This is shown by the fact that, when the buffer size is reduced, at low power, the gap between MG and RR is less while for the high power range, the gap between MG and RR is widen. This change in the relative performance is explained by the fact that, when there are less storage space, users are less capable of holding back data to wait for a good channel model, i.e., it is more costly to do max-gain scheduling. This also means that there is more advantage in scheduling every user regularly like in RR.
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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Average transmit power (dB)
Normalized packet loss rate
RR MG MP Opt
Figure 5.5: Performance, in terms of the normalized packet loss rate versus the average transmit power for different adaptive scheduling/transmission policies:
Opt, MP, MG, RR. Number of users N = 2, data packets arrive at rate λ = 0.5 packets/time slot with Poisson distribution, buffer length B = 12 packets, channel model is the same as in Tab. 5.1 except that the probability of staying in each channel state after each time slot is set to PG(k, k) = 0.8, k = 0,1,2, probabilities of going up or down one channel state are equal.
Next, we look at the effect of changing the degree of fluctuation in the channel gains. In particular, if in Fig. 5.2, the channel gains in three states are 0, i.e. outage, 0.1, and 0.9, then in 5.4, we set these gain to 0, 0.5, 0.9. This means that there is less difference in the channel conditions in states 1 and 2.
Now, there is less channel diversity for Opt and MG to take advantage of. On the other hand, RR, which schedules user without taking the channel conditions into account, will suffer less performance loss. This is shown in Fig. 5.4. As can be seen, the gap between MG and RR is less at the low power range and is more at the high power range.
The last parameter of concern is how fast the channel changes. We vary
the frequency at which channel changes by changing the probability that the channel stay in each state after each time slot. In 5.2, this probability is set to 0.6 while it is increased to 0.8 in Fig. 5.5. This means the channel changes less frequently. When the channel changes slowly, max-gain scheduling will suffer, as some user with the best channel condition will hold the channel for long time, leaving others no chance to empty their buffers. As a result, the performance of MG decreases, relative to that of RR.