針對IEEE 802.16 寬頻無線網路的睡眠模式運作之效能分析及以部分可探測馬可夫判斷過程為基礎之睡眠訊框決策

國 立 交 通 大 學

電信工程研究所

碩 士 論 文

針對 IEEE 802.16 寬頻無線網路的睡眠模式

運作之效能分析及以部分可探測馬可夫判

斷過程為基礎之睡眠訊框決策

Comprehensive Performance Analysis and

POMDP-based Sleep Window Determination for

IEEE 802.16 Broadband Wireless Networks

研究生：陳俊宇

針對 IEEE 802.16 寬頻無線網路的睡眠模式運作之效能分析

及以部分可探測馬可夫判斷過程為基礎之睡眠訊框決策

Comprehensive Performance Analysis and POMDP-based Sleep Window

Determination for IEEE 802.16 Broadband Wireless Networks

研究生：陳俊宇 Student：Chun-Yu Chen

指導教授：方凱田 Advisor：Kai-Ten Feng

國 立 交 通 大 學

電信工程研究所

碩 士 論 文

Submitted to Institute of Communications Engineering College of Electrical and Computer Engineering

National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Master of Science

in

Communications Engineering

October 2010

針對

針對

針對

針對 IEEE 802.16

IEEE 802.16

IEEE 802.16 寬頻無線網路的睡眠模式運作之效能分析

IEEE 802.16

寬頻無線網路的睡眠模式運作之效能分析

寬頻無線網路的睡眠模式運作之效能分析

寬頻無線網路的睡眠模式運作之效能分析

及以部分可探測馬可夫判斷過程為基礎之睡眠訊框決策

及以部分可探測馬可夫判斷過程為基礎之睡眠訊框決策

及以部分可探測馬可夫判斷過程為基礎之睡眠訊框決策

及以部分可探測馬可夫判斷過程為基礎之睡眠訊框決策

研究生：陳俊宇 指導教授：方凱田 教授

國立交通大學電信工程研究所碩士班

摘

摘

摘

摘

要

要

要

要

IEEE 802.16 標準是為了支援下一代無線寬頻存取網路中高資料

率及高移動性之服務而發展出來的。在這一系列的標準當中，為了使

行動裝置可達到節能的目的，具體制訂了一些睡眠模式運作的機制。

在本論文中，首先分別針對 IEEE 802.16e 以及 IEEE 802.16m 提出分

析模型，其中下行（downlink）與上行（uplink）鏈路傳輸所造成的

效果，皆被審慎納入分析模型的考慮當中，並在隨後利用模擬以驗證

這些模型的有效性。然而，根據 IEEE 802.16e/m 兩系統之省電效能

評估的結果，可以發現由既有機制（例如：頻繁的狀態切換、使用率

低的聆聽訊框、以及利用二進制指數成長的睡眠訊框長度）所產生的

效能低下。因此，此論文提出一個以部分可探測馬可夫判斷過程為基

礎之睡眠訊框決策（PSWD）方式，其可利用目前傳輸鏈路之統計特性，

決定出每個睡眠訊框適合的長度。而根據目前傳輸鏈路之狀態，且考

慮到可容忍之網路延遲之下，PSWD 提供一個以耗能為基準的睡眠訊

框決定策略。模擬結果可顯示出 PSWD 方法在節能方面優於傳統的

IEEE 802.16e/m 省電機制，並且同時滿足不同傳輸需求所對應到之

延遲限制。

Comprehensive Performance Analysis and

POMDP-based Sleep Window Determination for

IEEE 802.16 Broadband Wireless Networks

Student：Chun-Yu Chen Advisor：Kai-Ten Feng

Institute of Communications Engineering

National Chiao Tung University

Abstract

The IEEE 802.16 standard is developed to support services with

high data rate and high mobility for the next generation broadband

wireless access networks. There are existing sleep mode operations

specified in the series of IEEE 802.16 standards in order to provide

energy conservation for the mobile devices. In this work, the analytical

models for the sleep mode operations of both the IEEE 802.16e and IEEE

802.16m standards are proposed respectively. The effects of both

downlink and uplink traffic are properly considered in the proposed

models. Simulations are performed in order to validate the effectiveness

of the proposed system models. However, according to the performance

evaluation for the IEEE 802.16e/m system, inefficiency is observed

which can be resulted from specific mechanisms within the sleep mode

operations, such as frequent state transitions, under-utilized listening

windows, and the adoption of binary-exponential growth of sleep window

size. A POMDP-based sleep window determination (PSWD) approach is

proposed in this thesis, which stochastically determines the adequate

length of each sleep window according to the traffic pattern. Based on the

estimated traffic state, an energy cost-based sleep window determination

policy is provided within the PSWD approach in consideration of

tolerable network delays. Simulation results show that the proposed

PSWD approach outperforms the conventional IEEE 802.16e/m

power-saving mechanisms in terms of energy conservation while the

delay constraints are also satisfied with various traffic demands.

誌

誌

誌

誌 謝

謝

謝

謝

一篇論文的完成，所代表的不僅是兩年研究生涯劃下了句點，其

中更包含了學業上的歷練、生活經驗上的積累、以及身旁家人、師長

及朋友的鼓勵與協助。

在此我首要感謝張仲儒教授及王蒞君教授特地撥冗擔當俊宇的學

位考試委員，兩位老師於口試時的指導與批評，使得這份論文內容不

盡完美之處得以改善，也讓我體會到電信這個領域之博大精深、自己

的研究在整個學術大海中的渺小與微不足道。另外，我更想謝謝指導

教授方凱田老師，剛進入碩班時由老師引導我進入當時最熱門的

WiMAX 之大門，並多次帶著我前往合作企業進行報告與參觀，我在那

裡體會學習到了許多，像是報告技巧、待人處事、以及公司內部運作

與氣氛等等，可說碩士生涯一大半的收穫都來自於此，這可能是光在

實驗室中無從得到的。

實驗室的前輩：建華、柏軒、佳仕及裕彬學長們，在研究與課業

甚至生活上給了我不少建議與幫助，尤其同組的文俊及仲賢學長，更

是我常諮詢的活字典，也特別感謝仲賢學長雖已畢業投入職場，仍於

百忙之中協助批改我的研討會論文，讓我有機會參與 PIMRC 國際會議

增廣視野。而同為 97 級的伙伴們：萬邦、承澤、與其懋同學，從大

學即同校以來六年的深厚情誼，使我們彼此不僅在課業及研究上相互

扶持打氣，更在研究之餘留下了不少歡樂和難忘的回憶，我們終於達

陣了，可喜可賀！實驗室的學弟妹們：惟能、劭凱、宥儒、瑞鴻、及

昭華，祝福你/妳們能夠在 MINT LAB 研究順利成功且獲得比我們更加

豐碩的成果；更年輕的裕平、智偉、景維、修銘、及族繁不及備載的

學弟妹，前面的路還很長，希望你們能夠漸漸發掘並享受研究的樂

趣。還要提到一路情義相挺陪伴我多年的死黨：聖鈞、善淳、育誠、

家峻、智翔與達偉，謝謝你們幫忙分擔壓力且不時給予我鼓勵。

最後，我最感激的，還是莫過於陪我走過這段漫長時光的家人，

爸爸、媽媽、和弟弟，他們是我最溫暖的依靠，也是遭遇挫折時最有

力的精神支柱。

這本論文，獻給以上的大家，及曾經幫助我、鼓勵我的好朋友們。

陳俊宇謹誌 于國立交通大學 新竹

民國九十九年九月

Contents

Chinese Abstract i

Abstract ii

Acknowledgements iii

Contents iv

List of Figures vii

1 Introduction 1

2 Preliminary 5

2.1 IEEE 802.16e Sleep Mode Operation . . . 5

2.2 IEEE 802.16m Sleep Mode Operation . . . 8

2.3 Improvements in Sleep Mode Operations of IEEE 802.16m on IEEE 802.16e 10 3 Modeling of Sleep Mode Operations 12 3.1 Analytical Model for IEEE 802.16e . . . 12

3.1.1 Power Saving Class of Type I . . . 13

3.1.2 Power Saving Class of Type II . . . 15

3.2.1 Condition A . . . 19

3.2.2 Condition B . . . 19

3.2.3 Condition C . . . 21

4 Performance Analysis of IEEE 802.16e/m Systems 22 4.1 Sleep Ratio . . . 22

4.1.1 As for IEEE 802.16e . . . 22

4.1.1.1 Type I . . . 24

4.1.1.2 Type II . . . 25

4.1.2 As for IEEE 802.16m . . . 26

4.2 Mean Packet Delay . . . 28

4.2.1 As for IEEE 802.16e . . . 28

4.2.1.1 Type I . . . 29

4.2.1.2 Type II . . . 29

4.2.2 As for IEEE 802.16m . . . 31

5 Proposed POMDP-based Sleep Window Determination (PSWD) Ap-proach 32 5.1 Traffic State Estimation . . . 35

5.2 Evaluation Metrics . . . 37

5.2.1 Average Energy Cost . . . 38

5.2.2 Mean Packet Delay . . . 39

5.3 Sleep Window Determination Policy . . . 40

6 Performance Evaluation 43 6.1 Model Validation . . . 43

7 Conclusions 52

List of Figures

2.1 Schematic diagram of sleep mode operation for PSC of Type I in IEEE

802.16m: (a) with regular termination and (b) with interrupted termination 6

2.2 Schematic diagram of sleep mode operation for IEEE 802.16m: (a) with

DL traffic and (b) with DL and UL traffic. . . 8

5.1 Schematic diagram of ideal sleep mode operation for an AMS. . . 32

5.2 Schematic diagram of POMDP model for PSWD approach . . . 35

6.1 Numerical evaluation for Type I of the IEEE 802.16e/m with: (a) sleep ratio vs. packet arrival rate λ; (b) mean packet delay vs. packet arrival

rate λ. . . 44

6.2 Numerical evaluation for Type II of the IEEE 802.16e/m with: (a) sleep ratio vs. packet arrival rate λ; (b) mean packet delay vs. packet arrival

rate λ. . . 45

6.3 An exemplified sleep mode operation among Type I/II of IEEE 802.16e/m

and PSWD approach. . . 47

6.4 Performance comparison among Type I of IEEE 802.16e/m and PSWD

approach under NRT/BE traffic. . . 48

6.5 Performance comparison among Type I of IEEE 802.16e/m and PSWD

6.6 Performance comparison among Type I of IEEE 802.16e/m and PSWD

Chapter 1

Introduction

The IEEE 802.16 working group has drawn up a series of standards for wireless metropoli-tan area networks (WMANs) and next generation broadband wireless access systems. The IEEE 802.16-2004 [1] specifies the access between a base station (BS) and fixed subscriber stations (SSs); while movable mobile stations (MSs) are further supported by the IEEE 802.16e [2], which lead to the issues of energy-saving and handover. The IEEE 802.16-2009 [3] consolidates the two standards above and adds additional management information. The latest progress under standardization is the IEEE 802.16m [4] which is developed to achieve the requirements for future IMT-Advanced networks with higher data rate and higher mobility. Since mobility is considered a key feature in wireless networks, how to prolong the battery lifetime of MSs has been recognized as one of the critical issues.

The sleep mode of IEEE 802.16 systems, first introduced by the IEEE 802.16e stan-dard, is aimed to conserve the energy of MSs. By means of a pre-negotiation process, an MS can be absent from the air interface of its serving BS. In other words, the MS may power down some physical operation components or perform other activities that do not require communication with the BS. Three types of power-saving classes (PSCs)

are defined in the sleep mode to satisfy demands for packets with different traffic pat-terns. The PSC of Type I with binary-exponential growing sleep windows is suitable for both best-effort (BE) and non-real-time variable-rate (NRT-VR) service flows; while quality-of-service (QoS) guaranteed services, including unsolicited grant service (UGS) and real-time variable-rate (RT-VR) traffic, are recommended to the PSC of Type II, wherein the length of each sleep window is constant along with the periodic occurrence of transmission-allowed listening windows. The PSC of Type III is appropriate for mul-ticast connections and control management signals. It is noted that connections having similar traffic properties are gathered into a single PSC. Multiple connections with dis-tinct PSCs may exist between a single pair of an MS and its serving BS. Furthermore, for the case that there are mixed real-time and non-real-time traffic, constant length of sleep windows will be adopted in order to guarantee the QoS requirements of real-time traffic [5] [6].

There are several works focused on the performance analysis and modeling of the IEEE 802.16e sleep mode operation. Xiao [7] and Zhang [8] set up analytical models for the sleep mode with the Poisson arrival process and the hyper-Erlang distribution, respectively. A traffic model with mixture exponential distribution is utilized by J. Almhana et al. [9] to approximate packets inter-arrival times, which possess the char-acteristics of heavy-tailed distributions. On the other hand, in the work of [10], Y. Park et al. model the system by an M/G/1/K finite queue with multiple server vaca-tions. Moreover, the research proposed in [11] fully considers the mixed effect from both downlink (DL) /uplink (UL) traffic and multiple connections between an MS and its serving BS in the IEEE 802.16e power-saving operation. The sleep mode with general-ized traffic processes is analyzed in [12], wherein an enhanced scheme is also addressed to improve the performance of power management by adjusting the trade-off between energy consumption and packet delay. From the analytical results of these studies, it

can be realized that the inefficiency of the IEEE 802.16e comes from the configuration of sleep mode operation, e.g. the mechanism of binary-exponential traffic detection, and frequent transitions between sleep modes and normal modes. Hence some enhanced sleep mode mechanisms have been designed, e.g. the work in [13] [14] dynamically adjust the length of initial sleep window in order to reduce the number of unused lis-tening windows resulted from the binary-exponential growing of sleep windows; while the adaptively control of the initial and final sleep windows is proposed in [15]. For the sake of improving the power-saving efficiency of MSs, some notions of sleep mode mechanism are also proposed in the IEEE 802.16m by the IEEE 802.16 working group. The IEEE 802.16m adopts the virtues of the sleep mode operation in the IEEE 802.16e, such as the allowance of transmission within the listening windows of PSC of Type II, and gets rid of the aforementioned disadvantages.

As for the sleep mode of the new IEEE 802.16m standard, a few studies have been investigated. In [16], the authors deploy a modified M/D/1 system with vacations to evaluate message delays and MS’s power consumption in DL channels. On the other hand, a two-dimensional Markov chain is constructed by Baek et al. [17] to model the sleep mode operation for DL traffic and to analyze the average power consumption of MSs. The authors of [18] propose a new sleep mode scheme with periodically-sent traffic indication messages in order to trace traffic more precisely. However, the influence of UL traffic on the IEEE 802.16m sleep mode operation has not been investigated in the existing literature. In this work, based on the concept of [11], analytical models for both the IEEE 802.16e and IEEE 802.16m sleep mode operations are proposed. The integrated effect of DL and UL service flows are investigated in order to evaluate sleep ratio and mean packet delay of both PSC of Type I and Type II. The performance of the proposed analytical model is evaluated and validated via simulation studies. However, inefficiency can still be observed from the existing mechanism of sleep mode operation

in IEEE 802.16m system which can be improved accordingly.

A partially observable Markov decision process (POMDP) model is suitable for the purpose of conjecturing the unobservable present traffic state. Therefore, in this thesis, a POMDP-based sleep window determination (PSWD) approach is proposed in order to improve the performance of energy conservation in the IEEE 802.16m systems. Based on the present traffic state with consideration of tolerable delay, the proposed PSWD approach determines the appropriate length of each sleep window. In accordance with the rewards calculated via POMDP formulation, an energy cost-based sleep window determination policy can be acquired. The efficiency of proposed PSWD approach is evaluated via simulations in terms of average energy cost and mean packet delay. Simulations results show that the proposed PSWD approach outperforms the IEEE 802.16e/m systems in the aspect of energy conservation while the delay constraints are also fulfilled under various traffic demands.

The rest of the thesis is organized as follows. Chapter 2 briefly introduces the IEEE 802.16e and IEEE 802.16m sleep mode operations respectively, and the comparisons between these two mechanisms.. The proposed analytical models for these two stan-dards are described in Chapter 3; while the performance analysis of the models are investigated in Chapter 4. The detailed procedures of proposed PSWD approach are described in Chapter 5. Chapter 6 validates the effectiveness of the two analytical models and conducts the performance evaluation of proposed PSWD method. Chapter 7 draws the conclusion.

Chapter 2

Preliminary

In this chapter, the behavior of sleep mode operations of the IEEE 802.16e and the IEEE 802.16m are introduced separately by the following sections, and some comparisons between the two standards are drawn afterwards.

2.1

IEEE 802.16e Sleep Mode Operation

Fig. 2.1 shows a schematic diagram of the IEEE 802.16e power-saving mechanism, which includes both the normal mode and the sleep mode. The MS enters the sleep mode while it has been idle for a predefined idle period τ and negotiates with the BS by a request message MOB SLP-REQ and an approval message MOB SLP-RSP in the normal (active) mode. Within the sleep mode, a series of sleep cycles are provided for the MS. Each sleep cycle consists of a sleep window followed by a listening window with fixed time duration. In other words, the length of the nth sleep cycle can be

represented as TCn = TSn + TL, where TSn denotes the length of the sleep window at

the nth sleep cycle; while TL indicates the length of a listening window. According to

the IEEE 802.16e standard for PSC of Type I, the MS is designed to be in the awake state within the listening windows for examining the MOB TRF-IND message, which

L MS BS 1st S ●● ● frame )-( D NI-F R T _ B O M DL PDU UL PDU P S R-PL S _ B O M Q E R-PL S _ B O M L S ts 1 (b) (a) Analysis Period : nth sleep window L ●● ● ● ●● TB0 TI1 TB1 TI2 τ =TIn+1 2nd S L 3rd S )-( D NI-F R T _ B O M ) +( D NI-F R T _ B O M P S R-PL S _ B O M Q E R-PL S _ B O M 1st S )-( D NI-F R T _ B O M L 2nd S ) +( D NI-F R T _ B O M L nth

S L : Listening window : Busy frames in NM : Idle frames in NM

TS1 =TSmin TS2 TS3 TL TL TL TD1 TD2 TD3 Sleep Mode (SM)

Normal Mode (NM) Normal Mode Sleep Mode

Analysis Period L MS BS 1st S ● ●● frame )-( D NI-F R T _ B O M P S R-PL S _ B O M Q E R-PL S _ B O M L S ts 1 Analysis Period ● ●● ●● ● 2nd S L 3rd S )-( D NI-F R T _ B O M P S R-PL S _ B O M Q E R-PL S _ B O M 1st S )-( D NI-F R T _ B O M L 2nd S ) +( D NI-_F R T _ B O M L SM NM SM T d,1 t s e u q e R ht di w d n a B T u,1 T u,1 r = T u,2 T u,2 r T u NM Analysis Period ●● ● ● ●● NM

Figure 2.1: Schematic diagram of sleep mode operation for PSC of Type I in IEEE 802.16m: (a) with regular termination and (b) with interrupted termination

is a traffic indication message broadcasted from the BS. In the case that there are no DL packets destined for the MS, MOB TRF-IND will be given a negative value in the field corresponding to the MS. Upon receiving the negative MOB TRF-IND, the MS will continue staying in the sleep mode. When consecutive negative traffic indication messages are obtained by the MS, the length of its sleep window will be doubled from the previous one until the maximum size of sleep window is reached, which can be represented as

TSn = min(2

n−1_{· T}

Smin, TSmax) (2.1)

where TSmin and TSmax are the initial (minimum) and the maximum sleep window sizes

defined by the pre-negotiated MOB SLP-REQ and MOB SLP-RSP messages. Further-more, the reference period of each traffic indication message is called the detection window. The length of the detection window at the nth sleep cycle (as in Fig. 2.1(a)) is defined as TDn =      TSn for n = 1 TL+ TSn otherwise. (2.2)

In the case there are DL data bursts addressed to the MS arriving during a specific detection window, the serving BS will buffer these packets until the subsequent listening window of the MS. Thereupon a positive MOB TRF-IND will be sent in order to inform the MS of the arrived packets. Once receiving the positive traffic indication message, the MS will consequently return into the normal mode afterwards. Specifically, provided that any UL packet is ready for being transmitted, the sleep mode of the MS will be terminated and switched to the normal mode immediately.

AMS ABS 1st S ● ● ● frame )-( D NI-F R T _I A A DL PDU P S R-PL S _I A A Q E R-PL S _I A A L (b) (a) Analysis Period : nth sleep window ● ● ● ● ● ● τ 2nd S ) +( D NI-F R T _I A A L 3rd S L nth S L : Listening window TS1 TL TS2 TLext TC1 = TCmin TC2 Sleep Mode (SM)

Normal Mode (NM) Analysis Period

S ts 1 2nd S )-( D NI-F R T _I A A )-( D NI-F R T _I A A L (extended) TC1 T‘S1 AMS ABS 1st S ● ● ● frame L ● ● ● 2nd S 3rd S L SM Analysis Period )-( D NI-F R T _I A A Renewal Renewal L ) +( D NI-F R T _I A A L UL PDU t s e u q e R ht di w d n a B 3rd S Tu )-( D NI-F R T _I A A )-( D NI-F R T _I A A ● ● ● ● ● ● ● ● ● nth S

Figure 2.2: Schematic diagram of sleep mode operation for IEEE 802.16m: (a) with DL traffic and (b) with DL and UL traffic.

the following differences: (a) the sleep window becomes fixed time duration, which is

redefine as TSn = TSmin, and (b) Packet transmission is allowed within the listening

window. Moreover, so long as the amount of packets does not exceed the capacity of the listening window, it is unnecessary for the MS to deactivate the ongoing sleep mode.

2.2

IEEE 802.16m Sleep Mode Operation

The sleep mode operation of the IEEE 802.16m is illustrated in Fig. 2.2 by two ex-amples. The terms advanced BS (ABS) and advanced MS (AMS) indicate a BS and an MS that support the functions of the IEEE 802.16m, respectively. Moreover, in the following paragraphs, IEEE 802.16e and IEEE 802.16m are represented as 16e and 16m

for the convenience of description. As shown in Fig. 2.2(a), the sleep mode mechanism of 16m is almost similar to that of 16e in Fig.. However, it is contrary to 16e that each sleep cycle is composed of a listening window followed by a sleep window except for the first one, which contains only a sleep window. Therefore, the length of the nth sleep cycle of 16m can be represented as

TCn =      TSn for n = 1 TL+ TSn otherwise (2.3)

where TSn denotes the length of the regular sleep window at the nth sleep cycle; while

TL is the default length of a listening window.

During the sleep mode of 16m, the AMS shall also wake up at every listening window and check the value of the traffic indication message AAI TRF-IND so as to determine whether there is incoming DL traffic buffered at the ABS or not. In case of receiving the negative AAI TRF-IND, the AMS then goes into the sleep window for the rest of the current sleep cycle. Furthermore, the length of the sleep cycle (instead of sleep window as in 16e) will be twice the length of the previous one until the maximum sleep cycle, which can thus be expressed as

TCn = min(2

n−1

· TCmin, TCmax) (2.4)

where TCmin and TCmax are the length of the initial sleep cycle and the maximum sleep

cycle respectively. Moreover, the nth detection window TDn is just equal to the nth

sleep cycle, that is, TDn = TCn.

On the other hand, as for the positive AAI TRF-IND received, the length of the current sleep cycle shall be renewed to the initial sleep cycle, as the points ”Renewal” marked in Fig. 2.2. Accordingly, the listening window in this cycle is used to receive

the buffered DL data or transmit the AMS’s own UL packets without the need of returning to the normal mode. If all the packets can be transmitted completely during

the listening window, its length will be equal to default TL (as shown in the first sleep

cycle of Fig. 2.2(b)). Otherwise, extension of the listening window will be conducted

in order to satisfy the demand of transmission as depicted in Fig. 2.2(a), where TLext

is the length of the extended listening window. It is noticed that the limit of extension is constrained by the end of the sleep cycle where the listening window is located.

The sleep mode mechanism described above is recommended for BE traffic, and the name “Type I” is given here in contrast with the similar operation of PSC of Type I for 16e. On the other hand, “Type II” of 16m is referred to the operation with

fixed-duration sleep cycles, i.e., TCn = TCmin, which is suitable for real-time traffic-only or

real-time and BE-traffic mixed scenarios.

The AMS will keep staying in the sleep mode, and the process described above will be iterated until an explicit termination is introduced by the AMS or the ABS.

2.3

Improvements in Sleep Mode Operations of IEEE

802.16m on IEEE 802.16e

As can be observed from Fig. 2.1, a series of alternative of normal modes and sleep modes are operated by the MS of 16e. The MS always tends to deactivate the sleep mode and return to the normal mode for the sake of data transmission, then wait for another idle period and reactive the sleep mode. This configuration is inferred as the major cause of inefficiency for energy conservation in 16e. Furthermore, every time

when reactivating the sleep mode, the initial length of the sleep will be reset to TSmin,

and continue to utilized a binary-exponential growing algorithm to detect incoming traffic. This will bring about a great deal of listening windows with low utilization,

especially for listening windows of PSC of Type I in 16e, which merely function as checkpoints for traffic indication message. An evolutional sleep mode mechanism is developed in 16m in order to cope with aforementioned disadvantages of 16e, and a more flexible scheme for sleep mode operation is also provided. The major differences and improvements are summarized as follows:

• Concise sleep cycle setting : In 16e, the operation of sleep cycles is determined by connection-based factors; while an AMS-based scheme is considered for 16m. A single sleep cycle setting, indicated by a sleep cycle ID (SCID), is applied among all the connections of an AMS in the 16m.

• Ongoing sleep mode parameter update: An AMS of 16m may send/receive data and MAC control signaling, or update parameters (e.g. the length of a sleep window) without deactivating the sleep mode. In other words, the AMS does not have to wake up into the normal mode for the sake of data transmission, then wait for another idle period τ without issued traffic, exchange the MAC control messages, and return to the sleep mode again.

• Adjustable listening windows with higher utilization: In 16m, all the listening windows of an AMS can be utilized to transmit packets, including DL and UL service flows. Moreover, the length of each listening window is adjustable depending on the amount of data need to be transferred.

• Consistent length of sleep cycles from UL transmission: According to the specification of 16m [4], the interruption resulted from UL transmission at any time will have no impact on the length and phase of the sleep cycles, as shown in Fig 2.2(b). It means that an AMS shall resume the original paused sleep mode operation after accounting for the time elapsed during UL transmission.

Chapter 3

Modeling of Sleep Mode Operations

the mechanism of 16m1_{. Moreover, the analyses consider an error-free environment}

and there is sufficient bandwidth for the transmission related to the MS/AMS regard-less of DL or UL traffic, so every packet and MAC control messages are transmitted successfully all the time.

3.1

Analytical Model for IEEE 802.16e

For analysis models of 16e, the Analysis Period is defined the interval between the starting point of the normal mode and the termination of the sleep mode, as illustrated in Fig. 2.1(a).

1_{The previous chapter points out all the discrepancy between Type I/Type II of 16e and 16m. The}

following paragraphs will adopt (if necessary) either the superscript “(eI_{)”, “(e}II_{)”, “(m}I_{)”, or “(m}II_)”

for distinguishing the notations between Type I/Type II of 16e or 16m, e.g. TS(enII) and T

(mI₎

3.1.1

Power Saving Class of Type I

As shown in Fig. 2.1(b), the parameters Td,i _{and T}u,i _{are defined as the packet}

inter-arrival times of the ith DL and UL connections; while their mean packet inter-arrival rates are

denoted as λd,i _{and λ}u,i_{. It is assumed that T}u,i

r represents the remaining inter-arrival

time of Tu,i_{. According to the residue life theorem [19], the cumulative distribution}

function (CDF) of Tu,i

r (denoted as FTru,i(·)) can be expressed as

F_Tu,i r (t) = λ u,i Z t 0 [1 − FTu,i(x)]dx. (3.1)

In the case that the traffic is assumed as the Poisson distribution, F_Tu,i

r (t) as obtained

from (3.1) can be rewritten as F_Tu,i

r (t) = 1 − e

−λu,i_t

. The minimum value of Tu,i

r in

terms of the various connections i can be denoted as Tu , min{Tru,i}ni=1u , where nu is

the total number of the UL connections within a power-saving class. Consequently, the

CDF of Tu can be computed as FTu(t) = 1 − Pr[Tu > t] = 1 − nu Y i=1 h 1 − F_Tu,i r (t) i . (3.2)

Similarly, (3.2) can be simplified as FTu(t) = 1 − e

−λut _{while the Poisson traffic is}

assumed, where λu =Pni=1u λu,i. For further exploitation, the following two parameters

are defined: λd, Pn_i=1d λd,i and λ, λu+ λd. It is noted that nd is the total number of

DL connections in a power-saving class. Due to the random property of a UL packet while it is available to be transmitted from the MS, it is required to define a random

arrives at, that is, where Tu lies in, i.e. T_u,n(eI)=      Tu if SCn−1 < Tu < SCn 0 otherwise (3.3) where SCn = Pn

i=1TCi. Consequently, its Probability Density Function (PDF) can be

obtained as f Tu,n(eI)(t) =        λue−λut RSCn SC_n−1λue−λuxdx if SCn−1 < Tu < SCn 0 otherwise. (3.4)

As a result, the average value of Tu,n can be computed as

T(e_u,nI) = RS_Cn S_Cn−1xλue−λuxdx RS_Cn S_Cn−1λue−λuxdx . (3.5)

It is noticed that (3.5) will be utilized for performance analysis in the next chapter. In order to consider different effects that are induced from the arrivals of the UL and the DL packets, two distinct conditions are examined: The regular termination is considered as the case while the sleep mode terminates at the end of the listening window. In other words, the regular termination in the nth cycle is due to the combined effects as follows:

(a) there does not exist any UL or DL packets arrived in the duration of SCn−1 and

SDn−1 respectively (where SDn =

Pn

i=1TDi); (b) there is no UL packets that arrived

during the time interval TCn; and (c) At least one DL packet has arrived within the

duration of TDn. Therefore, the probability for regular termination occurring at the

nth cycle (denoted as φR n) can be computed as φR(e_n I)= n−1 Y i=1 e−λdT_Di ! 1 − e−λdTDn
n Y i=1 e−λuT_Ci ! . (3.6)

On the other hand, the interrupted termination represents the case while the sleep mode is terminated at a time instant other than at the end of the listening window. The interrupted termination in the nth cycle can be attributed to effects as follows: (a) there does not exist either the UL or the DL packets that arrived in the time duration

of SCn−1 and SDn−1 respectively; and (b) At least one UL packet has arrived during the

time interval TCn. Consequently, the probability for interrupted termination (φ

I n) can be obtained as φI(e_n I)= n−1 Y i=1 e−λdTDi ! _n−1 Y i=1 e−λuT_Ci ! 1 − e−λuTCn
. _(3.7)

Note that it is not required to define and compute the average remaining inter-arrival time for the DL traffic, as defined in (3.5). The reason is attributed to that the DL traffic will be buffered until the beginning of the normal mode in PSC of Type I

in 16e, i.e. by adopting the regular termination. Furthermore, TBi is denoted as the

duration of the busy period within the normal mode as shown in Fig. 2.1(a) . It is also

noted that the first busy period TB0 not only contains the packets arrived in the normal

mode but also includes the additional packets that were buffered before entering the

normal mode. On the other hand, the parameter TIi indicates the idle duration which

lies in between the busy periods.

3.1.2

Power Saving Class of Type II

The most remarkable feature of PSC of Type II in 16e is allowance of packet delivery in listening windows. Considering that η is denoted as the total number of packets acquired from both the DL in the detection window and the UL in the subsequent

as ωη,n= η X j=1 e−λdTDn j! (λdTDn) j _· e−λuTL (η − j)!(λuTL) η−j_{. (3.8)}

The capacity of the listening window is denoted as the maximum number of packets (DL

plus UL) that can be served within the duration TL. The average value of capacity can

be represented as C = ⌊TL· µ⌋, where 1/µ is the mean service time for both the DL and

the UL packets. If η is less than or equal to the capacity C, the data transmission will be completed in the listening window, which results in the preservation of the sleep mode. Moreover, the regular termination for Type II shares the same definition with Type I, however, the causes that induce this termination is considered different. The regular termination for Type II in the nth cycle can be attributed to the composite effects as

follows: (a) there is no UL packets arrived during the time interval TSk ∀ k ≤ n, (b) the

parameter η ≤ C for all the sleep cycles less than n, and (c) the parameter η > C at the nth sleep cycle. Therefore, the probability of regular termination for PSC of Type II at the nth cycle can be redefined as

φR(e_n II) = n Y i=1 e−λuT_Si ! _n−1 Y i=1 πi ! (1 − πn) (3.9) where πi , PCη=0ωη,i.

On the other hand, the interrupted termination is redefined as the case that the sleep mode is terminated at a random time instant within the “sleep window” because of the transmission allowance during the listening window. Consequently, the interrupted termination for Type II at the nth cycle is obtained as follows: a) There is no UL

packets arrived during TSk ∀ k ≤ n − 1; b) The parameter η ≤ C for all the sleep cycles

Therefore, the probability for interrupted termination for PSC of Type II at the nth cycle can be expressed as

φI(e_n II) = n−1 Y i=1 e−λuT_Si ! _n−1 Y i=1 πi ! 1 − e−λuT_{Sn
. (3.10)}

Furthermore, the random variable Tu,nas denoted in (3.3) should be redefined for Type

II as T_u,n(eII) =      Tu if SCn−1 < Tu < SCn− TL 0 otherwise (3.11)

where the PDF of Tu,n becomes

f Tu,n(eII)(t) =        λue−λut RSCn −TL SC_n−1 λue−λuxdx if SCn−1< Tu< SCn−TL 0 otherwise. (3.12)

The average value of Tu,n for Type II can also be computed as

T(e_u,nII) = RS_Cn−TL S_Cn−1 xλue −λux_dx RS_Cn−TL S_Cn−1 λue−λuxdx . (3.13)

3.2

Analytical Model for IEEE 802.16m

Utilizing the approach similar to the previous section, the proposed analytical model for 16m sleep mode mechanism is properly examined in the following few paragraphs.

Assuming that Poisson arrival rates of DL and UL packets are also denoted by λd

and λu respectively, and λ , λd + λu. The average service rate of packet delivering

equals µ. The analysis will be focused on the sleep mode operation for Type I of 16m.

that the Analysis Period of the proposed model represents the duration between the start of initial sleep cycle and the renewal point, as illustrated in Fig. 2.2 (The duration of normal mode is assumed to be omitted herein due to its instant occurrence compared to the whole executing time line).

As indicated in (3.3), (3.4), and (3.5), according to the remaining inter-arrival time

of the UL packets in 16m (Tu(mI)), the random variable T(m

I₎

u,n , its PDF f

Tu,n(mI)(t), and

the average value T(m_u,nI) can be defined in the same way. It is noticed that herein the

remaining inter-arrival time of the UL packets only owns a single value (unlike Tu,i

r for

the ith connection in 16e), owing to all the connections of the AMS are bound into a sleep cycle setting, which is so called an AMS-based scheme of 16m.

It has been mentioned in Section 2.2, UL traffic in the IEEE 16m does not affect the operation of the sleep mode. It is also specified that if the ABS receives the bandwidth request from the AMS, it shall regard that both DL and UL data transmission are allowed. In other words, during the UL transmission, the DL packets buffered at the ABS can be sent to the AMS at the same time. Note that if a DL packet arrives at the listening window of the current sleep cycle, it should wait for transmission until the next listening window, unless there is UL traffic transmitted during the period of the remaining detection window.

In order to decide whether the listening window in the renewed initial sleep cycle is

extended or not, a probability factor χn should be defined at first based on probability

distribution of the amount of issued packets, ωη,n, in (3.8). The average value of the

capacity of the default listening window is also expressed as C = ⌊TL· µ⌋. Therefore,

the probability that the listening window in the renewed initial sleep cycle will not be

extension will be 1 − πn. The probability factor χn is thus defined as χn,      πn not extended 1 − πn extension happened. (3.14)

For fully consideration of the situations that the DL and UL traffic occur in differ-ent order, three conditions of termination of the Analysis Period are listed as follows, wherein the renewal point occurs at the end of the nth sleep cycle, i.e. the AMS receives

the positive traffic indication for the sake of DL traffic coming within TCn.

3.2.1

Condition A

There is DL traffic only throughout the Analysis Period. This condition is caused by the integrated effects as follows: (a) there does not exist any UL and DL packets arrived

in the duration of SCn−1 and SCn respectively (where SCn =

Pn

i=1TCi), and (b) at least

one DL packet arrives within the duration of TCn. The probability of Condition A can

be expressed as φA(m_n I)= n−1 Y i=1 e−λdT_Ci ! 1 − e−λdTCn
n Y i=1 e−λuT_Ci ! · χA_n (3.15) where χA n = χn in (3.14).

3.2.2

Condition B

There are DL data arriving before the the transmission of UL traffic located in the nth sleep cycle. This situation should be considered as one of the terminations of the Analysis Period, because during the UL transmission, the arrived DL packets will be served together, however, these DL data will originally make the subsequent traffic indication message become positive, that is, the occurrence of the renewal point. This

condition can be attributed to the following effects: (a) there does not exist any DL

packets arrived in the duration of SCn−1, (b) at least one UL packet is sent in TCn,

and (c) at least one DL packet arrives before the transmission of the UL data. The probability for Condition B can be obtained as

φB(m_n I) = n−1 Y i=1 e−λdT_Ci ! h 1 − e−λd(Tu,n−S_Cn−1)i_· 1 − e−λuT_{Cn
· χ}B n. (3.16) It is noted that χB

n is redefined with some modification in ωη,n as:

ω_η,nB ≅ η X j=1 e−λd(SCn−Tu,n(mI)) j! [λd(SCn− T (mI₎ u,n )]j· e−λuTL (η − j)!(λuTL) η−j_{. (3.17)}

Furthermore, due to the randomness of the variable Tu,n(mI), average values of (3.16) and

(3.17) shall be acquired as φB(m_n I) = Z S_Cn S_Cn−1 φB (m_n I)f Tu,n(mI)(t)dt (3.18) and ωB_η,n = Z S_Cn S_Cn−1 ω_η,nB f Tu,n(mI)(t)dt. (3.19) Accordingly, χB

3.2.3

Condition C

There is at least one UL data packet arriving before the renewal point, and DL data arrive in behind. Three events are account for this condition: (a) there does not

exist any DL packets arrived in the duration of SCn−1, (b) at least one UL packet is

transmitted within the duration TCn, and (c) at least one DL packet occurs after the

transmission of UL packets. The probability of Condition C can be computed as

φC(mI) n = n−1 Y i=1 e−λdT_Ci ! 1 − e−λuTCn
·  1 − e−λd(SCn−Tu,n(mI))  · χC_n (3.20)

At the same time, the presentation of χC

n needs some modification in ωη,n:

ωC_η,n = η X j=1 e−λdT_Cn∗ j! (λdT ∗ Cn) j_· e−λuTL (η − j)!(λuTL) η−j _(3.21) where T∗ Cn = SCn − T (mI₎

u,n − E[Tnu trans], and the term E[Tnu trans] denotes the mean

time duration utilized to UL transmission in the nth sleep cycle, i.e. E[Tu trans

n ] = 1 µ P∞ i=0i · e−λuTCn(λuT_Cn)i

i! . The mean value of ω

C

η,n is obtained by the same way in (3.19).

Consequently, χC

n can be expressed as (3.14) by applying ωCη,n as well.

These probabilities of conditions will be used for the performance evaluation in the next chapter.

Chapter 4

Performance Analysis of IEEE

802.16e/m Systems

In this chapter, two performance metrics, the sleep ratio and mean waiting time, are discussed in the following two sections. Both the 16e and 16m systems are investigated in accordance with the two metrics.

4.1

Sleep Ratio

4.1.1

As for IEEE 802.16e

In this subsection, the sleep ratio R of 16e is defined as the ratio of the average sleep

time to the average Analysis Period, i.e.1

R(e) , E[T

∗ (e)

S ]

E[T_S(e)] + E[TN]

(4.1) 1_{It is noticed that the superscript (e}I_{) and (e}II_{) are simplified to (e), which indicates it is suitable}

for PSC of Type I and Type II for 16e, i.e., both Type I and II share the common expression. For example, (4.2) is a simplified form of E[TS(eI)] =

P∞ n=1(φ R(eI₎ n · SCn+ φ I(eI₎ n · T (eI₎

u,n) and E[T (eII₎ S ] = P∞ n=1(φ R(eII₎ n · SCn+ φ I(eII₎ n · T (eII₎ u,n ).

where T_S(e) and TN represent the lengths of the sleep mode and the normal mode of 16e

as shown in Fig. 2.1. The parameter T_S∗ (e) in (4.1) is the length of sleep mode excluding

total involved listening windows, i.e. the summation of the pure sleep windows. The

mean value of T_S(e) can be calculated according to conditional probabilities of both the

normal and the interrupted terminations as

E[T_S(e)] = E[T_S(e)|regular termination]

+E[T_S(e)|interrupted termination]

= ∞ X n=1 (φR (e)_n · SCn + φ I (e) n · T (e) u,n) (4.2)

Considering that δ is denoted as the δth sleep cycle where E[T_S(e)] exists, i.e.

δ = max ( n : n X i=1 TCi < E[T (e) S ] ) + 1. (4.3)

Therefore, E[T_S∗ (e)] can be acquired as

E[T_S∗ (e)] = δ−1 X i=1 T_S(e) i + min n

(E[T_S(e)] − SCδ−1), T_S(e)

δ

o

(4.4)

On the other hand, the expected value of TN can be obtained by referring from [20]

as

E[TN] = E[TB0] + κ · (E[TIi] + E[TBi6=0]) (4.5)

where the meanings of TB0, TBi6=0, and TIi have been explained in Section 3.1.1. The

parameter κ is denoted as the average number of alternated cycles before the idle period

has reached the timeout value τ , which is determined as κ =P∞

i=0i · (1 − Pτ)i· Pτ =

as in [21], both E[TBi6=0] and E[TIi] can be obtained as E[TBi6=0] = 1 µ − λ (4.6) E[TIi] = 1 λ. (4.7)

Assuming that the probability of i packets coming before the beginning of the normal

mode is denoted as ϕi, the mean value of the first busy period can be computed by

extending the concept from [22] as

E[TB0] =

∞

X

i=1

(i · E[TBi]) · ϕi (4.8)

It is noticed that ϕi is the only remaining parameter that is required to be determined

in order to complete the modeling of the sleep ratio of 16e. The computation of ϕi will

be separately discussed for Type I and Type II as follows.

4.1.1.1 Type I

The parameter ϕ(e_i I) will be acquired based on both the regular and the interrupted

terminations. For regular termination at the nth cycle, the probability of i packets that are initiated before the start of the normal mode can be represented as

ϕR(e_i,nI) = Φ

R(eI₎

i,n

1 − ΦR(e_0,nI) (4.9)

with i ≥ 1. ΦR(e_i,nI) is the probability of i DL packets in both the nth detection window

and the next listening window as

ΦR(e_i,nI) = e

−λd(TDn+TL)

i! [λd(TDn+ TL)]

On the other hand, for the interrupted termination case at the nth cycle, the probability of i packets (DL plus UL) before the initiation of the normal mode is acquired as

ϕI(e_i,nII)= ΦI(e_i−1,nII) (4.11)

with i ≥ 1. ΦI(e_i,nII) is the probability of i DL packets arrived before the start of the

interrupted termination at the nth cycle as

ΦI(e_i,nI) = e −λd(Tu,n(eII)−S_Dn−1) i! h λd(T(e II₎ u,n − SDn−1) ii (4.12)

Due to the randomness of the variable Tu,n(eII), the mean value of (4.11) is acquired as

ϕI(e_i,nII)=

Z S_Cn

S_Cn−1

ϕI(e_i,nII)f_T(e_u,nII)(t)dt. (4.13)

As a result, ϕ(e_i II) can be derived by combining (3.6), (3.7), (4.9), and (4.13) as

ϕ(e_i II)=

∞

X

n=1

ϕ_i,nR(eII)φR(e_n II)+ ϕ_i,nI(eII)φI(e_n II). (4.14)

4.1.1.2 Type II

Similar to the above discussion, both the regular and the interrupted termination cases are considered for the PSC of Type II in 16e. For regular termination, a portion of the data packets will be transmitted within the listening window; while the remaining packets will be delivered by starting the normal mode at the end of the listening window. Therefore, the probability of i packets initiated before the start of the normal mode is acquired as

ϕR(e_i,nII) = ω(i+C),n

1 −PC

ωj,n

with i ≥ 1, where ω(j,n is same as (3.8). For interrupted termination, the probability

ϕI(II)_i,n becomes

ϕI(e_i,nII) = ΦI(e_i−1,nII) with i ≥ 1 (4.16)

ΦI(e_i,nII) = e −λd(Tu,n(eII)−S_Dn−1) i! h λd(T(e II₎ u,n − SDn−1) ii . (4.17)

The mean value of ϕI(II)_i,n can also be obtained as

ϕI(e_i,nII)=

Z S_Cn−TL

S_Cn−1

ϕI(e_i,nII)f_T(e_u,nII)(t)dt. (4.18)

Consequently, ϕ(II)_i is computed by combining (3.9), (3.10), (4.15), and (4.18) as

ϕ(e_i II)=

∞

X

n=1

ϕ_i,nR(eII)φR(e_n II)+ ϕ_i,nI(eII)φI(e_n II). (4.19)

4.1.2

As for IEEE 802.16m

On account of the continuous proceeding of sleep mode in 16m, the sleep ratio R needs to be redefined as R(m) , E[T ∗ (m) S ] E[T_S(m)] + E[TU L] (4.20)

where T_S(m) is the length of the summation of sleep cycles within the Analysis Period,

and TU Lindicates the additional time duration used for UL data transmission. The term

T_S∗ (m) also denotes the amount of pure sleep windows, i.e., the length of the Analysis

Period excluding any awake state, such as the listening windows and the transmission

of the aforementioned three conditions:

E[T_S∗ (m)] = E[T_S∗ (m)|Condition A] + E[T_S∗ (m)|Condition B] +

E[T_S∗ (m)|Condition C] = ∞ X n=1 {(φA(m)_n + φB(m)_n + φC(m)_n ) n X i=1 TSi ! +φA ext(m)_n " _n X i=2 TSi+ (TCmin− TLA_ext) # +φB ext(m)_n " _n X i=2 TSi + (TCmin− TLB_ext) # +φC ext(m)_n " _n X i=2 TSi + (TCmin − TLC_ext) # } (4.21)

where φk ext(m)n represents φk(m)n with χk_n = 1−πnare substituted, k ∈ A, B, C. Moreover,

the length of extended listening windows can be obtained by following the notion of (4.5) as TLext = ∞ X i=1 i ·  1 µ − λ  · Ωi (4.22)

with Ωi equals to ϕR(e

II₎

i,n in (4.15). It is noted that the superscript k of TLk

ext in (4.21),

the corresponding ωk

η,n, k ∈ A, B, C should be exploited.

Suppose that δ∗_{is regarded as the average δ}∗_{th sleep cycle where E[T}∗ (m)

S ] is located, that is, δ∗ _{= min} ( n : n X i=1 TSi > E[T ∗ (m) S ] ) . (4.23)

Consequently, the remaining parameters in (4.20) can be determined as

E[TU L] =

E[Number of occured UL packets] µ = 1 µ ∞ X i=0 i · e −λuE[TS(m)](λ uE[TS(m)])i i! (4.24)

where E[T_S(m)] =Pδ∗

i=1TCi.

4.2

Mean Packet Delay

Considering that the serving policy of the BS in 16e or the ABS in 16m is first-come-first-serve (FCFS) and the M/G/1 queueing system is adopted, the average packet delay is evaluated as follows.

4.2.1

As for IEEE 802.16e

The mean waiting time of a packet in 16e is defined by including both the queueing time and the service time as

E[W(e)_{] =E[W}

B0]PB0 + U(E[WL1]PL1 + E[WLi6=1]PLi6=1)

+ E[WBi6=0](1 − PB0 − U(PL1 + PLi6=1)) (4.25)

where U = 0 for PSC of Type I and U = 1 for Type II. WBi is the waiting time

in the ith busy period with probability PBi. WLi represents the waiting time in the

listening window with its probability PLi while Type II is considered. According to

the Pollaczek-Khintchine mean value formula of M/G/1 queueing system as in [21],

E[WBi6=0] can be obtained as

E[WBi6=0] =

ρ

λ +

ρ2_{+ λ}2_σ2

2λ(1 − ρ) (4.26)

where σ2 _{is the variance of the service time and ρ = λ/µ stands for the traffic intensity.}

waiting time in the first busy period can be calculated as

E[WB0] = E[WBi6=0] + E[TV]. (4.27)

The parameter TV is the remaining vacation time, which can be expressed as (4.28)

because of the average sleep cycle δ.

E[TV] = TDδ + TL 2 · PR + (1 − PR)(1 − ΦI(e)0,δ ) · T(e)_u,δ− SCδ−1 2 (4.28)

where PR = (φR(e)_δ )/(φR(e)_δ + φI(e)_δ ). The remaining terms within (4.25) will be computed

for both Type I and Type II below.

4.2.1.1 Type I

The only parameter that is left to be determined for Type I is the probability of the average number of packets initiated in the first busy period, i.e.

PB0 = ϕ(eI₎ + λ · E[TB0] λ · E[TN] + ϕ(eI) (4.29) where ϕ(eI₎ = P∞ i=1i · ϕ (eI₎

i represents the average number of packets happened at the

start of the normal mode.

4.2.1.2 Type II

Considering νi,n is denoted as the probability of i DL packets at the nth detection

parameter νi,n can be obtained as νi,n= e−λdTDn i! (λdTDn) i_· C−i X j=0 e−λuTL j! (λuTL) j ! · 1 πn . (4.30)

Its expected value in terms of i can be computed as

νn =

C

X

i=0

i · νi,n. (4.31)

Moreover, according to the M/G/1 queueing system with multiple vacations, the mean waiting time in the listening window can be approximated as

E[WLi] ≅ TDi 2 + νi 2 · 1 µ. (4.32)

It is noted that the waiting time from the UL packets happened within the listening window is ignorable considering the comparably smaller time duration of the listening window. Consequently, the other parameters within (4.25) for Type II of 16e can be calculated as follows according to the average sleep cycle δ.

PB0 = λ · E[TB0] + ϕ (eII₎ λ · E[TN] + ϕ(eII)+ ν1+ ν · (δ − 1) (4.33) PL1 = ν1 λ · E[TN] + ϕ(eII)+ ν1+ ν · (δ − 1) (4.34) PLi6=1 = ν · (δ − 1) λ · E[TN] + ϕ(II)+ ν1+ ν · (δ − 1) (4.35) where ϕ(eII₎ = P∞ i=1i · ϕ (eII₎

i and ν = νi6=1 since the value of νi6=1 are the same for all

4.2.2

As for IEEE 802.16m

On the other hand, the average packet delay for 16m can be computed as the sum of the wait time for serving in the listening window and the time spent by the UL packets

within the additional duration of the UL transmission, i.e. E[W(m)_{] = E[W}

L] + E[WU L]

Similarly, E[WL] can be further expressed as

E[WL] = E[WM/G/1] + E[TV] (4.36)

where E[WM/G/1] is the waiting time of a normal M/G/1 queuing system, which is

equal to (4.26). Also, E[WU L] = 1 µ + (λu/µ)2+ λ2uσ2 2λu(1 − λu/µ) . (4.37)

Furthermore, TV is the remaining vacation time of the system and its average value

would be E[TV] = TCδ∗ 2 · PA+ (T(m)_u,δ∗− S_Cδ∗−1) 2 · PB+ TC∗ δ∗ 2 · PC (4.38)

according to the average sleep cycle δ∗_{. Moreover, P}

k = Φkδ∗/(ΦA_δ∗ + ΦB_δ∗ + ΦC_δ∗), where Φk δ∗ = φ k(m) δ∗ + φ k ext(m) δ∗ , k ∈ A, B, C (mean values of φ k(m) δ∗ and φ k ext(m) δ∗ shall be utilized for k = B, C).

Chapter 5

Proposed POMDP-based Sleep

Window Determination (PSWD)

Approach

According to the performance analysis, it is intuitively observed that the 16m seems to be more power efficient than that of 16e. However, there are numbers of redundant under-utilized listening windows in the sleep mode operation of 16m owing to the scheme of binary-exponential growth of sleep cycles adopted by 16m. Moreover, it is also responsible for excessive energy cost during state transition, i.e., switching from sleep

AMS ABS S₁ ●●● frame pkt1 ● ●● ●● ● τ L TS1 TL TS2 Sleep Mode Normal Mode S ts 1 Decision Epoch d1 L δ δ 1st Control Cycle C1

Decision Epoch d2 Decision Epoch d3 2nd Control Cycle C2

TL

S2 S3

windows to listening windows and vice versa. It is thus motivated that a more flexible sleep mode mechanism, i.e., a sleep windows decision approach should be designed which adaptively adjusts the length of sleep windows based on the traffic state. In [24] recently published, a statistical sleep window control (SSWC) approach has been proposed for the sleep windows decision problem under tolerable average packet delay for non-real-time DL traffic, that is, Type I in 16m. In this work, the design concept is further extended in order to be fulfilled for all traffic patterns and power-saving types in 16m, including both Type I and Type II. Furthermore, both the DL and UL traffic are also considered during the selection of sleep windows sizes. First of all, the definition of control cycles for the PSWD approach is stated as follows.

Definition 1 (Control Cycle). Given an ABS and an AMS that expects to enter the

sleep mode or has stayed in the sleep mode, a control cycle Ci is defined as a time

duration consisting of a decision epoch di, a sleep window Si, and a listening window

Li. The ABS determines the length of the sleep window Si at the decision epoch di. The

AMS stays in the power-saving mode during the sleep window with length TSi and wakes

up for data transmission in the listening window Li until finishing serving all packets,

then enters the subsequent control cycle.

Fig. 5.1 illustrates the ideal sleep mode operation of a 16m AMS which the proposed PSWD approach intends to achieve, wherein all the control signals are omitted for the

sake of description convenience. Each control cycle Ci (i 6= 1) is overlapped with the

adjacent control cycles Ci−1and Ci+1. The first control cycle C1begins at the last frame

of AMS’s idle period in the normal mode. The remainder control cycles are individually started at the end of every listening window within the previous control cycle.

The target of PSWD approach is to find adequate length of sleep window in each control cycle in light of present traffic state, which meets the delay constraint of packets and maximizes the power-saving efficiency as possible. According to the process of

ongoing sleep mode parameter update mentioned in Section 2.3, in the proposed PSWD approach, the ABS can inform an AMS about the calculated length of each sleep window without any additional control overhead by using originally defined messages, such as AAI SLP-RSP or AAI TRF-IND. On the contrary, an AMS may also send its UL traffic condition through AAI SLP-REQ in order to provide the reference UL information to the serving ABS. It is noted that by means of exploiting such parameter negotiation scheme, each sleep window in every control cycle belongs to a brand-new initial sleep cycle, hence the proposed PSWD approach can be applied to no matter Type I or Type II of 16m.

As shown in Fig. 5.1, the calculated length of sleep window should meet the tolerable

delay, e.g. for the first sleep window S1, it shall be terminated before the expiration of

the first coming packet pkt1, that is, the termination selected at the decision epoch d1

has to fall within the range δ. Consequently, it is inferred that the determined length of each sleep window is dominated by the knowledge of the current traffic patterns, especially DL traffic in 16m, for the interruption resulted from UL transmission at any time may have no impact on the length and phase of the sleep cycles. Nevertheless, these kinds of traffic states are considered difficult to be acquired directly. Only the number of packets arrived in the buffer during the previous control cycle can be observed, which may provide sufficient information for the ABS to estimate the potential state of present traffic.

For the situation described above, a POMDP [25] [26] technique is fairly feasible for the ABS to speculate about the present state of traffic at each decision epoch by the observed information from the buffers. In the following three sections, details of the proposed PSWD method will be introduced, which consist of the estimation procedure for current traffic state by the POMDP scheme, the evaluation metrics, and the sleep window determination policy of PSWD approach.

B(dt) Belief state Sleep window determinaon Arrived PDUs observaon (from buffer) Traffic state B(dt+1) S(dt-1) _S(dt) _S(dt+1) z(dt-1) _z(dt) _z(dt+1) B(dt-1) Hidden Observable dt-1 Decision epoch dt dt+1 a(dt-1) _a(dt) _a(dt+1)

Figure 5.2: Schematic diagram of POMDP model for PSWD approach

5.1

Traffic State Estimation

The procedure of traffic state estimation resorts to a POMDP model in order to conjec-ture the present traffic state at each decision epoch. A typical POMDP model can be expressed by a tuple hS, A, T , Z, O, Ri, where S is a set of states, A is a set of actions, T is a set of state transition probabilities, Z is a set of observations, O is a set of observation probabilities, and R is a set of immediate rewards. In the proposed PSWD approach, the source of DL and UL traffic are generated by a discrete-time Markov-modulated Poisson process (dMMPP), which is considered more general than the con-ventional Poisson traffic, and can be capable of capturing the correlation characteristics in the modern Internet and multimedia traffic at multiple time scales [27] [28] [29]. Here

S consists of two components: Sd and Su which correspond to the set of dMMPP states

of DL and UL traffic, respectively. Also, {Td, Tu} ∈ T are related to the state transition

probability matrixes of DL/UL direction. Furthermore, the set of actions is defined as

A = {a1, a2, · · · , aN} where an represents the action of selecting a sleep window of

length TSan corresponding to the outputs of the PSWD approach.

Considering a sequence of control cycle {C1, C2, · · · , CT} in the proposed SSWC

Fig. 5.2 depicts the schematic diagram of the POMDP model for the proposed PSWD

approach (as for DL traffic). At each decision epoch dt ∈ D, the traffic state s(ddt) or

s(dt)

u ∈ S is considered hidden and unobservable. However, the number of packets that

arrived in the buffer of ABS/AMS during the previous control cycle Ct−1 is available

and can be acquired. Thus the set of observations on the quantity of arrivals is written

as Zd = {z_d(d1), z_d(d2), · · · , z(d_dT)} where z_d(di) denotes the number of DL packets arrived at

the ABS in the interval between the (i − 1)th and the ith decision epoches, and Zu can

also be defined in this way. The observation probability of DL packets can be defined as o(z(dt) d , a (dt−1)_{, s}(dt) d ), P r(z (dt) d |a (dt−1)_{, s}(dt) d ) = (λ (dt) d TS_a(dt−1))z (dt) d z(dt) d ! e−(λ (dt) d TS a(dt−1))_{, (5.1)}

which is a conditional probability of an observation z(dt)

d ∈ Z at decision epoch dtgiven

the action (i.e. length of previous sleep window) a(dt−1) _{∈ A chosen at d}

t−1 and the

present DL traffic state s(dt)

d ∈ S at dt, in which arrival rate equals λ(ddt).

In order to nearly achieve the optimal results, the notion of belief state is introduced in the POMDP model by referring to the recent history of previous observations so as to estimate the present traffic state more precisely than merely by utilizing most recent

observations from the buffer. Given a decision epoch dt ∈ D, the set of belief state

of DL traffic is defined as Bd(dt) = {b(s(dd 1t)), b(s

(dt)

d 2), · · · , b(s

(dt)

d M)}, which represents the

estimated probability distribution over the set of traffic states S = {sd 1, sd 2, · · · , sd M}.

Each element b(s(dt)

d j ) denotes the probability of DL traffic state sd j at decision epoch

dt. It is noted that 0 ≤ b(s(d_{d j}t)) ≤ 1, ∀sd j ∈ Sd and P_{∀sd j} b(s(d_{d j}t)) = 1, ∀dt ∈ D since

the DL traffic must belong to one of the states within the Sd set at any given decision

by exploiting previous action a(dt) _{∈ A and the corresponding observation z}(dt+1)

d ∈ Z.

Thus each element b(s(dt)

d j ) of the belief state Bd(dt+1) can be derived as 1

b(s(dt) d j ) = P r(s (dt) d j |Bd(dt−1), a(dt−1), zd(dt)) (5.2) = P r(z (dt) d |a(dt−1), s (dt) d j , Bd(dt−1))P r(sd j(dt)|a(dt−1), Bd(dt−1)) P r(z(dt) d |a(dt−1), Bd(dt−1)) (5.3) = o(z(dt) d , a(dt−1), s (dt) d j ) P s(dt−1)_{d i} ∈Sdpi,jb(s (dt−1) d i ) P s(dt−1)_{d i} ∈Sd P s(dt)_{d j} ∈Sdb(s (dt−1) d i )pi,jo(zd(dt), a(dt−1), s (dt) d j ) . (5.4)

It is noted that the belief state is a integrated statistics for the entire history of the process, which progressively merges the effect of previously determined action and the corresponding observation at each decision epoch. Since the belief state is updated at each decision epoch, the time complexity can be calculated as O(|S|), where |S| represents the total number of states in S, including both DL and UL traffic. By means of the belief state, more precise traffic states can be appraised via exploiting the proposed PSWD approach.

5.2

Evaluation Metrics

Since the proposed PSWD approach intends to determine the appropriate action, i.e. selection of the length of each sleep window based on the estimated traffic state, the per-formance should be evaluated first by a variety of state/action pair. Owing to frequent state transition in 16m between sleep windows and listening windows, two performance metrics, average energy cost and mean packet delay, are investigated in order to mani-fest the improvement in the PSWD approach by taking the power consumption of state 1_{For UL traffic, the observation probability and the belief state can be derived in the same way as}

(5.1) and (5.2) by substituting λ(dt)

switching into consideration. The evaluation metrics corresponding to each state/action

pair (sd i, su k, an), ∀sd i ∈ Sd, ∀su k ∈ Su and ∀an∈ A, are described as follows.

5.2.1

Average Energy Cost

To evaluate the power consumption of an AMS in the sleep mode, the energy cost is

defined as the average energy consumption per frame during a control cycle. Let εS and

εB denote the energy consumption per frame within the sleep window and busy frame

in each listening window, respectively. Moreover, the energy consumption of switching

between listening windows and sleep windows is considered as εSW. The average energy

cost of the (sd i, su k, an) pair can be expressed as

E(sd i, su k, an) ={2εSW + εSE[TS(sd i, su k, an)] + εBE[TL(sd i, su k, an)]

+ (1 − e−λu kT_San)(2ε

SW + εBE[TU L(sd i, su k, an)])}

/{E[TS(sd i, su k, an)] + E[TL(sd i, su k, an)] + E[TU L(sd i, su k, an)]},

(5.5)

wherein E[TS(sd i, su k, an)] and E[TL(sd i, su k, an)] represent the expected length of

the sleep window and the following listening window, respectively. Since the action an

is determined according the state (sd i, su k), E[TS(sd i, su k, an)] is intuitively equal to

TSan; while E[TL(sd i, su k, an)] can be derived by applying the Little’s theorem [21] as

E[TL(sd i, su k, an)] =

λd iTSan

µ − λd i

Furthermore, E[TU L(sd i, su k, an)] denotes the average length of additional duration

utilized for UL packets transportation in each control cycle, which is expressed as

E[TU L(sd i, su k, an)]) =

λu k

µ (E[TS(sd i, su k, an)] + E[TL(sd i, su k, an)]) . (5.7)

5.2.2

Mean Packet Delay

The packet delay can be acquired by the aforementioned process of 16e/m analysis. Since the packet arrival follows the Poisson distribution in each state ∈ S and the service rate is also assumed as general distribution, a dMMMP/G/1 queueing model (that is, an M/G/1 queueing model for each individual state) with server vacation is utilized to describe the packet arrival and departure. The expected packet delay of the

(sd i, su k, an) pair can be expressed as

D(sd i, su k, an) =E[TV(sd i, su k, an)] + E[WM/G/1]

+(1 − e−λu kT_{San) (−E[T}

V(sd i, su k, an)]/2 + E[WU L]) (5.8)

where E[TV(sd i, su k, an)] stands for the average remaining length of sleep window

(remaining vacation time) for arriving packets, which equals to TSan/2; while E[WM/G/1]

and E[WU L] can be obtained directly from (4.26) and (4.37) by substituting λd i and

λu k, respectively. It is noted the negative term of (5.8) means the allowance of delivery

for some buffered DL packets during UL transmission which averagely decrease half the remaining vacation time of total packets.

Based on the evaluation metrics, the immediate rewards of the POMDP model can be assigned, and consequently a suboptimal policy for choosing the length of each sleep window can be constructed afterwards.