物聯網資訊採集與群組多播的機制設計

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國立臺灣大學電機資訊學院電信工程學研究所博士論文

Graduate Institute of Communication Engineering College of Electrical Engineering and Computer Science

National Taiwan University Doctoral Dissertation

物聯網資訊採集與群組多播的機制設計 Mechanism Design for IoT

Information Gathering and Multicast Distribution

柯君翰 Chun-Han Ko

指導教授：魏宏宇博士 Advisor: Hung-Yu Wei, Ph.D.

中華民國 106 年 6 月 June 2017

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國立臺灣大學博士學位論文口試委員會審定書

物聯網資訊採集與群組多播的機制設計

Mechanism Design for IoT Information Gathering and Multicast Distribution

本論文係、柯君翰君（學號：D01942010）在國立臺灣大學電信工程學研究所完成之博士學位論文，於氏國－

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列考試委員審查通過及口試及格，特此證明

口試委員：

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說玄寺（指導教授簽名）

三在乏長吽 ^U

V芳 ^、多手之

？等 L ^Ji ^海

多家三台

：多乏自件透支后

（簽名）

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致謝

能順利完成博士論文，最要感謝的是指導教授「魏宏宇」老師！博士班就學以來，風雨飄搖，每當研究遇到瓶頸之際，老師給予我的指導與建議猶如點亮風雨中屹立不搖的燈塔，使我終能抵達彼岸。彼岸並不是終點，眼前迎來的是更開闊的道路，我會善用學習過程中所學到的一切，期望自己更加成熟以迎接更開闊的未來與挑戰。真的很感謝老師！

在家庭方面，最要感謝親愛的家人，包括爸爸「錫福」、媽媽「碧梅」、姊姊「翠婷」，還有族繁不及備載等人，有你們的支持與體諒，我才能全力完成學業。書念了這麼久，我自覺還是很不會寫作文，時常辭不達意，長話不如短說：謝謝您們，我愛您們！

感謝一同奮戰的同學們，與你們的討論總是獲益良多，我也很懷念一起吃飯、打網球的時光。相信與大家相處的時光在未來一定會是讓我回憶最深的。

最後，必須感謝我的老婆「幸芸」，多虧妳覺得我的口試投影片看

起來都不重要，硬是要我刪了好多張投影片……我能把報告時間從 75

分鐘濃縮於一小時以內，以致於順利完成口試，妳絕對是最大功臣，真

的很「幸運」有妳。未來還請妳多多指教，我愛妳喔～

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doi:10.6342/NTU201701588

中文摘要

物聯網是智能設備、車輛、機器還有其他智能物體等互相聯通而形成的網路。實現複雜物聯網的關鍵因素則在於許多新型通信協定和技術的整合，它們將使物聯網設備能夠進行協作、溝通並作出決策。物聯網設備的互相聯通作用可以簡單的資料流說明：諸如無線感應器的物聯網設備從環境中收集資料，並將資料傳輸到資料伺服器進行信息處理。爾後伺服器會將處理獲得的信息傳輸分送到諸如用戶設備的物聯網設備以實現更好的使用者效用。由於物聯網的快速發展，無處不在的信息收集、處理和分送，均使無線電資源的需求不斷上升，這也使原本就有限的無線電資源更為稀少。此外，無線傳輸通道會隨著時間波動。

而能量採集技術雖能實現自我維持運作的物聯網設備，但採集的能量

通常是間歇並隨時間變化的。因此，考量到無線電資源的稀少性、無線

通道的時間波動和能量的時間變化，如何有效地在空間和時間上分配

運用無線電資源將是物聯網中極為重要的一項議題。此外，我們也考慮

了物聯網設備的自私特性與物聯網環境的不完整信息。不完整信息意

味著網路環境中如無線通道狀況與設備的能量儲存量等信息通常僅為

設備本身所知。為了最佳化網路效能，網路設計者將需要設備回饋這些

不完整信息。由於整體網路最佳化通常會犧牲部分設備的個別效能，因

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doi:10.6342/NTU201701588

此自私的設備可能會通過虛假的信息回饋來操縱網路最佳化結果，以使自己的效能表現變得更好。此時整體網路效能表現將可能不是網路設計者所希望達到的最佳結果。有鑑於此，我們在物聯網中制定了無線電資源分配問題，並以機制設計的概念提出了創新的物聯網資源分配機制。透過理論研究，我們證明設計的資源配置機制將可使物聯網設備回饋真實的信息，並從而實現最佳的均衡資源分配。均衡資源分配實現了數個效率和公平的度量，包括最大系統吞吐量/環境資料保真度，柏拉圖效率，最大公平性，與比例公平性。而透過提出的定價方案，我們證明均由設備付錢給機制。換言之，我們設計的機制將不需要付錢給設備才能確保真實的反饋（預算平衡）。此外，我們也證明所有設備將加入設計的機制以獲得比沒有加入時更高的效用（個別理性）。

關鍵詞：物聯網；能量採集；無線電資源分配；機制設計；賽局理論。

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Abstract

The Internet of Things (IoT) is the inter-networking of smart devices, vehicles, machines, and other items. The key factor for enabling this sophisticated paradigm is the integration of novel communication protocols and technologies, which allows IoT devices to cooperate, communicate, and make decisions. The interconnection of IoT devices can be explained in simple data flows: Devices such as wireless sensors gather data from the environment and transmit the data to data servers for information processing. The processed information is then distributed to devices such as user equipments to achieve greater user utility. Due to the rapid development of the IoT, ubiquitous information gathering, processing, and distribution have escalated the demand of radio resources, which makes radio resources even scarcer. In addition, wireless channels are time-fluctuating.

Energy harvesting technology enables self-sustainable IoT devices but harvested energy is usually intermittent and time-varying. Therefore, taking into account radio resource scarcity, channel fluctuations, and energy variations, efficient radio resource allocation in space and time is particularly important in the IoT. Moreover, we also consider selfishness of IoT devices and incomplete information of the network environment. Incomplete information means that the network environment, such as channel conditions and energy levels, is only known to devices themselves. To optimize the network performance, feedback of the incomplete information from devices is required. Note that overall network optimization usually sacrifices individual performance of some devices. Selfish devices can manipulate the network optimization result through untruthful feedback if doing so increase their own performance. The network performance may not be optimal. In this regard, we formulate radio resource allocation problems in the IoT and adopt a mechanism

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design approach to propose novel IoT resource allocation mechanisms. Our theoretic findings show that the proposed resource allocation mechanisms can induce truthful information feedback from devices so as to achieve optimal equilibrium resource allocation.

The equilibrium resource allocation achieves several efficiency and fairness metrics, including maximum system throughput/data fidelity, Pareto efficiency, max-min fairness, proportional fairness. With the proposed pricing schemes, the payment is always made from the devices to the mechanisms. In other words, the mechanisms do not need to pay to ensure truthful feedback (budget balance). Moreover, all devices will join the proposed mechanisms to gain higher utility than without joining (individual rationality).

Keywords: The IoT; energy harvesting; radio resource allocation; mechanism design;

game theory.

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List of Figures

1.1 Illustration of the IoT from the viewpoint of data flows. . . 2 2.1 System model. The BS provides multiple multicast flows to wireless UEs. 14 2.2 The flow diagram of the proposed resource allocation mechanism. . . 18 2.3 The UE’s utility under different PEP values. (a) Loss-tolerant flow. (b)

Loss-sensitive flow. . . 39 2.4 The UE’s utility with respect to the reported PEP. (a) The UE’s true re-

source demand is ”greater” than the group resource demand, and the group ”fulfills” its group resource demand. (b) ”less” and ”fulfill”. (c)

”equal” and ”fulfill”. (d) ”greater” and ”not fulfill”. (e) ”less” and ”not fulfill”. (f) ”equal” and ”not fulfill”. . . 40 2.5 Performance comparison among the proposed mechanism, the weighted

scheme, and the random scheme: (a) Weighted proportional fairness. (b) Weighted max-min fairness. . . 41 2.6 PSNR evaluation of the proposed mechanism in LTE MBMS: (a) Average

PSNR. (b) Standard deviation of the PSNR. . . 42 3.1 System model. The BS provides multiple multicast flows to energy har-

vesting devices. The energy source can be solar power, radio-frequency (RF) energy, etc. Each device accesses only one flow. Devicei accessing flowg is denoted by device (i, g). . . 48 3.2 The block diagram of the proposed resource allocation mechanism. The

detailed designs are specified in each subsection. . . 55

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3.3 Illustration of three different information stages in a time slot. Each time slot can be broken into ex-ante, interim, and ex-post stages according to what information is known at different time instants. . . 57 3.4 The utility of each device in all possible feedback states. . . 70 3.5 Budget balance and individual rationality: (a) The net payment from the

devices to the BS in all system states. (b) The utility of each device in all system states. . . 71 3.6 Performance comparison in the system throughput: (a) The weighted sys-

tem throughput of the proposed resource allocation mechanism, and other schemes. (b) The weighted system throughput of the proposed resource allocation mechanism with different values of the discount factorβ. . . . 72 3.7 Trade-off among the signaling overhead, the system throughput and the

time complexity: (a) The weighted system throughput under feedback frequencies from per time slot to per 5 time slots. (b) The number of iterations and the total time complexity under feedback frequencies from per time slot to per 5 time slots. . . 73 3.8 Throughput performance of each device and the system with/without the

proposed weight design. . . 74 4.1 A model of the energy-harvesting IoT. There are one BS and multiple sen-

sor nodes owned by different servers. Sensor nodei owned by server g is denoted by node(i, g). The nodes can harvest energy from the environment. The BS decides to activate nodes to sense and transmit data back through the BS to their servers. The node activationa^t_i,g = 1 means that the BS activates node(i, g) in time slot t. . . 80 4.2 The block diagram of the proposed node activation mechanism. The

servers and the nodes are required to feedback the data statistics and the energy states, respectively. The BS makes the node activation decision and also charges the servers prices. . . 86

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4.3 Incentive compatibility, budget balance, and individual rationality: (a) The utility of each server under all possible one-shot deviation strategies in time slot0. (b) The price charged by the BS in all system states. (c) The utility of each server in all system states. . . 104 4.4 Impacts of the parameter change on the system data fidelity: (a) The

discount factorβ = 0, 0.4, 0.8, 0.9, 0.95, .099. (b) The energy capacity ECi,g = 1, 2. (c) The spatial kernel lx = 0, 5, 10 and the temporal kernel lt = 0, 1, 2. (d) The number of resource blocks R = 1, 2, 3, 4, 5, 6. (e) The number of nodes|Ig| = 2, 3, 4. . . 105 4.5 Comparison of the synchronous and the asynchronous feedback designs:

(a) The system data fidelity. (b) The complexity. . . 107

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List of Tables

2.1 Notation of the multicast system model . . . 17

2.2 Notation of the multicast resource allocation mechanism . . . 26

2.3 Parameter setting . . . 38

5.1 Summary of the significant results . . . 108

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Chapter 1 Introduction

The Internet of Things (IoT) is a novel paradigm that is rapidly emerging in modern wireless communications. It is the inter-networking of smart devices, vehicles, machines, and other items. Fig. 1.1 uses simple data flows to show the interconnection of IoT devices.

In the IoT, devices such as wireless sensors and radio-frequency identifiers (RFID) first sense and gather data from the environment. The gathered data are then transmitted to data centers or servers for processing and analysis to gain meaningful information. The information is then distributed to devices such as user vehicles and machines to achieve greater user utility. Wireless multicast, a promising technology for common information delivery to multiple devices, can be adopted. The key factor for enabling the sophisticated paradigm of the IoT is the integration of novel communication protocols and technologies, which allows IoT devices to cooperate, communicate, and make decisions [1, 2].

Despite the promising future of the IoT, new design challenges are imposed due to the rapid development of the IoT with a numerous number of devices. In particular, ubiquitous information gathering, processing, and distribution have escalated the demand of radio resources, which makes radio resources even scarcer. Efficient radio resource allocation is especially important in the IoT. In addition, wireless channel conditions are time-fluctuating, which can severely affect the quality of data transmission. On the other hand, emerging energy harvesting technologies enable wireless devices to scavenge energy from the ambient environment [3] and to achieve self-sustainable operation. How- ever, the randomness and intermittence of renewable energy also bring design challenges.

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Therefore, channel fluctuations and energy variations should also be important consider- ations in radio resource allocation design.

1.1 Selfish Devices and Incomplete Information

Unlike most of the existing works, we also consider selfishness of IoT devices and incomplete information of the network environment. Incomplete information means that the network environment, such as channel conditions and energy states, is only known to devices themselves. To optimize the network performance, feedback of the incomplete information from devices is required. Note that overall network optimization usually sacrifices individual performance of some devices. Therefore, devices may be selfish and feedback their own incomplete information dishonestly so as to maximize their own performance. Therefore, the overall network operation may not be optimal.

Consider a very simple toy model where there exist a base station (BS) and 3 wireless devices. Each device requires one data packet. The BS has 2 radio resource blocks where one radio resource block can be used to transmit one packet. Suppose that devices 1 and 2 both have packet success probability (PSP) 0.9 and device 3 has PSP 0.2. To maximize

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the system throughput (expected number of packets received successfully), the BS should transmit one packet to device 1 and one packet to device 2. The optimal system throughput is 1.8. However, the throughput of device 3 is 0. If the PSP is only known to the devices and feedback is required, device 3 can untruthfully feedback PSP 1. In this case, the BS may transmit one packet to device 1 and one packet to device 3. By such untruthful feedback, device 3 gets throughput 0.1, higher than that in the optimal resource allocation.

However, the real system throughput becomes 1.1, which is less than the optimal system throughput 1.8. From this example, we see that selfishness and incomplete information of devices can cause severe system performance degradation. Traditional solutions that do not consider selfishness and incomplete information may not work effectively. To this end, we adopt a mechanism design approach to designing novel resource allocation mechanisms.

1.2 Problem Overviews and Contributions

In this dissertation, we play the role of the radio resource providers. We aim to design IoT radio resource allocation mechanisms where IoT devices and servers who use radio resources are the participants. Selfishness of IoT devices and incomplete information of the network environment are considered. By using the divide-and-conquer method, we formulate the resource allocation problems in the IoT scenarios of information gathering and distribution, as illustrated in Fig. 1.1. Novel resource allocation mechanisms are proposed to induce truthful information feedback from selfish devices so as to achieve optimal resource allocation. The problem overviews and contributions for each design block are given as follows:

1.2.1 Strategy-Proof Resource Allocation Mechanism for Multi-Flow Wireless Multicast (Chapter 2)

In Chapter 2, we consider downlink multimedia multicast. The BS can send multiple multicast flows to multiple groups of devices. The channel-quality information (CQI) is

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devices’ private information. Resource allocation to multiple multicast flows to achieve maximum system throughput is the major objective. To solve the problem, we have the following contributions:

1. We provide the theoretical foundation for the multi-flow multicast communication, constructing an application-layer error correction framework and designing an on- demand resource allocation mechanism for the future Multimedia Broadcast Mul- ticast Services (MBMS).

2. The proposed mechanism performs access control via pricing. The proposed pricing scheme only enables the users with the channel qualities better than the system- defined threshold to join the mechanism and gain positive utility.

3. The proposed mechanism induces truthful feedback of the CQI in a dominant- strategy equilibrium (strategy-proofness).

4. The resource allocation in the equilibrium is Pareto efficient. No other resource allocation can make all the users better off in utility.

5. The resource allocation also achieves flow-level weighted max-min and proportional fairness.

6. There is no net payment from the BS to the devices. In other words, the BS does not need to pay to ensure truthful feedback (budget balance).

1.2.2 Wireless Multicast over Time-Varying Channels for Energy- Harvesting Devices (Chapter 3)

Chapter 3 studies the downlink multicast scenario on an infinite time horizon. Common data multicast, e.g., small data and control signal transmissions, to energy-harvesting devices over time-varying channels is considered. The energy and channel states of the devices are time-varying and only known to themselves. We aim to decide resource allocation to different multicast flows over time to achieve maximum system throughput. Our contributions are given as follows:

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1. We propose a resource allocation mechanism induces the devices to feedback their true energy and channel state information in a perfect ex-post equilibrium (perfect ex-post incentive compatibility).

2. The equilibrium resource allocation maximizes the system throughput.

3. The payment is always made from the devices to the BS The BS does not need to pay to ensure truthful feedback (budget balance).

4. Moreover, all devices will obtain higher utility when joining the proposed resource allocation mechanism (individual rationality).

1.2.3 On Maximizing Data Fidelity in Energy-Harvesting IoT: A Me- chanism Design Approach (Chapter 4)

Chapter 4 focuses on correlated data gathering of energy-harvesting devices. The data correlations and the energy states are only known to devices. A node activation decision problem over an infinite time horizon is studied, with spatial-temporal data correlations and incomplete information on the data statistics and the energy states. Resource allocation to devices for information gathering and uplink transmissions to achieve maximum system data fidelity is then the major design goal. Our contributions are given as follows:

1. The proposed node activation mechanism ensures truthful feedback of the true data statistics and energy states in a perfect ex-post equilibrium (perfect ex-post incentive compatibility).

2. The proposed node activation mechanism maximizes the system data fidelity.

3. The proposed node activation mechanism also ensures that the payment is always made from the data servers to the BS. In other words, the BS does not need to pay to guarantee truthful feedback (budget balance).

4. All data servers and their sensor nodes will join the proposed node activation mechanism to obtain higher utility than without joining (individual rationality).

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1.3 Mechanism Design

A mechanism design approach is adopted in this dissertation to inducing truthful feedback of incomplete information from selfish devices to achieve desirable resource allocation.

Before going to the design details of following chapters, we provide some basic knowledge of mechanism design.

1.3.1 Basic Knowledge

Mechanism design is a sub-field of economics and game theory that takes an engineering approach to designing mechanisms or incentives to achieve desirable outcomes in a strategic setting. Such a strategic design is necessary since players are selfish, act ratio- nally, and usually have private preferences. In the following, we use resource a allocation mechanism to shortly explain mechanism design. A mechanism designer first designs an outcome rule, i.e., a resource allocation rule plus a pricing rule. The game induced by the mechanism has the following main components:

• Players: Devices are players in the game.

• Types: Channel conditions, energy states, and data correlations are types of players.

Types are usually incomplete information that is known to players themselves, but not known to each other or the mechanism designer.

• Strategies: Players have strategies that decide how to report types to the mechanism.

• Outcomes: With the reported types received and according to the resource allocation rules and the pricing rules, the mechanism decides resource allocation and prices charged to devices.

• Utility: Players have different utility with respect to the outcomes.

1.3.2 Equilibrium Concepts

The main objective in mechanism design is to design the resource allocation rule and the pricing rule such that reporting the true types maximizes players’ utility in an equilibrium.

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The most well-known equilibrium concept is a Nash equilibrium, which states that in an equilibrium each player will select a utility-maximizing strategy given the strategies of the other players. Although the Nash equilibrium concept is fundamental, it makes very strong assumptions about players’ information and beliefs: Each player must have perfect information about the types of the other players.

A stronger solution concept is a dominant-strategy equilibrium. In a dominant-strategy equilibrium each player has the same utility-maximizing strategy regardless of the strategies of other players. A dominant-strategy equilibrium is very robust, as it makes no assumptions about the information available to players about each other. As will be shown in Chapter 2, the proposed mechanism will be implemented in a truthful dominant-strategy equilibrium.

1.3.3 Infinite Time Horizon Mechanisms

Mechanism design for infinite time horizons is required when the types, i.e., channel conditions, energy states, and data correlations, vary with time and are incomplete information. In addition to the basic components in Chapter 1.3.1, we should also consider Markov type transitions and ex-post utility:

• Markov type transitions: Players have different types in different time slots. We assume that types have Markov transitions. That is, the types of the players in the next time slot only depend on the types and the resource allocation in the current time slot.

• Ex-post utility: Players also have different utility with respect to the outcomes. A slight refinement from one-shot utility is that we define utility in the ex-post stage.

An ex-post stage is defined as the timing after players report the types in each time slot. Therefore, ex-post utility represents the utility seen in the ex-post stage of each time slot.

With the refinement of ex-post utility, the equilibrium concept we will use in infinite time horizon mechanisms is a perfect ex-post equilibrium. A perfect ex-post equilibrium

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means that each player maximizes the ex-post utility in any subgame by playing a strategy given the strategies of the other players. The perfect ex-post equilibrium concept is also strong in infinite time horizon mechanisms as it makes no assumptions about the type information available to players about each other in each time slot. As will be shown in Chapters 3 and 4, the proposed mechanisms will be implemented in a truthful perfect ex-post equilibrium.

To sum up, according to different network scenarios on one-shot or infinite time horizons, different mechanisms will be proposed and different equilibrium concepts will be applied. Desirable properties of the outcomes will also be analyzed. More design details, equilibria, and property analysis will be provided in the following chapters.

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Chapter 2 Strategy-Proof Resource Allocation Mechanism for Multi-Flow Wireless Multicast

2.1 Introduction

Wireless multicast/broadcast, also known as one-to-many communication, is a promising technology for delivering information from a server to a group of wireless users. As users have become more data hungry and service demanding, multicast/broadcast service is a solution that can cater this need efficiently. One-to-many communication can be per- formed via unicast. Employing unicast involves multiple transmissions to a group of users which results in severe waste of radio resources especially when the group size gets larger.

Therefore, wireless multicast techniques have been extensively studied and widely used because of the efficient usage of radio resources. However, wireless multicast requires the network, including the server and routers, to route packets such that each user receives a copy. Route establishment is then one of the most basic and challenging issues in wireless multicast. Many multicast protocols come up with solutions to set up and maintain routes.

In addition, on the basis of multicast routing, the issues on network resource utilization, packet scheduling, adaptive rate control, power control, and throughput maximization,

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have been jointly investigated [4].

Multicast/broadcast service is supported in the 4G communication networks such as Long Term Evolution Advanced (LTE-A) and Worldwide Interoperability for Microwave Access (WiMAX) IEEE 802.16m. In 3GPP LTE systems, Multimedia Broadcast Mul- ticast Services (MBMS) is a mechanism for multicasting video streams [5]. To provide transmission reliability, application-layer error correction framework is applied. By applying fountain (rateless erasure) coding techniques [6], application-layer data files are encoded into source data packets and repair data packets, which provide redundancy for data delivery [7]. Recently, 3GPP has started working on providing dynamic and on- demand MBMS [8]. Dynamic radio resource allocation and adaptive error correction configuration could be applied to ensure efficient resource utilization and user satisfac- tion for multi-flow multicast video services. As different users may face different wireless channel qualities, one key issue for multicast configuration is to determine the appropri- ate application-layer error correction level so that the users are satisfied with the reception quality. On the other hand, since radio resources are limited, resource allocation among different multicast streams needs to be carefully considered. Our previous works investigated adaptive modulation/coding schemes [9], game-theoretic configuration [10], and optimal pricing [11] for wireless multicast. On the basis of the previous works, a new research problem of resource allocation for wireless multicast in the next-generation networks will be of interest.

In this research work, we provide the theoretical foundation for the multi-flow multicast communication schemes, which will be an indispensable part of the future MBMS wireless multimedia delivery. In the proposed scenario, a base station (BS) is capable of sending multiple data flows to multiple groups of user equipments (UEs). The BS aims to provide efficient and fair multicast services by sending redundancy for data delivery, which requires the feedback of the channel-quality information (CQI) from the UEs. The channel qualities are, in general, time-varying and can only be correctly measured by the UEs themselves, which means the CQI is the UEs’ private information. Regarding the CQI feedback, this chapter further considers the rational and selfish user characteristic.

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When the UEs have the private CQI, the rational and selfish UEs may intentionally report the false CQI to manipulate the BS’s multicast configuration if they can benefit from such untruthful feedback. The multicast service may turn out inefficient and unfair. Hence, it will be a significant issue to ensure reliable and truthful feedback from the UEs. To elicit the true CQI and to achieve efficient and fair network operation, we propose a multicast resource allocation mechanism with the designs of the access-control pricing scheme and the weighted water-filling resource allocation. Our analysis indicates that the proposed mechanism can elicit the true CQI from the UEs, avoiding any manipulation of multicast configuration and thereby guaranteeing efficient and fair network operation. The detailed contributions are stated as follows:

1. We provide the theoretical foundation for the multi-flow multicast communication, constructing the application-layer error correction framework and designing the on- demand resource allocation mechanism for the future MBMS.

2. The proposed mechanism performs access control via pricing. The proposed pricing scheme enables the UEs with the channel qualities better than the system- defined threshold to join the mechanism and gain positive utility. On the other hand, the UEs with the channel qualities worse the threshold will not join the mechanism since they will never gain positive utility.

3. The proposed mechanism is strategy-proof. It induces the selfish UEs to truth- fully report their private CQI. Therefore, the system operates at the truth-revealing dominant-strategy equilibrium.

4. The resource allocation at the equilibrium operating point is Pareto efficient. No other resource allocation can make all the UEs better off in utility. The resource allocation also achieves flow-level weighted max-min and proportional fairness.

Moreover, there is no net payment from the BS to the UEs. In other words, the BS does not need to pay the UEs to ensure strategy-proofness of the proposed mechanism (weak budget balance).

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2.2 Related Work

Many research papers studied the issues on multicast flow accommodation and resource allocation. Some papers conducted theoretical analysis on the maximum concurrent flow problem in wireless networks. Tu studied the efficient utilization of network resources for increasing the number of concurrent multimedia flows when a channel becomes sat- urated [12]. Jain et al. worked on maximizing throughput in any given wireless network with any given traffic workload, using a conflict graph to model wireless interference [13]. As the throughput maximization problem was shown to be NP-hard, they instead provided methods to compute the upper and lower bounds for this problem. Kodialam et al. analyzed the problem of joint flow routing and transmission scheduling to achieve given throughput [14, 15]. They developed sufficient and necessary conditions and derived upper bounds for the achievable throughput. Wan et al. investigated the maximum concurrent flow problem in multi-hop wireless networks subject to both bandwidth and interference constraints [16, 17]. They also developed polynomial-time algorithms to de- rive approximation bounds. Kumar et al. conducted the study of the maximum throughput capacity of the network given the collection of source-destination pairs [18]. The algo- rithmic aspects of the above problem were discussed as well. Ozdaglar and Bertsekas proposed a method for solving the multi-commodity flow problem, relying on the con- vexity of the cost function [19].

Some papers focused on designing efficient resource allocation methods that improve wireless networks’ ability to accommodate more multicast flows. Cruz et al. used a primal-dual approach to compute joint routing, scheduling, and power control policies [20]. Middleton et al. developed a framework allowing scheduling, routing, and power allocation for multiple flows in polynomial-time [21]. Their study was subsequently ex- tended to allocate resources in networks with streaming-packet data flows [22]. Baghaie et al. studied multi-flow transmission in delay constrained wireless multi-hop networks to minimize power consumption for prolonging network life [23]. Tu et al. investigated video multicasting in large-scale areas using wireless mesh networks. They designed a set of heuristic-based algorithms to improve network throughput [24]. Some other pa-

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pers also investigated the issue on private information in multicast networks. In [25, 26], Gopinathan et al. studied the multicast problem in an ad-hoc wireless network. They designed inter-node cost sharing schemes for the information dissemination to achieve group strategy-proofness. They also showed that to achieve group strategy-proofness a compromise in routing optimality and budget balance is inevitable.

Jakubczak and Katabi proposed SoftCast, a novel cross-layer design for video multicast [27, 28]. SoftCast provides a joint source-channel coding scheme linearly transform- ing a video stream into coded packets such that each packet contains approximately the same amount of information and is uncorrelated to each other. In this way, each receiver can decode the received packets into the video whose quality is proportional to its channel quality. As the authors proposed and demonstrated SoftCast in a single-flow scenario, SoftCast configuration in a multi-flow scenario will also be of interest. In a multi-flow scenario, whether the system applies SoftCast or other coding schemes, feedback of the CQIs from the UEs may be needed to decide the redundancy level of each flow and to optimize the system performance. Therefore, resource allocation mechanism design with feedback decisions in a multi-flow scenario will be important and interesting.

In summary, different from the papers of [25, 26] that designed the cost sharing methods for single-flow multicast, this chapter proposes a resource allocation framework with feedback decisions for multi-flow multicast. Besides, unlike the other previous works, this chapter makes the practical assumption that UEs are self-interested, have private CQI, and make feedback decisions in a distributed way. While the system requires the UEs’ private CQI, the UEs that are selfish in improving their own performance may manipulate the multicast configuration by falsely reporting the CQI. Without the correct CQI, the resource allocation may turn out inefficient and unfair. With regard to the issue on UEs’

manipulating the system operation, this chapter is the first applying incentive mechanism design to propose a resource allocation mechanism in a multi-flow multicast scenario.

The proposed mechanism is shown to induce the selfish UEs to reveal the true CQI and to achieve efficient and fair system operation.

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Figure 2.1: System model. The BS provides multiple multicast flows to wireless UEs.

2.3 Multicast System Model

We consider a wireless multicast system consisting of a BS and multiple wireless UEs, as illustrated in Fig. 2.1. Time is divided into periods of equal length and the system has R resource blocks in each time period. The BS provides a set of multicast flows G = {1, 2, . . . , G} where each flow g is accessed by a group of UEs NG = {1, 2, . . . , Ng}.

We denote each UEi accessing flow g by UE (i, g), i ∈ NG andg ∈ G. Note that each UE only accesses one flow, i.e., each UE belongs to only one group. Throughout the rest of the paper, we will use the terms flow and group interchangeably.

2.3.1 Multicast Flows

The number of packets in flowg is denoted by Mg. For simplicity, we assume that each packet has equal length and transmission of one packet requires one resource block. Each flow can be either loss-tolerant or loss-sensitive. a UE that accesses a loss-tolerant flow obtains a fixed amount of utility from each packet received, and the utility reaches the maximum once it receives all the packets. In contrast, a UE that accesses a loss-sensitive flow must receive all the packets to obtain the maximum utility; otherwise, it gains nothing.

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2.3.2 Lossy Channels and Generalized Erasure Coding

Wireless channels are not perfect in general. Transmission through wireless channels may suffer from packet loss. To accommodate dynamic channel fading scenarios, we assume that each UE experiences the constant channel quality in a time period, but the channel quality varies from period to period. In the rest of the paper, we will study a single time period. Nonetheless, the designs and analysis can be applied to multiple time periods as well.

We use the binary-symmetric channel model [29]. Each UE(i, g) suffers from constant bit error probability (BEP) bi,g, 0 ≤ bi,g ≤ 1. Since each packet in a flow is assumed to have equal length, UE(i, g) suffers from constant packet error probability (PEP) ei,g = 1 − (1 − bi,g)^L whereL is the packet length. Note that each UE’s CQI, i.e., BEP and PEP, are assumed to be private information. This assumption is reasonable as only the receiver can correctly measure its channel quality.

Since the channels are lossy and unreliable, we apply the generalized erasure coding [30, 31] to control error.¹ The generalized erasure coding transforms a flow ofMgpackets into a longer flow of coded packets such that the data contents can be fully recovered from anyMg out of the coded packets. Thus, if a UE obtains a sufficient number of the coded packetsj ≥ Mg, it obtains the full valuation. However, if a UE obtains an insufficient number of the coded packetsj < Mg, it can recover only the portionj/Mgof the original packets. We define the UE’s valuation with respect to the number of the received coded packetsj as follows.

Definition 2.1. [UE’s valuation] If flow g is loss-tolerant, UE (i, g)’s valuation function with respect to the number of the received coded packetsj is

vg(j) = min

1, j

Mg

(2.1)

1As 3GPP MBMS has attracted a lot of attention in recent year, we follow the specification of 3GPP MBMS and propose a resource allocation framework that uses the fountain codes for application-layer error correction. The basic ideas of the proposed resource allocation framework may be applied with specific designs for different coding schemes.

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If flowg is loss-sensitive, UE (i, g)’s valuation function is

vg(j) =











1, j ≥ Mg

0, otherwise

(2.2)

2.3.3 UEs’ Utility

UEs receive any packet the BS transmits in perfect channels. However, this is not the case when the channels are lossy. In the lossy binary-symmetric channels, when the BS transmitsAg(coded) packets in flowg, UE (i, g) with the PEP ei,g will receivej packets, 0 ≤ j ≤ Ag, with probability ^A_j^g(1 − ei,g)^je^A_i,g^g^−j. Thus, each UE(i, g)’s valuation on the flow transmitted, denoted byvg(ei,g, Ag), is derived in Proposition 2.1. In the system meaning, UE (i, g)’s valuation vg(ei,g, Ag) can be viewed as the expected normalized throughput.

Proposition 2.1. The BS transmits Ag packets in flow g. If flow g is loss-tolerant, UE (i, g)’s valuation function is

vg(ei,g, Ag) =

Ag

X

j=0

min

1, j

Mg

Ag

j

(1 − ei,g)^je^A_i,g^g^−j (2.3)

If flowg is loss-sensitive, UE (i, g)’s valuation function is

vg(ei,g, Ag) =









 PAg

j=Mg

Ag

j (1 − ei,g)^je^A_i,g^g^−j, Ag ≥ Mg

0, otherwise

(2.4)

Lemma 2.1 shows that UE(i, g)’s valuation function vg(ei,g, Ag) is strictly decreasing with respect to the PEP ei,g and strictly increasing with respect to the number of the transmitted packetsAg. We put the proof for Lemma 2.1 in Appendix A.1.

Lemma 2.1. Whether flowg is loss-tolerant or loss-sensitive, each UE (i, g)’s valuation functionvg(ei,g, Ag) has the following two properties:

1. vg(ei,g, Ag) is strictly decreasing with respect to ei,g.

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Table 2.1: Notation of the multicast system model R Total resource blocks in the system.

G The set of multicast flows.G = {1, 2, . . . G}.

M_g The number of original packets of flow g.

A_g The number of coded packets of flow g.

NG The group of UEs accessing flow g.

NG= {1, 2, . . . , N_g}.

UE(i, g) UE i accessing flow g.

bi,g The true BEP of UE(i, g). 0 ≤ bi ≤ 1.

e_i,g The true PEP of UE(i, g). e_i,g = 1 − (1 − b_i,g)^Lwhere L is the packet length.

v_g(ei,g, A_g) The valuation function of UE(i, g) defined in Proposition 2.1.

cg(Ag) The price function for flow g.

u_i,g(e_i,g, A_g) The utility function of UE(i, g) defined in Definition 2.2.

2. vg(ei,g, Ag) is strictly increasing with respect to Ag.

In the next section, we will propose a resource allocation mechanism along with a pricing scheme. The pricing scheme means that the BS charges a price for each UE’s accessing a flow. The price function for flowg, denoted by cg(Ag), is a function of the number of transmitted packetsAg. It will be designed in Chapter 2.4.1. With the price function, we define UE(i, g)’s utility function, denoted by ui,g(ei,g, Ag), as the valuation function minus the price function in Definition 2.2. The notation is summarized in Table 2.1.

Definition 2.2. [UE’s utility] UE (i, g)’s utility function ui,g(ei,g, Ag) is defined as the valuation functionvg(ei,g, Ag) minus the price function cg(Ag).

ui,g(ei,g, Ag) = vg(ei,g, Ag) − cg(Ag) (2.5)

2.4 Resource Allocation Problem and Mechanism Design

In the proposed multicast system, the BS has no information on the UEs’ PEPs. The most direct way is to request the private PEP information from the UEs. However, as the UEs are self-interested in nature, they may falsely report the PEPs if doing so increases their own utility. Without the correct PEP feedback, the resource allocation may be suboptimal.

In the following, we design a truth-revealing resource allocation mechanism that can elicit

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Figure 2.2: The flow diagram of the proposed resource allocation mechanism.

the true PEP information from the UEs. Recall that time is divided into periods. Though the mechanism is proposed for a single time period, it can be run in every time period.

Mathematically, the proposed mechanism (the BS) requires each UE to report the private PEP informationeî,g. With the reported PEP profile ê = (êi,g)i∈N_G,g∈G, the BS decides the resource allocation profile

A(ê) = (A1(ê), A2(ê), . . . , AG(ê)) , s.t.

G

X

g=1

Ag(ˆe) ≤ R (2.6)

whereAg(ê) is the number of the packets transmitted to each group g ∈ G. Note that the reported PEP profileê may not be the true PEP profile e = (ei,g)i∈N_G,g∈G. Therefore, our design goals are (1) to elicit the true PEP information from the UEsê = e (truth-revelation in Chapter 2.6) and (2) to achieve efficient and fair resource allocation (efficiency and fairness properties in Chapter 2.7).

In design of the mechanism, we consider UEs’ group resource demands and priority (weights). A weighted water-filling method is proposed to allocate resources [32]. The flow diagram of the proposed mechanism is given in Fig. 2.2, and the detailed designs are specified as follows.

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2.4.1 Pricing and Access Control

The BS decides the price functioncg(Ag) for transmitting the number of the packets Ag

in flow g. We design the price function as the valuation function with respect to some system-defined PEP valueec,g,0 ≤ ec,g ≤ 1.

Design 2.1. [Price function] The price function cg(Ag) is the valuation function with respect to some system-defined PEP valueec,g,0 ≤ ec,g ≤ 1.

cg(Ag) = vg(ec,g, Ag) (2.7)

The design of the price functions has one major advantage of access control. When joining the mechanism, the UEs with the PEPs less thanec,g gain positive utility, and the UEs with the PEPs greater thanec,g gain negative utility. In other words, ec,g is like a threshold that enables only the UEs with the PEPs less thanec,g to join the mechanism. In the rest of the paper, we will focus on the UEs joining the mechanism, assuming that all UEs have the PEPsei,g < ec,g.

Lemma 2.2. For UE(i, g), the utility function ui,g(ei,g, Ag) is positive if ei,g < ec,g; the utility function is non-positive ifei,g ≥ ec,g.











ui,g(ei,g, Ag) > 0, ei,g < ec,g

ui,g(ei,g, Ag) ≤ 0, ei,g ≥ e_c,g

(2.8)

Proof. Notecg(Ag) = vg(ec,g, Ag). From Lemma 2.1, we know that vg(ei,g, Ag) is strictly decreasing with respect toei,g. Thus, ifei,g < ec,g,vg(ei,g, Ag) > vg(ec,g, Ag); otherwise, vg(ei,g, Ag) ≤ vg(ec,g, Ag). This implies (2.8).

Theorem 2.1. [Access control] UE (i, g) will join the mechanism and obtain positive util- ity if the PEPei,g < ec,g; otherwise, the UE will not join the mechanism. In the system meaning, the proposed mechanism grants access to each UE with the PEPei,g < ec,g. Proof. This is the direct result of Lemma 2.2.

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2.4.2 UE Resource Demands and Group Resource Demands

Another advantage of the proposed price functions is that each UE(i, g)’s utility function ui,g(ei,g, Ag) will be single-peaked over the number of the packets Ag. This is shown in Lemmas 2.3 and 2.4. For UE(i, g) (with the PEP ei,g < ec,g), we define

∆vg(ei,g, Ag) = vg(ei,g, Ag+ 1) − vg(ei,g, Ag) (2.9)

as the gradient of the UE’s valuation function with respect toAg(valuation gradient function for short). We also define

∆ui,g(ei,g, Ag) = ui,g(ei,g, Ag+ 1) − ui,g(ei,g, Ag)

= ∆vg(ei,g, Ag) − ∆vg(ec,g, Ag) (2.10)

as the gradient of the UE’s utility function (utility gradient function for short). These gradient functions will be used in Lemmas 2.3, 2.4, and 2.5. The proofs for Lemmas 2.3 and 2.4 can be found in Appendices A.2 and A.3.

Lemma 2.3. The valuation gradient function∆vg(ei,g, Ag) is single-peaked with respect to ei,g. Denote the point on the ei,g-axis that maximizes ∆vg(ei,g, Ag) by e^∗_g(Ag). The functione^∗_g(Ag) is strictly increasing with respect to Ag.

Lemma 2.4. For UE (i, g) (with the PEP ei,g < ec,g), the utility functionui,g(ei,g, Ag) is single-peaked. Mathematically, there exists uniquedi,g such thatui,g(ei,g, Ag) is maxi- mized atAg = di,g, and











∆ui,g(ei,g, Ag) > 0, Ag < di,g

∆ui,g(ei,g, Ag) ≥ 0, Ag = di,g

∆ui,g(ei,g, Ag) < 0, Ag > di,g

(2.11)

From Lemma 2.4, each UE(i, g)’s utility is maximized when the number of the transmitted packets isdi,g. We call thisdi,g UE (i, g)’s resource demand. Note that each UE

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(i, g) with different PEP values ei,g may have different amounts of the resource demand di,g. Therefore, we can define a functiondg(ei,g) = di,g as the UE resource demand function in flow g. The UE resource demand function is an increasing function of ei,g, as proven in Lemma 2.5. This means the proposed price functions ensure the UEs with the lower PEPs to demand less, and vice versa.

Lemma 2.5. The UE resource demand functiondg(ei,g) is an increasing function of ei,g. Proof. For UE (i, g), ui,g(ei,g, Ag) is maximized at Ag = dg(ei,g). With (2.10) and the first and second inequalities of (2.11), we have

∆vg(ei,g, Ag) − ∆vg(ec,g, Ag) ≥ 0, Ag ≤ dg(ei,g) (2.12)

Consider another UE (j, g) with the PEP ej,g satisfying ei,g < ej,g < ec,g. Due to the single-peaked property of the valuation gradient function in Lemma 2.3, (2.12) along withei,g < ej,g < ec,g implies

∆vg(ej,g, Ag) > ∆vg(ec,g, Ag), Ag ≤ dg(ei,g) (2.13)

Moreover, from (2.10) and the first inequality of (2.11), for UE(j, g) we have

∆vg(ej,g, Ag) − ∆vg(ec,g, Ag) > 0, Ag < dg(ej,g) (2.14)

Checking the conditions of (2.13) and (2.14), we must havedg(ej,g) ≥ dg(ei,g) for ej,g > ei,g.

In fact, the UE resource demand function is an increasing step (staircase) function.

This is because the resource allocation, as well as the resource demand, only takes integer values, and different PEP values on a consecutive interval may correspond to the same integer value of the resource demand. Such a step-like property of the UE resource demand function will result in similar step-like behavior of the UE’s utility function, as will be seen in Fig. 2.4 in Chapter 2.8.1.

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We can directly use every UE’s resource demand for resource allocation. However, as each group may have numerous UEs, a resource allocation method that considers every UE’s resource demand will be complex. A simpler way is to propose a flow-level method that jointly uses a single UE’s resource demand to represent the group resource demand, and a group weight to take the number of the UEs in the group into consideration. We design the group resource demandDg(eg) as the kg-th minimum resource demand of the UEs in flowg where kg ∈ NG. According to Lemma 2.5, the group resource demand is also the resource demand of the UE with thekg-th minimum PEP.

Design 2.2. [Group resource demand] In flowg, the group resource demand Dg(eg) is defined as the kg-th minimum resource demand of the UEs in the flow. It is also the resource demand of the UE with thekg-th minimum PEP.

Dg(eg) = minkg; dg(e1,g), dg(e2,g), . . . , dg(eNg,g)

= dg(min {kg; eg}) (2.15)

wherekg ∈ N_G, eg = (e1,g, e2,g, . . . , eNg,g) is the PEP profile of the UEs in flow g, and min {kg; ·} selects the kg-th minimum input element.

Besides reducing the complexity, the design of the group resource demand has another good property: In consideration of limited resources, the selection ofkg means that we fulfill the resource demands of the UEs with the first kg minimum PEPs. For the other UEs with the PEPs greater than thekg-th minimum PEP and less thanec,g, we grant them access (Theorem 2.1) but do not guarantee to fulfill their resource demands.

2.4.3 Group Weights

As mentioned above, group weights that consider the number of the UEs in each group are also used for resource allocation. To be specific, the weightwg for each group g is designed as an increasing and concave function of the number of the UEs ˆNg that report ˆ

ei,g < ec,g. (We have assumed that each UE has the PEP ei,g < ec,g for simplicity.

Though the UEs may falsely report the PEPs, they may not report the PEPs higher than

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ec,g. Otherwise, they gain nothing. Thus, ˆNg = Ng.) This design is desirable in that a group with more UEs will have a higher weight and thus higher priority to gain resources.

However, the increment of the weight becomes less when the number of UEs increases, which also balances the resource allocation to each group. One possible design of the weight is as follows.

Design 2.3. [Group weight] The group weightwg is increasing and concave with respect to the number of the UEsNg. One simple candidate is a log function

wg = log(1 + Ng) (2.16)

2.4.4 Weighted Water-Filling Resource Allocation

The core of the proposed mechanism is the weighted water-filling resource allocation. It has low complexity. With the proposed price functions, group resource demands, and group weights, the overall procedures for resource allocation are specified as follows.

1. [Pricing] The BS sets the price function cg(Ag) for each group g as in Design 2.1.

2. [Requesting the PEP feedback] The BS requires each UE (i, g) to report the PEP ˆ

ei,g. Note that the reported PEP may not be the true PEP.

3. [Computing the group resource demands] Receiving the PEP feedback, the BS com- putes each UE(i, g)’s ”reported” resource demand dg(êi,g) that maximizes the ”reported” utility functionuî,g(Ag) = vg(êi,g, Ag) − cg(Ag). The BS further decides the group resource demandDg(êg) as the kg-th minimum reported resource demand as in Design 2.2 whereêg = (ê1,g, ê2,g, . . . , êNg,g) denotes the reported PEP profile of the UEs in groupg.

4. [Computing the weights] The BS sets the weight wgfor each groupg as an increasing and concave function of the number of UEs Ng. For example, the BS sets wg = log(1 + Ng).

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5. [Sorting the groups] The BS sorts all groups in increasing order of the weighted resource demands{Dg(ˆeg)/wg}_g∈G. Without loss of generality, we assume that all groups satisfy this increasing order of the weighted resource demands

D1(ˆe1) w1

≤ D2(ˆe2) w2

≤ . . . ≤ DG(ˆeG) wG

(2.17)

6. [Weighted water-filling resource allocation] The BS allocates the total resources R to the sorted groups round-by-round: In ther-th round, r = 1, 2, ..., G, we define a resource allocation basear(ê) in (2.18). The BS allocates to every sorted group g, g = r, r + 1, ..., G, the resources wgar(ê) (on the base ar(ê) and proportional to the weight wg), until either group r’s unsatisfied resource demand, Dr(êr) − wrPr−1

l=1 al(ˆe), is satisfied or the total unallocated resources, R−Pr−1

l=1al(ˆe)PG h=lwh, are allocated. According to this procedure, the resource allocation base ar(ˆe), r = 1, 2, ..., G, can be expressed iteratively

ar(ê) = min{Dr(êr) − wrPr−1 l=1 al(ê) wr

,R −Pr−1

l=1 al(ˆe)PG h=lwh

PG h=rwh

} (2.18)

The resource allocation to each sorted groupg is

Ag(ˆe) = wg g

X

r=1

ar(ˆe) (2.19)

7. [Charging] The BS charges each UE in each group g the price cg(Ag(ˆe)).

Instead of the iterative expressions in (2.18) and (2.19), the resource allocation can also be directly expressed in terms of the group resource demands{Dg(ˆeg)}_g∈G. We first define (G + 1) traffic cases for the group resource demands where the traffic case Cj, j = 0, 1, . . . , G, is











Dg(ˆeg) wg

≤ R −Pg−1

k=1Dk(ˆeg) PG

k=gwk

, g ≤ j Dg(ˆeg)

wg

> R −Pj

k=1Dk(ˆek) PG

k=j+1wk

, otherwise

(2.20)