Energy-Efficient Multi-Polling Mechanism
5.4 Performance Evaluation
(5.17)
where SCPMP,i = (i − 1)(1 − p)L + (i − 1)Slot + (i − (i − 1)p)SIFS . Clearly, if x(tM P(i − 1) + SCPMP,i) À ERi, then y is close to x. The condition tends to be true when i is large and/or every STA transmits a large number of frames.
5.4 Performance Evaluation
Three examples are studied for the proposed WTS strategy. System parameters are shown in Table 5.2. The PHY parameters which conform to the IEEE 802.11a standard are available in [4]. More available non-overlapping channels in the 5 GHz band provide better flexibility to avoid interference. The power consumption in either state is according to [22]. Since the time spent on sensing is simplified in analysis, we conduct computer simulations using Matlab [33] as a comparison to reflect the real situation. The TSMP scheme is also studied in our simulations. An STA can enter the Doze state in both SCP and DTP, if it is worthy of energy saving. The considered scenario is composed of n STAs, 1 ≤ n ≤ 20, with i.i.d.
traffic in an infrastructure BSS with an AP. We allow 5% degradation of BU when deriving the proposed WTS for the examples.
5.4.1 Example 5.1
Assume that the pdf h(t) = p · δ(t) + (1 − p)δ(t − L), where L represents the time for exchanging a constant-length Data frame. The case of p = 0.6 is considered because it is a typical model for an on-off voice connection [18]. The frame exchange time, denoted by
L, is chosen to be 200µs which is equivalent to the transmission time of a 200-byte VoIP frame. The mean and standard deviation of the traffic model are µ = 0.4L and σ =√
0.24L, respectively. Fig. 5.6(a) shows the BU loss obtained from simulations for the first n STAs.
As revealed in this figure, the analytical results are quite accurate since the maximum error is under 2.5%. The first 4 STAs have no loss of BU since the original wake-up times are smaller than the time of switchover and thus have wake-up time zero. The simulation result is slightly larger than the planned 5% for STAs after STA 5. The reason is that the sensing time of an STA is slightly underestimated for the busy channel case and thus resulting in more optimistic wake-up time estimation. Fig. 5.6(b) shows the energy-saving performance of the proposed WTS compared with the CP-Multipoll. The energy saved increases as the number of STAs increases since the overhearing problem is getting severer for more STAs.
As for TSMP, there is no trade-off between energy saving and BU because the transmission time of each STA is exactly known. However, the SCP represents a significant overhead to affect BU, especially when each STA only demands short transmission time as shown in this example. Note that the loss of BU decreases as the number of STAs increases because the effect of the fixed fields in the multipoll frame diminishes. The energy saving performance shown in Fig. 5.6(b) decreases initially since STAs need to spend more energy in the SCP.
However, it is gradually improved when there are more than 9 STAs. The reason is that it becomes worthy for some STAs to switch states to save energy during the SCP.
5.4.2 Example 5.2
In the second example, we assume that pdf h(t) = √2πσ1 2e−(t−µ)22σ2 with µ = 1000µs and σ = 200µs to model the aggregated traffic of multiple connections from an STA. Since the required transmission time cannot be negative, a new value is generated if a negative transmission time is obtained. We also study the impact of channel error in this example.
The immediate retransmission scheme is adopted as the error recovery strategy. The frame error rate q is set to 0.1. Fig. 5.7(a) shows the BU degradation obtained with simulations.
0 2 4 6 8 10 12 14 16 18 20
(a) Performance of Bandwidth Utilization ( x = 5 )
Number of STAs
Figure 5.6: Performances of the derived wake-up time schedule for Example 1.
Note that the curves for analytical and simulation results cannot be distinguished clearly because they are almost identical. The situation of underestimated sensing time, as shown in Example 1, does not appear in this example. The reason is that the probability for an STA to have zero required transmission time is zero for continuous transmission time case.
Fig. 5.7(b) illustrates the energy- saving performance of the proposed WTS, compared with the CP-Multipoll. The saved energy is about 80% for 20 STAs that is much higher than 10%
obtained for Example 1. The reason is that the coefficient of variation (σ/µ) of the traffic model and the impact of overhead such as sensing and switchover time of this example are smaller than those for Example 1. The TSMP scheme performs much better in this example since the impacts of SCP on BU and energy saving are relatively smaller due to larger transmission time for each STA in this example. However, the proposed WTS with the EE-Multipoll scheme still outperforms TSMP for both comparisons due to less overhead.
In Fig. 5.7(b), the energy saving performance of TSMP declines by 6.1% from q = 0 to 0.1 because retransmissions delay the original transmission schedule and become a new source of overhearing which cannot be exactly predicted. For the EE-Multipoll mechanism with WTS considering retransmission time in advance, the improvement in energy saving is slightly increased since the overhearing problem of CP-Multipoll is aggravated in erroneous situation.
(a) Performance of Bandwidth Utilization ( x = 5 )
Number of STAs
Degradation (%)
Analytical result, q = 0 Analytical result, q = 0.1
Simulation result: Gaussian, q = 0 Simulation result: Gaussian, q = 0.1 TSMP: Gaussian, q = 0
Simulation result: Gaussian, q = 0 Simulation result: Gaussian, q = 0.1 TSMP: Gaussian, q = 0
TSMP: Gaussian, q = 0.1
Figure 5.7: Performances of the derived wake-up time schedule with different frame error rates for Example 2.
We also investigated the performance of the proposed WTS for this traffic model with different standard deviations. Table 5.3 shows the wake-up times of STAs, the corresponding target average access start times, and the saved energy for a network consisting of 8 STAs. To meet the same constraint of BU loss, STAs have to wake up earlier if the standard deviation is larger. This is intuitively true since higher standard deviation results in more conservative
estimates. The saved energy decreases by 5.21% as the standard deviation increases from
(a) Performance of Bandwidth Utilization ( x = 5 )
Number of STAs
Figure 5.8: The deviation of using Normal distribution as traffic model.
5.4.3 Example 5.3
In this example, we study the performance of using Normal distribution as an approximation of the density function of true traffic arrivals. The traffic arrivals are assumed to follow the Poisson and the Exponential distributions with identical means selected to be 1000µs.
As shown in Fig. 5.8, using Normal distribution as an approximate traffic model yields satisfactory results. As the number of STAs increases, the losses of BU for both traffic models approach the desired value, i.e., 5%. It conforms with the analysis we provided in the impact of estimation discrepancy. Based on the observations, we suggest using Normal
distribution as traffic model to reduce the complexity when accurate estimation of pdf is difficult. For Normal distribution, only estimates of mean and variance are needed.
5.5 Summary
Current ordered-contention multi-polling schemes significantly improve BU by reducing con-trol overhead. However, they suffer from useless energy consumption caused by overhearing which may largely decrease battery operating time. To solve the overhearing problem, we provide a PM method which aims to achieve maximum energy saving subject to a pre-defined degradation on BU. The derivations of WTS and saved energy are verified with computer simulations. According to numerical results, the saved energy is significant as compared with the original ordered-contention multi-polling schemes, especially when there are a large number of STAs. Moreover, when compared with the TSMP scheme, the simulation results reveal that the TDMA-like access method may not guarantee to bring better energy-saving performance since the prior handshaking can cause significant overhead to STAs. An inter-esting and challenging further research topic is to efficiently incorporate QoS guarantee into the proposed EEMP mechanism.
Table 5.1: Notations used in the analysis
Notations Descriptions
W Ti The wake-up time of STA i, 1 ≤ i ≤ n, relative to the end of the multi-poll frame.
l(t) The probability density function (pdf) of required trans-mission time conditioning on there are traffic arrivals.
L
The mean transmission time for the traffic arrival to an STA in one SI conditioning on there is something to transmit (L =R∞
0 tl(t)dt).
h(t)
The pdf of the required transmission time for traffic ar-rivals to an STA (h(t) = p · δ(t) + (1 − p)l(t), where p is the probability of no traffic arrival in one SI and δ(t) represents the Dirac delta function).
si(t) The pdf of the transmission start time for STA i if it has data to transmit.
Si
The mean transmission start time for STA i, relative to the end of the multi-poll frame, if it has data to transmit (Si =R∞
0 tsi(t)dt).
ui(t) The pdf of the total duration for STAs 1, 2, ..., and i to finish their transmissions.
Ui(t) The cumulative distribution function (CDF) of ui(t) (Ui(t) =Rt
0ui(τ )dτ ).
tMP(i) The time for receiving and verifying a multi-poll frame which contains i STAs.
Table 5.2: System parameters
Parameter Value
PHY Data Rate 54 Mbps
PHY Control Rate 6 Mbps
Transmission time for PHY header and
preambles 20 µs
Transmission time for an OFDM symbol 4 µs
SIFS 16 µs
Slot Time 9 µs
MAC frame header 30 bytes
ACK frame 14 bytes
IP header 20 bytes
UDP header 8 bytes
RTP header 12 bytes
Service Interval 25 ms
Beacon Interval 100 ms
Power Consumption in Awake state 1.4 W Power Consumption in Doze state 0.045 W
Hardware delay of switchover 250 µs
Table 5.3: The WTS for different standard deviations, the target transmission start time, and the corresponding energy saving performances.
STA i 2 3 4 5 6 7 8
Si (µs) 1099 2179 3258 4337 5417 6496 7576
W Ti (std
= 100 µs) 1051 2112 3180 4245 5318 6388 7465
Energy saved for the first i
STAs (%)
15.22 28.08 37.76 45.16 50.98 55.65 59.49
W Ti (std
= 200 µs) 969 1998 3045 4100 5166 6225 7305
Energy saved for the first i
STAs (%)
13.57 25.89 35.41 42.80 48.66 53.40 57.34
W Ti (std
= 300 µs) 866 1851 2871 3900 4955 5981 7030
Energy saved for the first i
STAs (%)
11.43 23.04 32.32 39.63 45.54 50.31 54.28