Proof of LSTS Algorithm

Theorem 1. Given a non-empty finite set Φ of DBLs, the LAFS algorithm has the least number of awake-frames.

Proof 2. According to the expression Φk+1= Φk− ΥΦk in the LAFS algorithm shown in Algorithm 1, the equation

Φ_k−1 = Φ_k∪ Υ_Φk−1 (4.8)

is also true. In addition, based on the loop discriminant and the property of the non-empty finite set Φ, there must exist an integer number of N such that Φ_N = ∅ and Φ_{N −1}6= ∅. Let L(Φ_k) = K be the least number of awake-frames of Φ_k for some integer K. Then, based on Equation 4.8 and Fact 1, L(Φ_k−1) = L(Φ_k∪ Υ_Φk−1) lies in the integer set {K, K + 1, ..., K + M}, where M is the size of ΥΦk−1. Based on Definition 2, there exists a GS in Υ_Φk−1 whose termination is equal to min(F_t(Φ_k−1)). This GS is not overlapped by the DBLs in Φ_k, causing L(Φ_k∪ Υ_Φk−1) 6= K. Moreover, according to Lemma 1, there must exist one kind of awake-frame selection that all DBLs in Φ_k are aggregated into K awake-frames and those in Υ_Φk−1 are merged into exact one awake-frame. Therefore, L(Φ_k−1) = L(Φ_k∪ Υ_Φk−1) = K + 1. By using the induction method with the initial condition L(∅) = 0, the equation L(Φ) = L(Φ₀) = N is always true. It is noted that the LAFS algorithm produces N HGs and selects exact one awake-frame from each corresponding RCS. Therefore, the LAFS algorithm has the least number of awake-frames i.e. N. It completes the proof.

Algorithm 2: LSTS Algorithm

let the awake-frame ω be the termination F_t(ζ)

6

Lemma 2. The RDBLs generated by the LAFS algorithm are non-overlapped.

Proof 3. Based on the expression Φ_k+1 = Φ_k− Υ_Φk in the LAFS algorithm shown in Algorithm 1, the inequality

min(Ft(ΥΦk)) < min(Fs(ΥΦk+1)) < max(Fs(ΥΦk+1)) (4.9)

is hold. Therefore, the termination of the RDBL derived from Υ_Φk is smaller than the start of the RDBL derived from Υ_Φk+1. It completes the proof.

Theorem 2. Given a non-empty finite set Φ of DBLs, the LSTS algorithm has the least number of switch times.

Proof 4. As shown in Algorithm 2, the LSTS algorithm is directly derived from the LAFS algorithm by simply changing the selection rule of the awake-frames of RDBLs.

Based on Lemma 2 and the fact that the number of adjacent awake-frames must be

maximized for minimizing the switch times, the awake-frame candidate must be either the start or the termination of a RDBL.

A RDBL ζ and a frame λ left-adjacent to the start F_s(ζ) of ζ are given. In the case that the size of ζ is unity, it is trivial that the optimal and the only awake-frame is F_s(ζ) = F_t(ζ), and in the opposite case that the size of ζ is not unity, this case can be further divided by whether λ is an awake-frame or not. If λ is an awake-frame, the optimal awake-frame is the start Fs(ζ) of ζ because the awake-frame in ζ has a single adjacent awake-frame at most. If λ is not an awake-frame, the optimal awake-frame is the termination F_t(ζ) of ζ since the probability of awake-frame adjacency is non-zero.

Using the above procedure on the very first RDBL, the LSTS algorithm has the maximum number of adjacent awake-frames, leading to the least number of switch times.

It completes the proof.

Chapter 5

Performance Evaluation

5.1 Evaluation Environment

In this section, simulations are conducted to evaluate the performance of the proposed HPSS scheduling algorithms in comparison with the original power-saving mechanism in the IEEE 802.16e specification. A single BS/MSS pair with multiple connections are considered as the simulation scenario. Only the DL traffic are adopted, which are randomly selected and dispatched in the connections between the BS and the MSS. The associated simulation parameters are listed as in Table I. Two metrics are utilized for performance comparison:

• Power Efficiency (PE): the ratio between the sleep interval to the combination of the sleep and listen intervals, i.e. PE = TS/(TS+ TL).

• Average Packet Delay: the average time delay which consists of both the process-ing delay and the schedulprocess-ing delay for a packet.

TABLE I

SIMULATION PARAMETERS

Parameter Type Parameter Value

Traffic Type Constant Bit Rate (CBR)

Data Rate [28.8, 57.6] Byte/ms

Bandwidth Allowance 216 Byte/ms Average Packet Service Time 2.5 ms

Duration of Time Slot 13 µs

Frame Duration 5 ms

Simulation Time 10 sec

Fig. 5.1 to 5.5 show the performance comparison (i.e. the PE and the average packet delay) under different scenarios. Figs. 5.1 to 5.3 are Three different situations, Figs. 5.1 within the range of D_i = [26, 50] and T I_i =[26, 50]. Figs. 5.2 within the range of D_i = [26, 50] and T I_i =[51, 75] and Figs. 5.3 within the range of D_i = [51, 75] and T I_i =[26, 50]. In other word, We consider three different situations, including D_i ≥ T I_i, D_i ≤ T I_i and both of these situation. It is also noted that the x-axis in all these three figures indicates the number of connections goes from one to five within the network. Figs. 5.4 show the PE and the average packet delay) variance under different D_i interval within the range [ [1 25], [26 50], [51 75], [76 100], [101 125] ], T_i is fix to [26, 50] and 5 connections are considered. Figs. 5.5 show the PE and the average packet delay) variance under different Bandwidth Allowance within the range [216 392.8] and 5 connections where the parameters of D_i and T_i is the same with Fig 5.1 are considered.

Other simulation parameters are listed in Table I.

The bandwidth allowance is unlimit in Fig 5.6, and We show the PE and the average packet delay) variance under different Di interval within the range [ [1 25], [26 50], [51 75], [76 100], [101 125] ], T_i is fix to [26, 50] and 5 connections are considered.

5.2 Evaluation Result and Analysis

As can be seen from the upper plot of Fig. 5.1 with random parameters, the pro-posed HPSS scheduling schemes can provide higher PE comparing with the conven-tional 802.16e power-saving mechanism, PS and AS. i.e. more than 60% of increased PE under 5 connections in the network. It can also be observed that the PE obtained from the conventional scheme goes down drastically as the number of connections is augmented, i.e. 60% of PE under 1 connection and 10% of PE with 5 connections.

Moreover, the HPSS scheme slightly outperforms the PS algorithm with around 2% to 7% of increases in PE under different numbers of connections. and it is outperforms the AS algorithm with around 2% to 5% of increases in PE under different numbers of connections. It is also noted that the packet aggregation based on the QoS constraints also incurs certain delay time under the single connection case. However, even though additional packet delay is resulted from these two proposed schemes, the outcomes are still within the QoS delay requirements for all the connections.

In case of D_i ≥ T I_i, It is also noted that the PE of the IEEE802.16e is better than the PS in 1 and 2 connections. it is because the PS tend to use the periodic scheduling and one condition of the PS is:

C1 : TS+ TL≤ min

∀i {Di} (5.1)

The T I_i ≥ D_i the performance might become bad since the periodic will be bounded smaller than D_i

In case of D_i ≤ T I_i, It is also noted that the PE of the IEEE802.16e is pretty inefficient than the PS, the AS and the HPSS. it is because these three scheduling algorithms have more space to schedule the data burst.

Fig. 5.4 shows the PE and the average packet delay) variance under different D_i

1 2 3 4 5

Figure 5.1: Performance comparison under the random traffic parameters: Power effi-ciency and average packet delay vs. number of connections.

1 2 3 4 5

Figure 5.2: Performance comparison under the T I_i ≥ D_i : Power efficiency and average packet delay vs. number of connections.

1 2 3 4 5

Figure 5.3: Performance comparison under the T Ii ≤ Di : Power efficiency and average packet delay vs. number of connections.

interval within the range [ [12 50], [26 50], [51 75], [76 100], [101 125] ], Ti is fix to [26, 50] and 5 connections are considered. We can easily observe the PE of the PS, the AS and the HPSS getting better with more loose delay constraints and the IEEE802.16 power-saving mechanism have the same performance even the loose delay constraints.

The HPSS scheme slightly outperforms the PS algorithm with around 3% to 19% of increases in PE under different numbers of connections. and it is outperforms the AS algorithm with around 1% to 6% of increases in PE under different numbers of connections.

Fig. 5.5 shows the PE and the average packet delay) variance under different band-width allowance within the range [216 392.8] and 5 connections where the parameters of D_i and T_i is the same with Fig 5.1 are considered. We can easily observe the PE of the PS, the AS and the HPSS getting better with more bandwidth allowance and the IEEE802.16 power-saving mechanism have the same performance even more bandwidth

1~25 26~50 51~75 76~100 101~125

1~250 26~50 51~75 76~100 101~125

20

Figure 5.4: Performance comparison under the different D_i : Power efficiency and average packet delay vs. number of connections.

allowance. The HPSS scheme slightly outperforms the PS algorithm with around 3%

to 7% of increases in PE under different numbers of connections. and it is outperforms the AS algorithm with around 1% to 3% of increases in PE under different numbers of connections.

Fig. 5.6 shows the PE and the average packet delay) under different D_i interval within the range [ [12 50], [26 50], [51 75], [76 100], [101 125] ], Ti is fix to [26, 50] and 5 connections are considered ,and the bandwidth allowance is unlimit. We can easily observe the PE of the PS, the AS and the LAFS getting better with more loose delay constraints. It is noted that the PS might better than AS and increasing of the D_i it may not get better performance in AS.

216 260.2 304.4 348.6 392.8

216 260.2 304.4 348.6 392.8

0

Figure 5.5: Performance comparison under the different bandwidth allowance : Power efficiency and average packet delay vs. number of connections.

1~25 26~50 51~75 76~100 101~125

0.5

1~250 26~50 51~75 76~100 101~125

20

Figure 5.6: Performance comparison under the different bandwidth allowance : Power efficiency and average packet delay vs. number of connections.

Chapter 6 Conclusion

In this paper, a Heuristic Power Saving Scheme (HPSS) Scheduling algorithm is pro-posed for the IEEE 802.16e broadband wireless network. With the consideration of multiple connections between the base station and a single mobile subscriber station, the HPSS scheme maximizes the duration of the sleep interval based on the pre-defined Quality-of-Service (QoS) requirements. Numerical results illustrate that the HPSS scheme outperforms the conventional IEEE 802.16e , Periodic On-Off Scheme (PS) an APeriodic On-Off Scheme (AS) power-saving mechanism, especially under the situa-tions with multiple connecsitua-tions.

In order to optimize the power saving efficiency, It is needed to assumed the resource of bandwidth is unlimited. An optimal algorithm called Least Awake Frame Scheme (LAFS) is proposed. This algorithm still satisfy the Delay QoS and it is the optimal power-saving algorithm, and it is proved in this paper. Moreover, a algorithm called Least Switching Times Scheme (LSTS) is proposed, too. base on LAFS. It is design for reducing the MSS switching times between listen interval and sleep interval. It not only optimize the power saving efficiency but also minimize the MS Switching Times and it is also be proved in this paper.

Bibliography

[1] IEEE Standard for Local and Metropolitan Area Networks - Part 16: Air Interfer-ence for Fixed Broadband Wireless Access Systems, IEEE Standard 802.16-2004, 2004.

[2] IEEE Standard for Local and Metropolitan Area Networks - Part 16: Air Inter-ference for Fixed Broadband Wireless Access Systems, Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands and Corrigendum 1, IEEE Standard 802.16e-2005, 2006.

[3] J. A. Stine and G. de Veciana, “Improving energy efficiency of centrally controlled-wireless data networks,” ACM/Baltzer Wireless Networks, vol. 8, pp. 681–700, 2002.

[4] R. Krashinsky and H. Balakrishnan, “Minimizing energy for wireless web access with bounded slow-down,” in Proc. ACM/IEEE International Conference on Mo-bile Computing and Networking (MobiCom), Sept. 2002, pp. 119–130.

[5] K. T. Feng and K. H. Chou, “Intelligent router-assisted power saving medium access control for mobile ad hoc networks,” in Proc. IEEE Vehicular Technology Conference (VTC-2006 Spring), Melbourne, Australia, May 2006, pp. 304–308.

[6] Y. Xiao, “Energy saving mechanism in the ieee 802.16e wireless man,” IEEE Com-mun. Lett., vol. 9, pp. 595 – 597, July 2005.

[7] K. Han and S. Choi, “Performance analysis of sleep mode operation in ieee 802.16e mobile broadband wireless access systems,” in Proc. IEEE Vehicular Technology Conference (VTC-2006 Spring), 2006, pp. 1141 – 1145.

[8] Y. Park and G. U. Hwang, “Performance modelling and analysis of the sleep-mode in ieee802.16e wman,” in Proc. IEEE Vehicular Technology Conference (VTC-2007 Spring), Apr. 2007, pp. 2801 – 2806.

[9] Y. Zhang, “Performance modeling of energy management mechanism in ieee 802.16e mobile wimax,” in Proc. IEEE Wireless Communications and Network-ing Conference (WCNC), Mar. 2007, pp. 3205 – 3209.

[10] Y. Xiao, “Performance analysis of an energy saving mechanism in the ieee 802.16e wireless man,” in Proc. Consumer Communications and Networking Conference (CCNC), Jan. 2006, pp. 406 – 410.

[11] L. Kong and D. H. Tsang, “Optimal selection of power saving classes in ieee 802.16e,” in Proc. IEEE Wireless Communications and Networking Conference (WCNC), Mar. 2007, pp. 1836–1841.

[12] J. Shi, G. Fang, Y. Sun, J. Zhou, Z. Li, and E. Dutkiewicz, “Improving mobile station energy efficiency in ieee 802.16e wman by burst scheduling,” in Proc. IEEE GLOBECOM 2006, Nov. 2006, pp. 1–5.

[13] Y.-L. Chen and S.-L. Tsao, “Energy-efficient sleep-mode operations for broadband wireless access systems,” in Proc. IEEE Vehicular Technology Conference (VTC-2006 Fall), Sept. (VTC-2006, pp. 1 – 5.