IEEE 802.16網路之無線資源管理

國

立

交

通

大

學

資訊科學與工程研究所

博

士

論

文

IEEE 802.16 網路之無線資源管理

Wireless Resource Management in IEEE 802.16 Networks

研 究 生：陳烈武

IEEE 802.16 網路之無線資源管理

Wireless Resource Management in IEEE 802.16 Networks

研 究 生：陳烈武 Student：Lien-Wu Chen

指導教授：曾煜棋 Advisor：Yu-Chee Tseng

國 立 交 通 大 學

資 訊 科 學 與 工 程 研 究 所

博 士 論 文

Submitted to Department of Computer Science College of Computer Science

National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Doctor of Philosophy

in

Computer Science

December 2008

IEEE 802.16 網路之無線資源管理

學生：陳烈武 指導教授：曾煜棋教授

國立交通大學資訊工程學系（研究所）博士班

摘 要

無線城域網路之國際標準 IEEE 802.16 已被定義出來滿足低成本的大範

圍寬頻無線存取(broadband wireless access)，在本篇論文中，我們將充分開發

頻譜再利用(spectral reuse)和競爭碰撞解決(contention resolution)之可能性來

進一步提昇無線頻寬的使用效率。本篇論文內容分為傳輸排程(scheduling)、

封包繞徑(routing)、以及頻寬要求(requesting)三大議題

在第一個研究主題中，我們深入地研究如何在 IEEE 802.16 網狀網路

(mesh network)的資源配置(resource allocation)中充分開發出頻譜再利用，其中

包括繞徑樹建構(routing tree construction)、頻寬配置(bandwidth allocation)、時

槽分派(time-slot assignment)、以及即時資料流(real-time flow)的頻寬保證

(bandwidth guarantee)。我們提出的頻譜再利用 framework 涵蓋了應用層

(application layer)的頻寬配置、媒體存取層(MAC layer)的繞徑樹建構與資源分

享、以及實體層(physical layer)的頻道再利用(channel reuse)。就目前所知，這

是第一個研究成果以數學方式分析出 IEEE 802.16 網狀網路的頻譜再利用程

度，並且設計出完整的 framework 來提昇頻譜再利用的效率。模擬結果顯示

我們所提出之 framework 大幅度地增加了 IEEE 802.16 網狀網路的網路產出量

(network throughput)。

在第二個研究主題中，當 IEEE 802.16 網狀網路的網狀傳輸站(mesh

station)具備移動能力之後，便形成一個由行動中繼傳輸站(mobile relay station)

所構成的行動隨意網路(mobile ad hoc networks)，行動隨意網路由於其極具彈

性的網路架構，已經廣受各方的注目，雖然有許多根據不同準則而為行動隨

意網路所設計的繞徑協定(routing protocol)，但是其中只有極少數考量到已被

許多無線網路設備所支援的多重速率傳輸(multi-rate)之影響。在給定一條傳輸

路徑(routing path)的情況下，我們提供了一套數學分析的工具，假設行動中繼

傳輸站以離散時間隨機方式(discrete-time, random-walk)來移動，進而計算出

此傳輸路徑的期望產出量(expected throughput)，並且將頻譜再利用的因素一

併考量進來。模擬結果顯示我們所提出之數學分析方法可準確地計算出傳輸

路徑的期望產出量，其推導結果可以作為更佳的傳輸路徑選擇(route selection)

準則。

在第三個研究主題中，為了更有效率地使用無線資源，我們進一步地研

究了兩個在 IEEE 802.16 網路中針對 best-effort traffics 解決頻寬要求

(bandwidth request)碰撞的機制。其中一個是定義在標準中的 exponential

backoff 機制，另外一個是我們所提出 single-frame backoff 的 piggyback 機制。

我們分析並比較了這兩個機制在 Poisson traffic 下頻寬要求成功機率(request

success probability)和封包傳輸延遲(packet delivery delay)方面的效能。分析和

模擬結果顯示 piggyback 機制的效能表現比 exponential backoff 要來得出色許

多，可以大幅度地減低頻寬要求的碰撞。

關鍵字：競爭碰撞解決、IEEE 802.16、媒體存取控制、行動計算、資源

配置、網狀網路、封包繞徑、頻譜再利用、WiMAX、無線通訊

Wireless Resource Management in IEEE 802.16 Networks

Student: Lien-Wu Chen Advisor: Prof. Yu-Chee Tseng

Department of Computer Science National Chiao Tung University

ABSTRACT

The IEEE 802.16 standard for wireless metropolitan area networks (WMAN) is defined to meet the need of wide-range broadband wireless access at low cost. In this dissertation, we exploit spectral reuse and contention resolution of IEEE 802.16 networks. This dissertation is composed of three works. In the first work, we exploits spectral reuse in an IEEE 802.16 mesh network through bandwidth allocation, time-slot assignment, and routing tree construction. In the second work, we provides an analytic tool to evaluate the expected throughput of the route with spectral reuse in an IEEE 802.16 relay network. To further improve wireless resource utilization, the last work analyzes and compares two collision-resolution requesting schemes for best-effort (BE) traffics in IEEE 802.16 networks.

In this dissertation, we first study how to exploit spectral reuse in resource allocation in an IEEE 802.16 mesh network, which includes routing tree construction, bandwidth allocation, time-slot assignment, and bandwidth guarantee of real-time flows. The proposed spectral reuse framework covers bandwidth allocation at the application layer, routing tree construction and resource sharing at the MAC layer, and channel reuse at the physical layer. To the best of our knowledge, this is the first effort which formally quantifies spectral reuse in IEEE 802.16 mesh networks and which exploits spectral efficiency under an integrated framework. Simulation results show that the proposed schemes significantly improve the throughput of IEEE 802.16 mesh networks.

On the other hand, when mesh stations have mobility, they form a mobile ad hoc network (MANET) consisted of mobile relay stations. While many routing protocols have been pro-posed for MANETs based on different criteria, few have considered the impact of multi-rate communication capability that is supported by many current wireless products. Given a rout-ing path, the second work provides an analytic tool to evaluate the expected throughput of the route with spectral reuse in a mobile relay network, assuming that hosts move following the discrete-time, random-walk model. The derived result can be added as another metric for route selection. Simulation results show that the proposed formulation can be used to evaluate path throughput accurately.

To utilize the channel bandwidth more efficiently, the third work studies two collision-resolution requesting schemes for best-effort (BE) traffics in IEEE 802.16 networks. One is the exponential backoff scheme defined in the standard and the other is a piggyback mech-anism enhanced by single-frame backoff, called the Request Piggyback (RPB) scheme. We analyze and compare their performance in terms of the request success probability and the packet delivery delay under Poisson traffic. The results show that the RPB scheme outper-forms the exponential backoff scheme and can reduce request collision. Based on the designed scheduling, routing, and requesting schemes, we can further improve the efficiency of wireless resource management in IEEE 802.16 Networks.

Keywords: contention resolution, IEEE 802.16, medium access control, mobile comput-ing, resource allocation, mesh network, routcomput-ing, spectral reuse, WiMAX, wireless communi-cation.

Acknowledgement

Special thanks go to my advisor Prof. Yu-Chee Tseng for his guidance in my dissertation work. I would also like to thank my dissertation committee members: Prof. Chien-Chao Tseng, Prof. Shiao-Li Tsao, Prof. Jan-Jan Wu, Prof. Da-Wei Wang, Prof. Kun-Ming Yu, and Prof. Tong-Ying Juang. They asked me some good questions and gave me useful comments so that I can improve my work in the future.

Let me also say thank to those HSCC members who co-work with me and all guys I meet in NCTU. Because of you, I can have a great time during these years. Finally, I will dedicate this dissertation to my families and Ms. Chen who is my girl friend in the past, my wife in the present, and my children’s mother in the future.

Contents

Abstract (in Chinese) i

Abstract (in English) iii

Acknowledgement v

Contents vi

List of Figures viii

List of Tables x

1 Introduction 1

2 Exploiting Spectral Reuse in Routing, Resource allocation, and Scheduling for

IEEE 802.16 Mesh Networks 4

2.1 Observations and Motivations . . . 4

2.2 Background and Problem Definition . . . 7

2.2.1 Resource Allocation in an IEEE 802.16 mesh network . . . 7

2.2.2 Problem Definition . . . 10

2.3 The Spectral Reuse Framework . . . 11

2.3.1 Basic Concept . . . 12

2.3.3 Routing Module . . . 19

2.4 Bandwidth Guarantee for Real-Time Flows . . . 22

2.5 Performance Evaluation . . . 28

2.5.1 Network Throughputs under Different Network Topologies . . . 29

2.5.2 Network Throughputs under Different Traffics Demands . . . 33

2.5.3 Packet Dropping Ratio of Real-Time Flows . . . 35

2.5.4 Real-Time Flow Granted Ratio . . . 35

3 Route Throughput Analysis with Spectral Reuse for IEEE 802.16 Relay Networks 39 3.1 Observations and Motivations . . . 39

3.2 System Model . . . 40

3.3 Route Throughput Analysis . . . 44

3.3.1 Estimation of the Function f (·) . . . . 46

3.4 Simulation Results . . . 48

4 Design and Analysis of Contention-based Request Schemes for Best-Effort Traf-fics in IEEE 802.16 Networks 52 4.1 Motivations . . . 52

4.2 The Request Piggyback Scheme . . . 52

4.3 Analytical Results . . . 54

4.4 Simulation Evaluation . . . 58

5 Conclusions and Future Directions 61

Bibliography 63

List of Figures

2.1 A bandwidth allocation example in the IEEE 802.16 standard. . . 9

2.2 System architecture of our spectral reuse framework. . . 12

2.3 An example of time-slot assignment for uplink traffics. . . 17

2.4 A special case of the RTC problem. . . 20

2.5 Flowchart of the admission control mechanism. . . 24

2.6 The regular and dense network topologies in our experiments. . . 29

2.7 Comparison of network throughputs in the regular network. . . 31

2.8 Comparison of normalized network throughputs in the dense and random net-works. . . 32

2.9 Comparison of normalized network throughputs under different number of SSs with various uplink traffic demands. . . 34

2.10 Comparison of normalized network throughputs under different uplink traffic demands. . . 34

2.11 Comparison of packet dropping ratios under different number of SSs. . . 35

2.12 Comparison of real-time flow granted ratios under different number of SSs. . 36

2.13 Comparison of real-time flow granted ratios under different traffic loads. . . . 37

2.14 Comparison of real-time flow granted ratios under different non-real-time traf-fic demands. . . 38

3.1 (a) a cellular system to model station mobility, and (b) the “folding” of link

states. . . 41

3.2 Example of link state changes. . . 42

3.3 State transition diagram of a wireless link when n = 5. . . . 43

3.4 A state transition matrix of a wireless link when n = 5. . . . 44

3.5 The 9-hop route with its most interfered region including host 5 ∼ 9. . . . 47

3.6 Expected route throughput vs. tmax 1 : (a) n = 15 and (b) n = 25. . . . 50

3.7 Expected route throughput vs. path length: (a) n = 15 and (b) n = 25. . . . . 51

4.1 The TDD frame structure defined in IEEE 802.16. . . 53

4.2 The state transition diagram of a SS under the RPB model. . . 56

4.3 Comparison of request success probabilities. . . 59

List of Tables

2.1 Comparison of prior works [1–3] and our spectral reuse framework. . . 6 2.2 Summary of notations. . . 11 3.1 The probability distribution for a wireless link to switch from state hx, yi to

Chapter 1

Introduction

To achieve the requirement of wide-range wireless broadband access at a low cost, the IEEE 802.16 standard [4] has been proposed recently. The goal of this standard is to solve the last-mile problem in a metropolitan area network in a more flexible and economical way as opposed to traditional cabled access networks, such as fiber optics, DSL (digital subscriber line), or T1 links [5, 6]. The IEEE 802.16 standard is based on a common MAC (medium access control) protocol compliant with different physical layer specifications. The physi-cal layer can employ the OFDM (orthogonal frequency division multiplexing) scheme below 11 GHz or the single carrier scheme between 10 GHz and 66 GHz.

The IEEE 802.16 MAC protocol supports the point-to-multipoint (PMP) mode and the mesh mode. In the PMP mode, stations are organized as a cellular network, where subscriber stations (SSs) are directly connected to base stations (BSs). Such networks require each SS to be within the communication range of its associated BS, thus greatly limiting the coverage range of the network. On the other hand, in the mesh mode, stations are organized in an ad-hoc fashion. Each SS can either act as an end point or a router to relay traffics for its neighbors. Thus, there is no need to have a direct link from each SS to its associated BS. This leads to two advantages: SSs may transmit at higher rates to their parent SSs or BS, and a BS can serve wider coverage at a lower deployment cost [7].

through multi-hop routing and scheduling, while there is no spectral reuse considered in the IEEE 802.16 standard. The proposed framework includes a load-aware routing algorithm and a centralized scheduling scheme, which consider both bandwidth demands and interference among SSs. Given traffic patterns of SSs, we show how to achieve better spatial reuse and thus higher spectral efficiency.

On the other hand, when mesh stations have mobility, they form a mobile ad hoc network (MANET) consisted of mobile relay stations. The MANET is a flexible and dynamic archi-tecture that is attractive due to its ease in network deployment. Routing is perhaps one of the most intensively addressed issues in MANET. Many different criteria have been used in route selection, including hop count [8], signal strength [9], route lifetime [10], and energy con-straint [11]. Among these metrics, hop count may be the most widely used metric in choosing routes. When a hop-count based routing protocol is given multiple paths, the shortest path is normally selected and a random path is selected when there is a tie. This metric has the advantage of simplicity, requiring no additional measurements and incurring the least number of transmissions. The primary disadvantage of this metric is that it does not take packet loss or available bandwidth into account, especially when network interfaces can transmit at multiple rates [12]. It has been shown in [13] that a route which minimizes the hop count does not necessarily maximize the throughput of a flow.

While it is true that there is no single route selection metric that is able to best fit all possible routing scenarios in MANET, few works have considered the impact of multi-rate communication capability that is widely supported by many current wireless LAN products. For example, IEEE 802.11b supports rates of 11, 5.5, 2, and 1 Mbps, while IEEE 802.11a supports rates of 6, 9, 12, 18, · · · , and 54 Mbps. Route selection is more complicated in a multi-rate MANET than in a single-rate environment. Also, there exists an inherent tradeoff between transmission rates and their effective transmission ranges [14]. To support reliable data transmissions, longer-range communications must use lower rates, and vice versa.

Auto-rate selection protocols [15, 16] do exist at the link level. Reference [17] proposes a multi-rate-aware topology control algorithm to enhance the network throughput in multi-hop ad hoc networks, and [18] uses fast links (with high nominal bit rate) to improve the system through-put in wireless mesh networks. However, they only focus on static network environment without taking mobility into account. Reference [19] proposes a multi-rate-aware sub-layer between the MAC and the network layers to improve resource utilization and to minimize power consumption, but the effect of multi-rate communications at the routing level is not yet fully addressed.

In the second work, we consider a MANET consisted of mobile relay stations where each wireless link can support multiple rates and has the auto-rate selection capability. Given a routing path, this work provides an analytic tool to evaluate the expected throughput of the route with spectral reuse, assuming that hosts move following the discrete-time, random-walk model.

To utilize the channel bandwidth more efficiently, we study the centralized, reservation-based bandwidth allocation mechanism defined in IEEE 802.16 for best-effort (BE) traffics. It adopts Time Division Multiplexing (TDM) for the downlink channel and Time Division Multiple Access (TDMA) for the uplink channel via a request/grant mechanism controlled by the BS. The uplink channel is modelled as a stream of time slots. SSs must send request messages to the BS to reserve uplink bandwidth. There are three factors that may affect the performance of the uplink channel: (i) the portion of request slots per frame, (ii) the collision-resolving procedure, and (iii) the allocation of slots to SSs’ requests. In the last work, we studies the collision-resolution mechanisms for transmitting uplink BE requests to the BS. The request scheme defined in the standard is compared against the proposed Request Piggyback (RPB) scheme.

Chapter 2

Exploiting Spectral Reuse in Routing,

Resource allocation, and Scheduling for

IEEE 802.16 Mesh Networks

2.1 Observations and Motivations

In this work, we study the spectral reuse issue in an IEEE 802.16 mesh network through multi-hop routing and scheduling, while there is no spectral reuse considered in the IEEE 802.16 standard. The proposed framework includes a load-aware routing algorithm and a centralized scheduling scheme, which consider both bandwidth demands and interference among SSs. Given traffic patterns of SSs, we show how to achieve better spatial reuse and thus higher spectral efficiency.

In an IEEE 802.16 mesh network, transmissions can undergo a multi-hop manner. The standard specifies a centralized scheduling mechanism for the BS to manage the network. Stations will form a routing tree rooted at the BS for the communication purpose. SSs in the network will send request messages containing their traffic demands and link qualities to the BS to ask for resources. The BS then uses the topology information along with SSs’ requests to determine the routing tree and to allocate resources. Resources in an IEEE 802.16 network are usually represented by time slots within a frame. Our goal is to solve the resource allocation problem, given the uplink/downlink bandwidth demands of each SS and their link

qualities. There are four issues to be considered:

• Tree reconstruction: How to determine the routing tree based on SSs’ current bandwidth demands and link qualities?

• Bandwidth allocation: How to determine the number of time slots of each SS according to its uplink and downlink bandwidth demands?

• Time-slot assignment: How to assign time slots to each SS in a frame?

• Bandwidth guarantee: How to schedule transmission on time slots for each SS, so that a fixed amount of bandwidth is guaranteed for each real-time flow?

In this work, we investigate the resource allocation problem by exploring the concept of spectral reuse. Although it is well-known that a time slot used by a station can be “reused” by another station if the latter is sufficiently separated from the former, the IEEE 802.16 stan-dard does not explore in this direction. We propose a spectral reuse framework to efficiently allocate resources in an IEEE 802.16 mesh network with global fairness in mind, that is, the bandwidths allocated to SSs will be proportionate to their requests, in an end-to-end (SS-to-BS) sense. Our framework includes a routing tree construction and a centralized scheduling algorithm. The former allows a BS to form an efficient routing tree according to SSs’ band-width demands and interferences. The latter helps a BS to determine bandband-width allocation and time-slot assignment. In particular, when time slots are tight, we show how to adjust scheduling to prioritize real-time from non-real-time traffics so as to guarantee some band-widths for real-time traffics. Note that the tree topology is consistent with the current IEEE 802.16 standard. Also, our framework does not require any change to the message structures and the signaling mechanism defined in the standard.

In the literature, early works on the IEEE 802.16 standard have primarily focused on the PMP mode [20–22]. For the mesh mode, former efforts have devoted to topology design [23],

Table 2.1: Comparison of prior works [1–3] and our spectral reuse framework.

reuse load tree time-slot bandwidth

features modeling1 _{awareness reconstruction allocation guarantee}3

reference [1] partial2 √

reference [2] partial2

reference [3] √ √

our framework √ √ √ √ √

1 _{Mathematical modeling is provided to evaluate the degree of spectral reuse.} 2 _{Initial tree construction is provided, but without tree reconstruction.} 3 _{The guarantee is for real-time flows.}

packet scheduling [24, 25], and QoS support [26, 27]. Reference [28] shows how to manage radio resources in a WiMAX single-carrier network in a distributed manner. Reference [29] discusses how to improve channel efficiency and provide fair access to SSs. The BS allocates time slots to SSs in a per-hop basis in such a way that one-hop nodes will have precedence over two-hop nodes (“hop” in the sense of nodes’ distances to the BS). Similarly, i-hop nodes will have precedence over (i+1)-hop nodes. However, this may lead to starvation of farther-away SSs as the network becomes congested, especially when SSs with smaller hop counts request larger bandwidths. On the contrary, our scheduling algorithm allocates time slots to SSs proportionate to their requests and thus avoids such starvation.

Several studies [1–3] have addressed the issue of spectral reuse to solve the resource allo-cation problem. Reference [1] proposes a routing tree construction and a scheduling algorithm by considering the interference among neighboring SSs. It attempts to find a route to reduce the interference among SSs, and then to maximize the number of concurrent transmissions. How to attach a new SS to a routing tree incurring the least interference is discussed in [2]. In [3], the authors indicate that the network performance highly depends on the order that SSs join the routing tree, and then propose a routing tree reconstruction and a concurrent trans-mission scheme to achieve spectral reuse. As can be seen, the prior works only discuss partial aspects of the resource allocation problem.

Table 2.1 compares the functions provided by other schemes and ours. Our framework offers the most complete solution to the resource allocation problem. The contributions of our framework are four-fold. First, it formally quantifies the spectral reuse in a mesh network, thus capable of achieving higher spectral efficiency. Second, it takes dynamic traffic demands of SSs into account and includes not only a tree optimization algorithm, but also a bandwidth allocation and a time-slot assignment. Third, we propose a way to prioritize real-time from non-real-time traffics, so that a fixed amount of bandwidth is maintained for each real-time flow when resources are stringent. Finally, the proposed framework covers bandwidth alloca-tion at the applicaalloca-tion layer, routing tree construcalloca-tion and resource sharing at the MAC layer, and channel reuse at the physical layer. Extensive performance studies are conducted and the simulation results show that our framework can achieve better spectral reuse and higher network throughput compared with existing results.

2.2 Background and Problem Definition

2.2.1 Resource Allocation in an IEEE 802.16 mesh network

An IEEE 802.16 mesh network is composed of a BS and several SSs. These stations form a routing tree rooted at the BS and transmissions between stations may undergo a multi-hop manner. The IEEE 802.16 MAC protocol supports both centralized and distributed scheduling methods. In this work, we focus on the centralized scheduling to fully exploit spectral reuse.

In the centralized scheduling, the standard supports two control messages, MSH-CSCF (Mesh Centralized Scheduling Configuration) and MSH-CSCH (Mesh Centralized Schedul-ing), to help the BS establish its routing tree and specify transmission schedules of SSs in the network. To achieve this, the BS first broadcasts an MSH-CSCF message containing the routing tree information to the network. An SS receiving such a message can know its par-ent and children in the tree and then rebroadcasts the MSH-CSCF message according to its

index specified in the message. This procedure is repeated until all SSs have received the MSH-CSCF message.

After constructing the routing tree by the CSCF message, SSs can transmit MSH-CSCH:Request messages to request time slots. The transmission order is from leaves to the root. An SS will combine the requests from its children into its own MSH-CSCH:Request message, and then transmits the message to its parent. In this way, the BS can gather band-width requests from all SSs and then broadcasts an MSH-CSCH:Grant message containing the slot allocations to all SSs. Note that the BS can also update the routing tree by containing tree update information in the MSH-CSCH:Grant message. In this case, SSs have to update their positions in the new tree according to the message. Otherwise, the routing tree remains the same as specified in the previous MSH-CSCF message. Note that according to the 802.16 standard, the period during which the MSH-CSCH schedule is valid is limited by the time that the BS takes to aggregate traffic requirements and distribute the next schedule. So the schedul-ing interval is about several frames dependschedul-ing on the size of the mesh network. Therefore, it is reasonable to assume that link data rates and bandwidth demands of SSs are constants during a short period of time.

To allocate bandwidths for SSs, the IEEE 802.16 standard gives an example, as illus-trated in Fig. 2.1. Each SS i first sends its uplink bandwidth demand bUL

i and downlink band-width demand bDL

i to the BS. Let the uplink and downlink data rates of SS i be riUL and

rDL

i , respectively. The ratios of uplink slots allocated to SS 1, SS 2, SS 3, and SS 4 will be bUL 1 +bUL3 +bUL4 rUL 1 : bUL 2 rUL 2 : bUL 3 rUL 3 : bUL 4 rUL

4 (= γ1 : γ2 : γ3 : γ4). Note that here the calculation also

in-cludes the relay traffics. If NUL

totalis the total number of uplink slots per frame, the numbers of

slots allocated to them are γ_P1·NtotalUL 4 i=1γi, γ_P2·NtotalUL 4 i=1γi, γ_P3·NtotalUL 4 i=1γi, and γ_P4·NtotalUL 4

i=1γi, respectively. The bandwidth

allocation for downlink traffics follows the same way.

However, the above bandwidth allocation is very inefficient because a slot is always al-located to only one SS. In fact, SS 2 and SS 3 can transmit concurrently without interfering

1 UL r 1 DL r 3 UL r 3 DL r 4 UL r 4 DL r 2 UL r 2 DL r 1 1 ( UL, DL) b b 3 3 ( UL, DL) b b 4 4 ( UL, DL) b b 2 2 ( UL, DL) b b + + 1 3 4 1 DL DL DL DL b b b r + + 1 3 4 1 UL UL UL UL b b b r 2 2 UL UL b r 3 3 UL UL b r 4 4 UL UL b r 2 2 DL DL b r 3 3 DL DL b r 4 4 DL DL b r

Figure 2.1: A bandwidth allocation example in the IEEE 802.16 standard.

with each other. We can quantify the waste of slots as follows: Given a routing tree T , the

aggregated uplink bandwidth demand dUL

i for each SS i is defined as

dUL i = bULi + X j∈child(i) dUL j , (2.1)

where child(i) is the set of SS i’s children in T . Then, the demand of uplink transmission time for SS i is TUL i = dUL i rUL i . (2.2)

Let us denote the sum of uplink transmission time of all SSs by

CUL total = X i∈T −BS TUL i ,

Therefore, only a ratio of TiUL

CUL

of transmission time of SS i and its interference neighbors be CUL i = X j∈Ei TUL j , (2.3)

where Ei = {i} ∪ I(i) and I(i) is the set of interference neighbors of SS i. From SS i’s perspective, it only sees a ratio of CULi

CUL

total of the uplink slots to be busy. In other words, the

remaining 1 − CULi

CUL

total portion of time is simply idle as seen by SS i. The downlink direction will

suffer from the similar waste.

2.2.2 Problem Definition

The problem with the above waste is due to lack of spectral reuse. Our goal is to solve the resource allocation problem in an IEEE 802.16 mesh network with spectral reuse. Given the uplink and downlink bandwidth demands bUL

i and bDLi and data rates riULand riDL, respectively, of each SS i, we will consider the following four issues:

1. Tree reconstruction: How to organize the routing tree according to SSs’ bandwidth demands and data rates, so that traffic loads among tree nodes can be balanced and the network throughput can be maximized?

2. Bandwidth allocation: How to allocate time slots to SSs according to their bandwidth demands and data rates, so that SSs can fully utilize the channel?

3. Time-slot assignment: How to assign slots of a frame for SSs with global fairness in mind, so that the transmissions between SSs will not conflict with each other?

4. Bandwidth guarantee: How to schedule real-time and non-real-time traffics when re-sources are stringent, so that bandwidth requirements of real-time flows can be main-tained?

2.3 The Spectral Reuse Framework

In this section, we propose our spectral reuse framework to solve the first three issues in the resource allocation problem. In Section 2.4, we will discuss how to extend our framework to provide bandwidth guarantee for real-time flows. Table 2.2 summarizes the notations used in this work. Fig. 2.2 shows the system architecture of our framework. First, the BS collects the MSH-CSCH:Request messages and passes the bandwidth demands and data rates of SSs to the scheduling and the routing modules. The scheduling module is a fast process, which determines the number of time slots and their positions allocated to each SS in each frame. The routing module is a slow process, which continuously monitors the quality of the routing tree and reconstructs the tree when the quality of the tree degrades. That is, when it is found that the tree cannot efficiently deliver the traffics of SSs, a new routing tree will be computed by the routing module. The BS then broadcasts a MSH-CSCH:Grant message containing the new routing tree and time slot allocation of each SS to the network.

Below, we first present the basic concept of our spectral reuse framework, followed by the designs of the scheduling and the routing modules.

Table 2.2: Summary of notations. notation definition

N number of time slots within a data subframe

NUL

total/NtotalDL number of uplink/downlink slots within a frame

NUL

i /NiDL number of uplink/downlink slots allocated to SS i

bUL

i /bDLi individual bandwidth demand of uplink/downlink traffics generated by SS i

dUL

i /dDLi aggregated bandwidth demands of uplink/downlink traffics delivered by SS i

rUL

i /rDLi uplink/downlink data rate of SS i

TUL

i /TiDL demand of uplink/downlink transmission time of SS i I(i) the set of interference neighbors of SS i

Ei set of SSs that contains SS i and its interference neighborhood I(i)

CUL

i /CiDL aggregated TjUL/TjDLof all SS j in Ei

CUL

total/CtotalDL aggregated TjUL/TjDLof all SS j in the network

CUL

MSH-CSCH:Request messages from SSs MSH-CSCH:Grant message to SSs routing module scheduling module

run LTC algorithm to construct a new routing tree if necessary

1. determine the ratios of uplink & downlink slots in a data subframe 2. calculate the numbers of uplink & downlink slots assigned to SSs 3. designate the positions of uplink & downlink slots of SSs

Figure 2.2: System architecture of our spectral reuse framework.

2.3.1 Basic Concept

Earlier, we have indicated that in the uplink case, the scheduling scheme in IEEE 802.16 only assigns pi = T

UL

i

CUL

total portion of uplink slots to each SS i. From each SS i’s view, the remaining

1 − CULi

CUL

total portion of uplink slots are idle. Ideally, SS i may expect the idle portion to be

fairly distributed to all SSs in Eiproportionally. This implies that SS i can share an additional

qi = ³ 1 − CiUL CUL total ´ × TiUL CUL

i portion of uplink transmission time. Thus, the total portion of uplink

transmission time assigned to SS i is

TUL i CUL total + µ 1 − C UL i CUL total ¶ × T UL i CUL i = T UL i CUL i . (2.4)

Similarly, the total portion of downlink transmission time assigned to SS i can be upgraded, ideally, to TiDL

CDL

i .

Unfortunately, the above Eq. (2.4) does not consider the congestion issue in the global net-work. In a non-congested network, the uplink bandwidth of an SS should be able to deliver all traffics from itself plus those from its children. Otherwise, congestion on that SS’s uplink will occur. Therefore, given a non-congested network, if an SS i’s uplink bandwidth is increased

by a ratio of α, a sufficient condition to avoid the network becoming congested is to enforce the parent of SS i to increase its uplink bandwidth by at least a ratio of α. Now, let αi be the ideal ratio of increase by SS i in the uplink direction,

αi = qi pi = ³ 1 − CiUL CUL total ´ × TiUL CUL i TUL i CUL total = C UL total CUL i − 1. The minimum ratio of increase among all SSs is

αmin = min ∀i {αi} = CUL total CUL max − 1 ≥ 0, where CUL

max= max∀i{CiUL}. Therefore, using αminas the global ratio of increase, the portion

of uplink transmission time for each SS i such that the network will not be congested is (1 + αmin) × T UL i CUL total = T UL i CUL max .

Similarly, the portion of downlink transmission time for each SS i such that the network will not be congested is TiDL

CDL

max, where C

DL

max= max∀i{CiDL}.

Note that the above calculation includes the demands of individual SSs as well as relay traffics. So our slot allocation is in an end-to-end sense. Next, we discuss how to adopt this concept to the scheduling module to increase channel efficiency. The routing module will reconstruct the routing tree to further improve the performance of the scheduling module. For readability, we first discuss how the scheduling module works, and then present how the routing module works.

2.3.2 Scheduling Module

Given a routing tree T , the scheduling module should properly allocate time slots to SSs in each frame so that the transmissions of nearby SSs will not cause collision and global fairness among SSs can be maintained. Assuming N to be the total number of slots in a data subframe, the scheduling module involves the following steps:

1. We first choose the ratio of the number of uplink slots to the number of downlink slots to be CUL

max : CmaxDL. Thus, the numbers of uplink and downlink slots in a data subframe

observed by the BS are NUL total = j CUL max CUL max+CmaxDL × N k and NDL total = j CDL max CUL max+CmaxDL × N k , respectively1_. 2. Based on NUL

totaland NtotalDL , we then allocate NiUL = TUL i CUL max × N UL total and NiDL = TDL i CDL max × NDL

totalslots to each SS i for its uplink and downlink traffics, respectively. Note that since

spectral reuse is considered, it is possible thatP_∀iNUL

i > NtotalUL and

P

∀iNiDL > NtotalDL .

3. Next, we need to allocate NUL

i collision-free uplink slots in each data subframe to SS i. These slots are divided into two parts. Part 1 contains TiUL

CUL

total×N

UL

totalslots. Part 2 contains

³ TUL i CUL max − TUL i CUL total ´ ×NUL

totalslots. Part-1 slots are more suitable for real-time traffics because

a packet issued by any SS in T can be delivered to the BS with a latency no more than one frame time (the reason will be explained in Theorem 1). Now we describe how these slots are determined.

• Part-1 slots: These slots are assigned in a bottom-up manner along the tree T . Specifically, we traverse SSs in T according to the transmission order of MSH-CSCH:Request messages. In IEEE 802.16, such order is reverse in hop-count to the BS (that is, largest hop-count first), and is retained as nodes’ IDs in the routing tree for SSs with the same hop-count. Thus, the order of a child SS is always before that of its parent. Following this transmission order, for each SS i being visited, we select the first TiUL

CUL

total × N

UL

total unoccupied slots as its part-1 slots, and then mark

these slots as occupied. This operation is repeated until all SSs are visited.

1_{Recall that C}UL

max and CmaxDL represent the maximum uplink and downlink demands, respectively, seen by

individual nodes. They are bottlenecks of uplink and downlink transmissions. So we use the ratio of CUL maxand CDL

maxto reflect the demands of uplink and downlink slots and use this ratio to distribute slots. Later on, we will

construct the routing tree by minimizing the sum of CUL

maxand CmaxDL to improve spectral reuse. Also, note that

the number of slots should be bounded to integers. However, in the following, we will avoid using floor and ceiling functions for ease of presentation.

• Part-2 slots: We also assign these slots following the transmission order of MSH-CSCH:Request messages. For every SS i being visited, each of its part-2 slots is selected from the first unoccupied slot by any SS in Ei. Then that slot is marked as occupied. The above operation is repeated until all SSs are visited.

Algorithm 1 gives the pseudo code of the above time-slot assignment scheme. 4. We then designate NDL

i collision-free downlink slots to each SS i. These slots are also divided into two parts, where part 1 contains TiDL

CDL

total × N

DL

total slots and part 2 contains

³ TDL i CDL max − TDL i CDL total ´ × NDL

totalslots. For each part, we assign their slots in a top-down manner

along the tree T . Specifically, we traverse SSs in T by the transmission order of MSH-CSCH:Request messages and then assign slots to these SSs following the reverse order. For each SS being visited, we assign downlink slots to them according to the rules specified in step 3.

Consider an illustrative example in Fig. 2.3, where we need to assign uplink slots for five SSs in the network. Let the demand of each of SSs a, b, c, and d be one slot and the demand of SS e be two slots. We assume that the interference neighborhood of an SS contains all its neighbors within two-hop range. First, part-1 slots can be assigned easily in a sequential man-ner (e → c → d → a → b). To assign part-2 slots, observe that the interference neighborhood I(a) of a includes c, d, and e. For e, we assign slot 8 as its part-2 slot since it is the first unoc-cupied slot by SSs in Ee = {a, c, d, e}. Similarly, we assign slot 10 as c’s part-2 slot because it is the only unoccupied slot by SSs in Ec= {a, b, c, d, e}. For a, since Ea = {a, c, d, e}, we assign slot 9 as its part-2 slot. Note that although slot 9 has already been assigned to b, it does not prevent a from using it because b /∈ Ea. From Fig. 2.3, we can observe that any packet issued in part-1 slots can always be delivered to the BS within one frame time. However, a packet issued by e in its part-2 slot takes totally 12 slots to be delivered to the BS, which exceeds one frame time. Note that the above scheduling employs a proportional allocation in

the sense that the bandwidth allocation for each SS is based on its own bandwidth demand, its children’s demands, and the sum of all SSs’ demands in the mesh network. The BS collects all SSs’ demands and allocates bandwidth to them by the ratio of their aggregated demands and CUL

max. Since all aggregated demands of SSs are divided by the same factor of CmaxUL , the

resource is proportionally allocated to SSs. Also, once a slot is allocated to an SS, relaying slots are allocated to its parent SS too. Therefore, the allocation is done in an end-to-end perspective.

Algorithm 1: Time-slot assignment for uplink traffics

Input: numbers of uplink slots for SSs, {NUL

1 , · · · , NnUL}

Output: result of slot assignment, transmit[n][NUL total]

// assign part-1 slots

let SS 1, 2, · · · , n be the transmission order of MSH-CSCH:Request messages in T ; free ← 1; for i = 1 to n do allocated ← free +TiUL CUL total × NUL total;

for j = free to allocated do slot[j] ← i; free ← allocated;

// assign part-2 slots for i = 1 to n do

for j = 1 to NUL totaldo

transmit[i][j] ← NULL;

for i = 1 to n do // mark occupied slots of SSs for j = 1 to N_totalUL do

if slot[j] ∈ Eithen transmit[i][j] ← slot[j];

for i = 1 to n do allocated = ³ TUL i CUL max − TUL i CUL total ´ × NUL total; for j = 1 to NUL totaldo

if allocated > 0 and transmit[i][j] = NULL then transmit[i][j] ← i;

allocated ← allocated −1; for k = 1 to n do

if k ∈ Eithen transmit[k][j] ← i;

deliv-e SS c SS a SS e SS d frame 1 SS b 1 2 3 4 5 6 7 8 9 10 e c c d c a a a b b frame 2 1 2 3 4 5 6 7 8 9 10 e c c d c a a a b b e a parent-child relationship communication link part-1 slots to transmit

SS s and its children s packets part-2 slots to transmit

SS s and its children s packets BS

. . .

. . .

, ,

, ,

Figure 2.3: An example of time-slot assignment for uplink traffics. ered to the destination station within one frame time.

We first prove that part-1 slots are collision-free. For the uplink case, since P_∀iTUL

i =

CUL

total, the total number of part-1 slots is

P ∀i ³ TUL i CUL total × N UL total ´ = NUL

total. Thus, there must be

enough slots assigned to all SSs for their part-1 slots. In addition, since step 3 in the scheduling module guarantees that any two SSs will not select the same uplink slot, part-1 slots in the uplink case are collision-free. Similarly, for the downlink case, sinceP_∀i

³ TDL i CDL total × N DL total ´ = NDL

total, it is guaranteed that there are enough slots assigned to all SSs. Again, since step 4

ensures that two SSs will not choose the same downlink slot, part-1 slots in the downlink case are also collision-free.

We then show that the latency of any packet issued in part-1 slots is bounded to one frame time. For the uplink case, we schedule SSs following the transmission order of MSH-CSCH:Requet messages. Since this order is reverse to the hop-count to the BS, it is guaranteed that we always assign uplink slots of a child SS before its parent. In addition, since each SS has enough uplink slots to relay its children’s packets, any packet issued in part-1 slots can be delivered to the BS within one frame time. For the downlink case, since we schedule SSs following the reverse order of the transmission order of MSH-CSCH:Request messages, we will always assign downlink slots of a parent SS before its children. Again, since each SS has enough downlink slots to relay packets from the BS, we can guarantee that any packet from the BS in part-1 slots can be delivered to the destination SS within one frame time.

Theorem 2 Part-2 slots are collision-free.

We first prove that part-2 slots in the uplink direction are collision-free. In Section 2.3.1, we have shown that each SS can be assigned with TiUL

CUL

max × N

UL

totalslots without congesting the

network. Thus, there are enough slots assigned to all SSs for their part-2 slots. In addition, step 3 in the scheduling module guarantees that any two SSs inside the interference range will not select the same slot. Thus, part-2 slots in the uplink case are collision-free. For the downlink case, since each SS can be assigned with TiDL

CDL

max × N

DL

total slots without congesting the

network, there are also enough slots assigned to all SSs. Similarly, by step 4, we can ensure that two SSs inside the interference range will not choose the same slot. Thus, this theorem still holds in the downlink case.

Remark 1 The IEEE 802.16 mesh mode only supports time division duplex (TDD) for uplink and downlink traffics. The TDD framing is adaptive in that the bandwidths allocated to uplink and downlink traffics can vary. Unlike the PMP mode, there is no clear boundary between uplink and downlink slots in the mesh mode. In this work, we assume that a slot will be used exclusively by only uplink or downlink throughout the whole network.

2.3.3 Routing Module

In Section 2.3.1, we have indicated that the uplink and downlink slots allocated to each SS is inversely proportional to the values of CUL

maxand CmaxDL, respectively. Therefore, the goal of this

routing module is to reconstruct the routing tree, whenever needed, to reduce both CUL max and

CDL

maxso that SSs can receive more time slots.

Definition 1 Given a mesh network G, and bandwidth demands and data rates of SSs in G, the routing tree construction (RTC) problem is to find a routing tree T in G such that the value

of CUL

max+ CmaxDL is minimized.

To prove that the RTC problem is NP-complete, we define a decision problem as follows: Definition 2 Given a mesh network G, bandwidth demands and data rates of SSs in G, and a real number R, the routing tree construction (RTC) problem is to decide whether G has a

routing tree T such that CUL

max+ CmaxDL ≤ R.

Theorem 3 The RTC problem is NP-complete.

First, given routing trees in G, we can calculate the values of their CUL

max and CmaxDL, and

check whether CUL

max + CmaxDL ≤ R. Clearly, this takes polynomial time. Thus, the RTC

problem belongs to NP.

We then prove that the RTC problem is NP-hard by reducing a NP-complete problem, the partition problem [30], to a special case of the RTC problem in polynomial time. Given a set

X where each element xi ∈ X has an associated size s(xi), the partition problem asks whether

it can partition X into two subsets with equal total size.

Consider a special case of the RTC problem in Fig. 2.4, where the interference neigh-borhoods I(a) and I(b) of SS a and SS b are not overlapped. The data rates and bandwidth demands of SSs in Ea∪ Ebare set to r and zero, respectively. Except for those SSs in Ea∪ Eb,

there are n SSs X = {x1, x2, · · · , xn} connected with both SS c and SS d, each with non-zero equal uplink and downlink bandwidth demands.

∪

a b

E

E

Figure 2.4: A special case of the RTC problem.

Here, we reduce the partition problem to the special case of the RTC problem. Let size s(xi) be the sum of uplink and downlink bandwidth demands of each xi ∈ X , and R =

5 2

P ∀i

s(xi)

r . From Fig. 2.4, we can observe that the parent of xi ∈ X is either SS c or SS d. Because the bandwidth demands of all SSs in Ea∪ Eb are zero, the only way to make CmaxUL +

CDL

max ≤ R is to partition X into two subsets (where the SSs in X select either SS c or SS d as

their parent) with equal total size. Thus, if there exists a routing tree in G such that CUL max+

CDL

max ≤ R, there must be a partition to divide X into two subsets with equal total size.

Obviously, this reduction can be performed in polynomial time. Therefore, the RTC problem is NP-complete.

Below, we propose a heuristic load-aware tree construction (LTC) algorithm to deal with the RTC problem. The LTC algorithm constructs the routing tree from leaves to the root. Let Pi = PiLS∪ PiEQ, where PiLS is the set of SS i’s neighbors whose hop counts to the BS are less than that of SS i, and P_iEQis the set of SS i’s neighbors whose hop counts to the BS are equal to that of SS i and these neighbors have already been assigned with parents. The LTC

algorithm works as follows:

1. Our goal is to form a routing tree T to connect all SSs. Initially, SSs are not connecting to any node. So we have a forest of trees, where each tree is an individual SS. Then we can use Eqs. (2.1) and (2.2) to calculate the aggregated uplink bandwidth demand

dUL

i , aggregated downlink bandwidth demand dDLi , demand of uplink transmission time

TUL

i , and demand of downlink transmission time TiDLof each SS i. However, note that to calculate Eq. (2.2), it is necessary to know the parent node of SS i (so as to estimate the transmission rate between i and its parent). To resolve this uncertainty, we assume that before an SS i decides its actual parent, it has a tentative parent SS j, where j ∈ Pi and the transmission rate between i and j is the highest among all candidates.

2. Since the demands of transmission times TUL

i and TiDLof all nodes i are known, we can apply Eq. (2.3) to calculate CUL

i and CiDLfor all SS i.

3. Let A be the set of SSs which have not decided their actual parents and which have the maximum hop counts to the BS.

4. This step will decide the actual parent of one SS in A.

(a) For each SS i ∈ A, connect SS i to each SS j ∈ Pi and recompute the new values of CUL

j and CjDL by assuming that i’s actual parent will become j. Note that in order to avoid forming a cycle, if the path from SS i to SS j results in a loop, we set the values of CUL

j and CjDLas ∞. We then choose the SS j with the minimum value of CUL

j + CjDLas the candidate parent of SS i.

(b) The above step (a) will choose a candidate parent, say, p(i) for each SS i ∈ A. Among these candidates, we choose the SS p(i) such that the value of CUL

p(i)+ Cp(i)DL is minimized as the actual parent of SS i and make a connection between i and p(i).

5. Repeat step 4, until the set A is empty.

6. Repeat steps 3, 4, and 5, until all SSs have decided their actual parents.

Step 4(a) is to build the subtree whose subtree root (SS j) has the minimum value of CUL

j +

CDL

j . Similarly, step 4(b) is to build the subtree whose subtree root (SS p(i)) has the minimum value of CUL

p(i)+ Cp(i)DL. This can help balance the distribution of forwarding traffics and keep the final value of CUL

max+ CmaxDL as small as possible in the constructed tree. Note that the above

calculations of CUL

i and CiDLare all tentative. Their values will keep on changing as the tree is building up. Algorithm 2 gives the pseudo code of the LTC algorithm.

Next, we analyze the time complexity of the LTC algorithm. Since each SS has exact one parent, step 4 will be repeated at most n times, where n is the number of SSs in the network. In step 4(a), at most m nodes will be checked and each will check at most d candidates, where m is the maximum number of SSs with the same hop count to the BS and d is the maximum degree of SSs. Thus, the time complexity is O(nmd).

Finally, we comment on the timing to invoke the routing module. Since reconstructing the routing tree causes communication cost, one possible moment to invoke the routing module is when the value of CUL

max + CmaxDL of the old tree is higher than that of the new tree by a

predefined threshold.

2.4 Bandwidth Guarantee for Real-Time Flows

The aforementioned spectral reuse framework can allocate time slots to SSs proportionate to their requests. However, when SSs request new flows or need more bandwidths for their old flows, the system may no longer guarantee enough bandwidths for the original flows. To solve this problem, we propose an admission control mechanism to extend our spectral reuse framework. Specifically, we separate flows into real-time and non-real-time flows. When an SS requests a new flow or more bandwidth for its old flows, we will check whether the

Algorithm 2: Load-aware tree construction (LTC) algorithm

Input: set G of all SSs in the network Output: routing tree T

foreach i ∈ G do let rUL

j(max)and rj(max)DL be the highest rates of uplinks and downlinks of SS j to SSs in Pj;

C_iUL ←P_j∈Ei bULj rUL j(max) ; CDL i ← P j∈Ei bDL j rDL j(max) ; while G 6= ∅ do

let A be the set of SSs without parents which have the largest hop counts to the BS; G ← G − A;

while A 6= ∅ do Cmin← ∞;

foreach i ∈ A do foreach j ∈ P_i do

calculate C_jULand C_jDLafter attaching SS i to SS j; if CUL j + CjDL< Cminthen Cmin← CjUL+ CjDL; parent ← j; child ← i; T [child] = parent; A ← A − {child};

foreach i ∈ E_parent∪ E_childdo update CUL

i and CiDL;

bandwidth requirements of all real-time flows can be still satisfied. If so, we will admit this request. Otherwise, we will reject this request to guarantee bandwidths of existing real-time flows.

Fig. 2.5 illustrates the flowchart of our admission control mechanism. The idea is to pri-oritize real-time from non-real-time flows. For each SS, we always ensure sufficient slots to satisfy the bandwidth requirements of all its real-time flows, and then distribute the remaining slots to its real-time flows. This is what we mean by prioritizing real-time from non-real-time flows. This implies that an SS can always admit more non-non-real-time flows since its real-time flows always have higher priority. However, when an SS j requests a new real-time flow i (or wants to increases bandwidth of a real-time flow i), the following steps will be

SS j requests a new flow i

Is i a real-time flow?

check whether SS j has enough slots to support all its real-time flows

reallocate slots to SSs by spectral reuse framework with the bandwidth

requirements of all flows reallocate slots to SSs by spectral reuse framework with the bandwidth

requirements of only real-time flows

reject flow i admit flow i no yes no no no yes yes yes

Figure 2.5: Flowchart of the admission control mechanism. executed:

1. Check whether SS j’s current slots can support required bandwidths of all its real-time flows (including flow i). If there are enough slots, we can admit flow i. Otherwise, it means that we have to reallocate slots in the system to support this new request (refer to step 2).

2. To reallocate slots of SSs in the network, we will execute our spectral reuse framework in Section 2.3. We will update the bandwidth requirement of SS j, run the routing module to reconstruct the routing tree, and then run the scheduling module to allocate slots to all SSs. Then we check whether this new allocation can support the real-time flows of all SSs. If so, we can admit flow i and adopt the new allocation. Otherwise, it

means that the new scheduling cannot satisfy some real-time flows, so we go to step 3. 3. Update the bandwidth requirements of all SSs by removing their non-real-time flows.

With these requirements, we execute our spectral reuse framework again. We run the routing module to reconstruct the routing tree, and then run the scheduling module to allocate slots to all SSs. Then we check whether this new allocation can support the real-time flows of all SSs. If so, we can admit flow i and adopt the new allocation. Otherwise, the system does not have enough slots to support flow i, so we should reject the request of flow i.

Note that although the above step 3 allocates slots to SSs based on their requirements of real-time flows, an SS can still transmit non-real-time flows, as long as its real-time flows do not consume all bandwidths of the SS. Also, we comment that although the above discussions only cover two classes (real-time and non-real-time) of traffics, general multiple m classes of traffics are applicable. In this case, we should check whether the addition of a new flow i (say, in class k < m) can still guarantee the bandwidth requirements of all flows in classes 1, 2, · · · , k. If not, we can remove flows in classes k + 1, k + 2, · · · , m and reallocate slots to check whether the system has enough slots to support the request of flow i.

Next, we formulate our admission control mechanism in a mathematical way for imple-mentation. Here we introduce an uplink channel usage threshold δU L _{to determine whether} the network for uplink traffics is congested. Let Fctrl and Fdata be the ratios of control and

data subframes in a frame. According to the scheduling module, we can obtain that

δU L₌ Fdata Fctrl+ Fdata × CmaxUL CUL max+ CmaxDL . Recall that CUL

max = max_∀i

© CUL i ª = max ∀i ( X j∈Ei TUL j ) = max ∀i ( X j∈Ei dUL j rUL j ) .

Since CUL

maxis the sum of ratios

dUL

j

rUL

j of the total transmission time allocated to each SS j in Ei

of the “bottleneck” SS i, we can use CUL

maxas the degree of uplink channel usage in the network.

Specifically, when CUL

max ≤ δU L, the network for uplink traffics is not congested and thus all

uplink flows can receive enough bandwidth to satisfy their QoS requirements. Similarly, we can determine whether the network for downlink traffics is not congested by CDL

max ≤ δDL,

where the downlink channel usage threshold δDL _is

δDL ₌ Fdata Fctrl+ Fdata × CmaxDL CUL max+ CmaxDL . Based on the above argument, once CUL

max> δU L, the network for uplink direction becomes

congested and we have to exclude some flows to alleviate congestion. The idea is to first ex-clude some non-real-time flows since they do not have stringent deadlines. When the network is still congested even if all non-real-time flows are excluded, we have to exclude some new real-time flows. Here a new real-time flow is defined as a real-time flow that does not exist in the previous scheduling result or that changes its bandwidth demand. Given the bandwidth demands of all flows in each SS, the extension of our framework involves the following steps: 1. Run the spectral reuse framework in Section 2.3 to determine the bandwidth allocated

to each SS. If CUL

max≤ δU L, it means that each SS can obtain enough bandwidth and thus

the BS will broadcast the scheduling result to all SSs through the MSH-CSCH:Grant message. Otherwise, we will go to step 2.

2. If there are non-real-time flows in the network, then go to step 3. Otherwise, go to step 5.

3. For each SS i, we check whether its allocated bandwidth can satisfy bandwidth require-ments of all its real-time flows. If not, without changing the total bandwidth allocated to SS i, we reduce the bandwidth allocated to SS i’s non-real-time flows until the band-width requirements of SS i’s real-time flows can be satisfied. If the bandband-width

require-ments of every SS’s real-time flows can be satisfied by the above operation, the BS will broadcast the new scheduling result to all SSs. Otherwise, there must be at least one SS whose allocated bandwidth cannot satisfy its real-time flows even if all its non-real-time flows are excluded. In this case, we will go to step 4.

4. For each SS i, we change its demand of uplink transmission time from TUL

i to Ti(RT)U L , where TU L

i(RT) is the demand of uplink transmission time of all real-time flows in SS i. Then, we execute the scheduling module to recalculate the new result of bandwidth allocated to each SS. After this operation, if CUL

max≤ δU L, we will conduct the following

actions:

• If there exists free slots, we will assign them to the non-real-time flows in the net-work. Specifically, we select the SS i with the minimum value of TU L

i(RT)and assign these free slots to its non-real-time flows. We continuously repeat this operation until there is no free slot.

• Broadcast the new scheduling result to all SSs.

Otherwise, the network is still congested even if we exclude all non-real-time flows in the network. In this case, we will go to step 5.

5. We then exclude some new real-time flows to alleviate the network congestion. Let nRT new be the total number of new real-time flows in the network. We sort these flows

by the following method:

(a) Select the SS i with the maximum value of TU L

i(RT). Then, from SS i, we pick the new real-time flow fj with the largest bandwidth demand b(fj).

(b) Remove fj from SS i and decrease Ti(RT)U L by b(fj)

ri .

We then exclude some new real-time flows from the network by the binary exclusion: (a) Set up two variables β = 1

2 and k = 2.

(b) Exclude the first bβ × nRT newc new real-time flows and execute the spectral reuse

framework to check whether CUL

max ≤ δUL. If so, it means that we may reject too

many new real-time flows. In this case, we update β = β − 1

2k. Otherwise, it

means that we have to reject more new real-time flows to alleviate the network congestion. In this case, we update β = β + 1

2k.

(c) Update k = k + 1 and repeat step (b) until nRT new ≤ 2k.

After the network becomes non-congested by the binary rejection, the BS will broadcast the scheduling result to all SSs.

For the downlink direction, we follow the similar way to exclude some flows to alleviate the network congestion.

2.5 Performance Evaluation

In this section, we present some experimental results conducted by the ns-2 simulator [31] to verify the effectiveness of the proposed framework. We adopt a single-channel OFDM physical layer and a two-ray ground reflection model for radio propagation, and extend the TDMA (time division multiple access) MAC module in ns-2 for the MAC layer. We consider three kinds of network topologies: regular, dense, and random. In a regular network, there are at most 84 SSs placed in a diamond mesh topology, as shown in Fig. 2.6. In a dense network, we add an extra SS in each position marked by ‘+’ in Fig. 2.6. In a random network, we arbitrarily select at most 84 positions from the dense network to place SSs. Note that the resulting network is connected. All SSs are stationary and work in half duplex. The interference neighborhood of an SS includes all its neighbors within two-hop range. So there

are at most 12 and 24 nodes in an SS’s interference range in the regular and dense networks, respectively. In the random network, an SS’s interference range contains 12 nodes in average. There are 512 time slots in a frame. The channel bandwidth is set to 50 Mb/s, and we assume that all links have the same data rates. For each experiment, at least 100 simulations are repeated and we take their average.

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Figure 2.6: The regular and dense network topologies in our experiments.

2.5.1 Network Throughputs under Different Network Topologies

We first evaluate the network throughputs under different network topologies. The network throughput is defined as the total amount of data received and transmitted at the BS. We compare our results against the basic 802.16 mesh operation and the concurrent transmission scheme with route adjustment proposed in [3]. For the 802.16 operation, the random routing tree is adopted and the numbers of uplink and downlink slots are set to equal. Each SS will

generate random traffic loads and request the same uplink and downlink bandwidth demands. For the regular and random networks, the number of SSs is set to 4, 12, 24, 40, 60, and 84. For the dense network, we set the number of SSs as 8, 24, 48, 80, 120, and 168.

Fig. 2.7 shows the network throughputs of different methods in the regular network. Clearly, the network throughput will decrease as the number of SSs increases because a packet needs to travel more hops in average as the network scales up. From Fig. 2.7, we can observe that the throughput of the 802.16 operation drops significantly when the number of SSs increases. This is because it adopts a random routing tree, which causes longer relay routes. Moreover, the neglect of spectral reuse greatly hurts the system performance. The improvement of through-put by the concurrent transmission scheme proposed in [3] is limited because it constructs the routing tree according to the SSs’ positions, rather than their traffic loads. Thus, the network bottleneck cannot be reflected and the benefit of route adjustment is limited. Besides, this concurrent transmission scheme restricts that SSs cannot transmit data earlier than their child SSs so that the throughput is reduced. Our framework performs better than these two schemes because it can estimate the degree of spectral reuse according to SSs’ traffic loads and thus allocates more time slots to SSs. As the network scale grows, the degree of spectral reuse can also increase. In addition, the LTC algorithm of the tree module can generate better routing paths to distribute the traffics more evenly. Therefore, the complete framework can result in the highest throughput.

We then verify the network throughputs of different methods in the dense and random networks, as shown in Fig. 2.8. All network throughputs are normalized by that of the basic 802.16 mesh operation. From Fig. 2.8, we can observe that the results are similar to that in Fig. 2.7. However, as compared with Fig. 2.7, the improvement of our framework slightly degrades. For the dense network, this is due to the decrease of degree of spectral reuse since the number of nodes in each SS’s interference neighborhood becomes double. For the random network, this is because the network bottleneck usually appears in the one-hop neighbors of