Comparison of the System Minimum Distance

Here we check the obtained minimum distances of the system for the scheduling algorithms by increasing the number of existing TSs in each class. For the LCS-APSD, the scheduling result depends on the joining order of TSs. If there are K TSs belonging to C classes, there are (K!/Q_C

i=1n_i!) possible combinations of the joining order, where the operator ”!” stands for factorial. For simplicity, we only consider several cases for the LCS-APSD as specified below:

1. The joining order is according to Class [i, i + 1, i + 2, i + 3, i + 4] (mod 5) for 1 ≤ i ≤ 5, and repeats till K is reached.

2. The joining order is according to Class [i, i − 1, i − 2, i − 3, i − 4] (mod 5) for 1 ≤ i ≤ 5, and repeats till K is reached.

3. The joining order is by the ascending order of periods 4. The joining order is by the descending order of periods

In Fig. 4.5, we record the worst, average, and best performance for the LCS-APSD scheme for the studied cases. As shown in Theorem 4.1, without producing the coprime situation, the system minimum distance is bounded by Gmin/2 = 50 for all algorithms. For the studied cases, the performance of the GMD greedy algorithm is better than the LCS-APSD on average especially when the number of TSs is large. This may because that the TSs forming aggregated TS had been distributed uniformly away from each other before the inter-group scheduling. Also, we schedule the aggregated TSs based on their levels of scheduling difficulty. As for the Simply Sorted greedy algorithm, it also performs well since the TSs are scheduled in ascending order according to the size of the period. Due to the fact that we do not divide any TS into the groups, the periods of the TSs are larger than using

1 2 3 4 5 6 7 8 9 10

Number of traffic streams in each class

Minimum distance (100µs)

LCS−APSD with the best case LCS−APSD with the worst case LCS−APSD with the average case GMD greedy method

Simply sorted greedy method

Figure 4.5: Comparison of the obtained maximum of minimum distance.

the GMD method and more positions can be chosen to maximize the minimum distance.

Thus intuitively it has better chance to find the offsets to maximize the minimum distance of the system. However, the Simply Sorted greedy algorithm requires much higher complexity than that of the other algorithms as shown in previous evaluation.

4.4.3 Comparison of Power Consumptions

In this evaluation, we fix the number of existing TSs at 50 (10 for each class) and use the LCS-APSD and OAS-APSD algorithms to schedule those TSs by the orders specified in pre-vious sub-section. The simulation is performed to model 300 seconds of the real time. The power consumptions of Active state and Doze state are listed in Table 4.3.

According to the usage of ap-plication and the distribution of scheduled instants resulted by individual algorithms, the average consumed power per TS is measured as the normalized

energy consumption. The derived power consumptions depend on the specified joining order and differ much for the LCS-APSD and OAS-APSD algorithm. As shown in Fig. 4.6, the proposed GMD greedy algorithm and the Simply Sorted greedy algorithm outperform the LCS-APSD algorithm with the specified cases. The largest improvement obtained is 6% for the considered scenarios. We find that although both the GMD greedy algorithm and the Simply Sorted greedy algorithm achieve the same system mini-mum distance, the obtained average power consumptions are not equal. This may be because that the determined offsets for the GMD greedy algorithm, due to the equal spacing grouping, are more uniform when compared with other algorithms. Also, the overlapping of SPs may depend on the durations of SPs. From the simulation results, it is also shown that the average consumed power for each STA is much smaller than that of the Active state which spends 1.4W. Therefore, it is worth to utilize the power saving scheduling even during active sessions.

1 2 3 4 5 6 7 8

70 72 74 76 78 80 82

Average Power Consumption (mW) GMD greedy

Simply Sorted greedy

LCS−APSD with the worst case OAS−APSD with the worst case LCS−APSD with the average cae OAS−APSD with the average cae LCS−APSD with the best case OAS−APSD with the best case

Figure 4.6: Comparison of the Average Consumed Power.

4.5 Summary

In this chapter, our contributions are summarized as follows. We first present the brute-force searching method to obtain the global optimum of rearranging scheduled instants. It is, however, infeasible because of the huge complexity when the number of TSs is large. To reduce complexity, we develop several solutions to fulfill the goal of rearrangement. We show that the maximum of minimum distance between two periodic scheduled events is closely related to the greatest common divisor of their periods. Taking advantage of this observation, we devise the GMD greedy scheduling to increase the tractability while improving the energy saving performance. From simulation results, both the proposed GMD greedy method and the Simply Sorted greedy method are able to obtain larger system minimum distance than that of the previous greedy-based scheduling method generally. Consequently, better power saving performance is attained as well. An interesting and challenging further research topic is to determine the optimal schedule when the durations of SPs are taken into account.

Table 4.1: Notations used in Chapter 4 Notations Descriptions

C The number of classes of applications.

K The number of existing TSs in the system.

i, j The indices to represent the classes, 1 ≤ i, j ≤ C. scheduled instants of the m^th TS.

X The aggregation of existing scheduled events: X =

1≤m≤K∪ X_m.

Xi A Class i sequence with period p_i and X_i = {x_i,r}^∞_r=−∞= {p_i× r}^∞_r=−∞.

Y

A periodic sequence to represent the new joining TS be-longing to Class j: Y = {y_l}^∞_l=−∞ = {p_j × l}^∞_l=−∞ = multi-ple of the period of p_i and those of other existing classes.

d(X, Y + k) The distance between the sequences X and Y + k.

A_i,j

Store [ d(X_i, X_j+ 0) d(X_i, X_j+ 1) ... d(X_i, X_j+ G_i,j− 1) ] which represents the impact of a Class i sequence to a sequence of Class j with offset k.

Table 4.2: Traffic Characteristics.

Class Application Mean Data

Rate

Service Interval 1 Real-time Voice (G.711) 64 Kbps 40 ms 2 Real-time Video (MPEG 4

Trace: Lecture Room Cam) 58 Kbps 60 ms

3 Streaming Audio 128 Kbps 150 ms

4 Streaming Video (MPEG 4

Trace: First Contact) 330 Kbps 300 ms

5 Real-time Gaming 20 Kbps 100 ms

Table 4.3: 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

Power Consumption in Awake state 1.4 W Power Consumption in Doze state 0.045 W

Hardware delay of switchover 250 µs

Chapter 5

Energy-Efficient Multi-Polling