Advances in Multi-ChannelResource Allocationroughput, Delay, and Complexity

Synthesis Lectures onCommunication Networks

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Founding Editor EmeritusJean Walrand,University of California, Berkeley

Synthesis Lectures on Communication Networks is an ongoing series of 50- to 100-page publications ontopics on the design, implementation, and management of communication networks. Each lecture isa self-contained presentation of one topic by a leading expert. e topics range from algorithms tohardware implementations and cover a broad spectrum of issues from security to multiple-accessprotocols. e series addresses technologies from sensor networks to reconfigurable optical networks.e series is designed to:

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Advances in Multi-Channel Resource Allocation: roughput, Delay, and ComplexityBo Ji, Xiaojun Lin, and Ness B. Shroff2016

A Primer on Physical-Layer Network CodingSoung Chang Liew, Lu Lu, Shengli Zhang2015

Sharing Network ResourcesAbhay Parekh and Jean Walrand2014

Wireless Network PricingJianwei Huang and Lin Gao2013

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Performance Modeling, Stochastic Networks, and Statistical Multiplexing, second editionRavi R. Mazumdar2013

Packets with Deadlines: A Framework for Real-Time Wireless NetworksI-Hong Hou and P.R. Kumar2013

Energy-Efficient Scheduling under Delay Constraints for Wireless NetworksRandall Berry, Eytan Modiano, and Murtaza Zafer2012

NS Simulator for BeginnersEitan Altman and Tania Jiménez2012

Network Games: eory, Models, and DynamicsIshai Menache and Asuman Ozdaglar2011

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Path Problems in NetworksJohn S. Baras and George eodorakopoulos2010

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Network SimulationRichard M. Fujimoto, Kalyan S. Perumalla, and George F. Riley2006

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Advances in Multi-Channel Resource Allocation: roughput, Delay, and Complexity

Bo Ji, Xiaojun Lin, and Ness B. Shroff

www.morganclaypool.com

ISBN: 9781627054614 paperbackISBN: 9781627059831 ebook

DOI 10.2200/S00739ED1V01Y201610CNT017

A Publication in the Morgan & Claypool Publishers seriesSYNTHESIS LECTURES ON COMMUNICATION NETWORKS

Lecture #17Series Editor: R. Srikant, University of Illinois at Urbana-ChampaignFounding Editor Emeritus: Jean Walrand, University of California, BerkeleySeries ISSNPrint 1935-4185 Electronic 1935-4193

Advances in Multi-ChannelResource Allocationroughput, Delay, and Complexity

Bo JiTemple University

Xiaojun LinPurdue University

Ness B. Shroffe Ohio State University

SYNTHESIS LECTURES ON COMMUNICATION NETWORKS #17

CM&

cLaypoolMorgan publishers&

ABSTRACTe last decade has seen an unprecedented growth in the demand for wireless services. eseservices are fueled by applications that often require not only high data rates, but also very lowlatency to function as desired. However, as wireless networks grow and support increasingly largenumbers of users, these control algorithms must also incur only low complexity in order to be im-plemented in practice. erefore, there is a pressing need to develop wireless control algorithmsthat can achieve both high throughput and low delay, but with low-complexity operations. Whilethese three performance metrics, i.e., throughput, delay, and complexity, are widely acknowledgedas being among the most important for modern wireless networks, existing approaches often havehad to sacrifice a subset of them in order to optimize the others, leading to wireless resource allo-cation algorithms that either suffer poor performance or are difficult to implement. In contrast,the recent results presented in this book demonstrate that, by cleverly taking advantage of mul-tiple physical or virtual channels, one can develop new low-complexity algorithms that attainboth provably high throughput and provably low delay. e book covers both the intra-cell andnetwork-wide settings. In each case, after the pitfalls of existing approaches are examined, newsystematic methodologies are provided to develop algorithms that perform provably well in allthree dimensions.

KEYWORDSmulti-channel, wireless networks, resource allocation, scheduling, utility maximiza-tion, throughput, delay, low-complexity, performance guarantee, CSMA

ix

To Siwei, Jacob, and my parents

– Bo Ji

To Lining, Alice, and Jenny

– Xiaojun Lin

To Jasmine, Sanaya, and Zarius

– Ness B. Shroff

xi

ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Intra-Cell Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 A Simple System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Pitfalls of the Classical MaxWeight Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Queue-length-based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Delay-based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6 Intuition of Achieving Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.7 Rate-function Delay Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.7.1 Assumptions on the Arrival Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.7.2 Upper Bound on the Delay Rate-function . . . . . . . . . . . . . . . . . . . . . . . . 232.7.3 Sufficient Condition of Rate-function Delay Optimality . . . . . . . . . . . . 252.7.4 Dominance Property: Frame-based Scheduling and Perfect Matching . . 272.7.5 Vector Matching in Bipartite Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.7.6 Proof Sketch of Rate-function Delay Optimality . . . . . . . . . . . . . . . . . . 33

2.8 roughput Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.8.1 Optimal roughput Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.8.2 Sufficient Condition of roughput Optimality . . . . . . . . . . . . . . . . . . . 37

2.9 Scheduling Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.9.1 Rate-function Delay-optimal Policies (DWM and DWM-n) . . . . . . . . 372.9.2 roughput-optimal Policies (DWM and D-MWS) . . . . . . . . . . . . . . . 412.9.3 Low-complexity Hybrid Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.10 Near-optimal Delay Rate-function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.10.1 Delay-based Server-Side Greedy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.10.2 Main Result and Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462.10.3 Equivalence Property: Delay-based Queue-Side-Greedy . . . . . . . . . . . . 50

2.11 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

xii

3 Network-Wide Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2 Single-Channel Solutions based on MaxWeight . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.2.1 A Simple Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.2.2 e MaxWeight Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.2.3 Low-Complexity Approximations to MaxWeight . . . . . . . . . . . . . . . . . . 623.2.4 Single-Channel CSMA Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.3 Using Multiple Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.3.1 Independent CSMA Chains across Channels . . . . . . . . . . . . . . . . . . . . . 693.3.2 Complementary Schedules across Channels: A Departure from

MaxWeight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.3.3 What to do if ere is Only One Physical Channel? . . . . . . . . . . . . . . . . 723.3.4 e Notion of Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.3.5 Utility-Maximization vs. roughput-Maximization . . . . . . . . . . . . . . . 74

3.4 Multi-Channel CSMA algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.5 roughput/Delay/Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.5.1 Utility Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.5.2 Delay Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.5.3 Computational Complexity and Communication Overhead . . . . . . . . . . 863.5.4 VMC-CSMA under Exogenous Packet Arrivals . . . . . . . . . . . . . . . . . . . 86

3.6 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.7 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.8 Inter-cell Coordination in OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.8.1 Model for an OFDM Multi-cell System . . . . . . . . . . . . . . . . . . . . . . . . . 943.8.2 Distributed Algorithms based on Multi-Channel Gibbs Sampling . . . . 96

3.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.10 Additional Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Authors’ Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

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PrefaceWith the advent of smart phones, smart devices, and the Internet of ings, wireless technologyhas become part of our daily lives. Wireless technology has spawned a plethora of services thatspan business, science and engineering, entertainment, safety and security, health monitoring,and cover a large portion of our social interactions. Due to the prevalence of these new services,today’s wireless networks are witnessing not only an unprecedented growth in the volume of traf-fic, but also a dramatic change in the types of traffic (e.g., a much higher percentage of voice/videotraffic with more stringent delay requirements). ese new trends require next-generation wire-less networks to provide not only high data rates (tens of gigabits per second), but also ultra-lowlatencies (sub-millisecond). Moreover, as wireless networks grow and support an increasinglylarge number of users, resource allocation algorithms must also incur low complexity in orderto be implemented in practice. is book presents an overview of recent development of newlow-complexity algorithms that achieve provably guaranteed performance in both throughputand delay for multi-channel wireless systems, which are increasingly common in modern wire-less networks. e new approaches and frameworks described in this book demonstrate that, bycleverly taking advantage of multiple channels, one can simultaneously achieve high throughput,low delay, and low complexity.

is book focuses on two important network settings of practical interest: intra-cellscheduling (Chapter 2) and network-wide scheduling (Chapter 3). In each chapter, we first ex-amine the pitfalls of existing approaches, and then describe new systematic methodologies thatexploit multiple physical or virtual channels for developing resource allocation algorithms thatare provably efficient in all three dimensions. In order to address the technical challenges, a widearray of analytic tools are exploited, such as stochastic optimization, queueing theory, algorithmdesign, large-deviations theory, and Lyapunov analysis. On the other hand, to make the bookaccessible to a wider audience, we provide several illustrative examples and numerical simulationresults, which aid readers in understanding the novel ideas and key intuitions behind the devel-oped algorithms. We believe that this book will be useful for both researchers and practitionersin the field of communications and networking.

We would like to thank Prof. Jean Walrand for reaching out to us and providing us theopportunity to work on this book. We thank Manu Sharma, Gagan R. Gupta, and Po-Kai Huangfor contributing to earlier text and results in the book. Many thanks also to Prof. Bin Li of theDepartment of Electrical, Computer, and Biomedical Engineering at the University of RhodeIsland and anonymous reviewers for reading an earlier version of the manuscript and providingvaluable feedback. We would also like to thank Prof. R. Srikant for serving as editor and Morgan& Claypool Publishers for helping us produce the final version of the book. Last but not least, the

xiv PREFACE

authors are indebted to their families for their constant and unyielding support, without whichthis book would not have been possible.

Bo Ji, Xiaojun Lin, and Ness B. ShroffOctober 2016

1

C H A P T E R 1

Overviewe last decade has witnessed an unprecedented growth in wireless services fueled in large part bythe rise of smart phones and tablets. It is estimated that within the next year we will have 1 billionconsumers across the world who have bought tablets and over 2 billion consumers who will havesmart phones [3, 5]. is growth in smart devices has also been responsible for the developmentof data-hungry applications that continue to put an enormous strain on the commercial wirelessinfrastructure.Wireless companies have responded by rapidly deploying additional infrastructure,while at the same time wireless service providers have put monthly caps on user data usage anddata rates (e.g., AT&T has eliminated its unlimited data subscription for new users). A sensibleapproach to designing these wireless networks is to add new infrastructure as needed, but to alsodevelop resource allocation algorithms that can most efficiently use the existing infrastructure.is is especially important for emerging applications which require not only high-throughputbut also low delay in ensuring a high-quality end-user experience.

is book describes new methods to design wireless resource-allocation algorithms formulti-channel wireless systems, which are increasingly common in modern wireless networks.For instance, 4G/LTE mobile wireless networks are based on OFDM (Orthogonal Frequency-Division Multiplexing) and OFDMA (Orthogonal Frequency-Division Multiple Access). In thefrequency domain, a wide spectrum is divided into many narrow subcarriers of 15kHz each. Everytwelve subcarriers are combined into a resource block, which can be dynamically assigned to users[46]. Multiple channels may also be provided by the wireless standards, e.g., the IEEE 802.11astandard can have twelve orthogonal channels in the 5GHz band [70].

e availability of multiple channels provides significant flexibility in designing high-performance wireless resource-allocation algorithms. Typically, there are a number of commonmetrics that one may consider in evaluating an algorithm: throughput, delay, and complexity.Although dividing a piece of spectrum into multiple channels may not automatically increase thethroughput, we have found that it will help to improve delay or reduce complexity. To see this,we compare the downlink of a typical wide-band 3G mobile system with that of a 4G system(Fig. 1.1). Suppose the 3G system uses a wide 5Mhz band to serve users. At any time, only oneuser can be chosen for service in the downlink of the given band.¹ Typically, in order to maximizethe spectrum efficiency, the base-station will pick the user with the best channel (compared toits mean channel). at would mean that, if a user has a poorer-than-average channel for a long

¹Although CDMA allows transmissions to multiple users to occur at the same time, in 3G CDMA systems each cell often onlyserves one user at a time, and the transmissions to multiple users are time-multiplexed. Such an operation model is consideredmore bandwidth-efficient for high-speed data-traffic [9, 53, 87, 108].

2 1. OVERVIEW

time, it may be starved from service. In contrast, in a 4G system, the 5Mhz channel is dividedinto multiple smaller sub-channels. It is unlikely that the user’s channel is simultaneously poor inall sub-channels. us, the user will typically wait less to be served. As a result, the delay perfor-mance can be significantly improved with the availability of multiple channels, even though thetotal bandwidth in each case is the same. In Chapter 2, we will make this intuition rigorous inthe context of a single cell in 4G/LTE systems. en, in Chapter 3, we will look at network-widescheduling for a larger system with multiple interference domains (e.g., in either a multi-cell sys-tem or an ad hoc network), and we will demonstrate how the availability of multiple channels willhelp us significantly reduce delay as well.

Good Channels

TimeSingle-Channel Systems

TimeMulti-Channel Systems

Fre

quen

cy

Fre

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Figure 1.1: A comparison between single-channel and multi-channel systems.

An equally important challenge that we need to address is that of computational complex-ity. In a single cell in a 4G/LTE system, the transmission time intervals (e.g., the TTI intervalin LTE/OFDM) is on the order of a few milliseconds. In this short time, scheduling decisionsmay need to be made for hundreds (or even thousands) of channels and users. Hence, even if onewere to design mechanisms that were throughput and delay efficient, these mechanisms wouldnot be useful in practice unless they also exhibited low computational complexity. erefore, anadditional important engineering challenge that needs to be addressed is to develop simple andeasy-to-implement algorithms. In Chapter 2, we will demonstrate how multi-channel schedul-ing algorithms with very low complexity can be developed for a single OFDM cell to attain highthroughput and low delay. Complexity is also a major challenge for network-wide scheduling,where the optimal scheduling policy (i.e., MaxWeight) is known to incur exponential computa-tional complexity. In Chapter 3, we will show how the availability of multiple channels can bethe key toward a new formulation that avoids the pitfalls of MaxWeight and that provably attainsgood performance in all three dimensions of throughput, delay, and complexity.

One may argue that the idea of channelization is probably as old as wireless systems them-selves. Once engineers figure out how to send information through the radio, a question that soonfollows is how to let multiple users operate at the same time, without interfering with each other.

3

A natural idea is to divide the radio spectrum into frequency channels, so that each user can oper-ate on a separate channel. ese channels are said to be “orthogonal” because the radio signals onone channel will create minimal interference to the other channel. is separation can be achievedby putting guard bands between neighboring channels and restricting each user’s signal to withinthe limit set by the guard bands. Such an FDMA (Frequency-Division Multiple Access) idea wasused in AM/FM radios and TVs, and was also later used in the first generation of mobile wirelessnetworks. FDMA is just one of the many ways to “orthogonalize” the channel. Another approachis to use TDMA (Time-Division Multiple Access). In this case, time is divided into frames, eachof which consists of multiple time-slots. Each user is assigned a given time-slot in all frames.GSM, one of the second-generation mobile wireless standards, uses a combination of FDMAand TDMA. A third approach is to use spread-spectrum codes, as in CDMA (Code-DivisionMultiple Access) systems. Once multiple orthogonal channels are set up (either via frequency,time, or code), the system can then simultaneously serve multiple voice users with stringent de-lay requirements. In such a system, a user is typically allocated a single channel for the durationof the call. Within each cell, the base-station only needs to make sure that each active user isassigned a different channel. Across cells, channels could be reused, as long as the same channelis not simultanously used in neighboring cells (Fig. 1.2). Based on such a framework, sophisti-cated channel-allocation algorithms have been developed to improve spectrum efficiency and thequality of service (QoS) to users [103].

However, there are two reasons why this classical multi-channel design methodology pri-marily for voice systems is not suitable for modern wireless networks. First, as mobile wireless traf-ficmoves from voice toward highly bursty data, the amount of resources that one user needs can behighly variable. us, it would be highly inefficient to assign each user a fixed channel. Indeed, in4G OFDM systems, even though the frequency/time division looks similar to FDMA/TDMAin 2G GSM systems, each user can be allocated a variable amount of frequency/time resource.Both the intra-cell and inter-cell resource allocation must take into account this dynamic nature.Second, as cells become smaller in order to accommodate the rapid increase of data traffic, theirplacement also becomes more and more ad hoc [6]. It is then difficult to use regular patterns asin the 7-reuse pattern shown in Figure 1.2 to control inter-cell co-channel interference. Hence,more sophisticated multi-channel resource allocation algorithms are needed to accommodate thishighly dynamic and ad hoc environment.

ere have also been significant advances in using an optimization-based approach to de-sign resource allocation algorithms for wireless networks, including both cellular and ad hoc net-works. However, these approaches have typically not been designed specifically either for multi-channel systems or for delay performance. For instance, a landmark result along this direction isthe so-called MaxWeight or back-pressure policy [118]. At each time-instant, resources shouldbe allocated to the set of the users that attain the maximum total weight. ese algorithms can beshown to achieve the optimal throughput. One may argue that, given that the model in [118] is sogeneral, it would be trivial to generalize the max-weight or back-pressure policy to multi-channel

4 1. OVERVIEW

A

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Figure 1.2: A 7-reuse channel-allocation pattern for 2G cellular systems.

systems. Unfortunately, if not carefully designed, such trivial generalizationmay lead to poor delayperformance. For example, in a single-cell setting, a user with the maximum weight in one chan-nel will likely be with maximum weight in many other channels. As a result, resources are favoredto a small set of the users. Although this is still optimal as far as throughput is concerned, therewill be many users who suffer poor delay. Further, for network-side scheduling, the MaxWeightalgorithm is known to incur computational complexity that grows exponentially with the net-work size. Due to these reasons, designing algorithms that can fully exploit the above-mentionedmulti-channel advantage is in fact not a trivial problem.

In this book, we will present new results on multi-channel resource-allocation algorithmsthat overcome these challenges. us, they will be able to fully exploit the multi-channel advan-tage to achieve both high throughput and low delay with low-complexity operations. We notethat in contrast to throughput maximization, delay is usually much more difficult to handle. Akey contribution of the methodology developed in this book is thus to provide tractable means toquantify the delay improvement of the system in a multi-channel setting, along with throughputand complexity characterizations.

In particular, in Chapter 2, we will focus on intra-cell scheduling for a single cell in anOFDM system. Here, the key difficulty is in determining which users to be assigned to whichchannels in order to achieve good performance in terms of throughput, delay, and complexity,while taking into account the practical requirements of today’s multi-channel systems. For ex-ample, in OFDM systems, while a user can be assigned several sub-frequency bands (channels),

5

multiple users cannot be assigned to one channel at the same time. A simple system model thatcaptures such practical requirements will be described in Section 2.2. Here, our delay metricof interest is the decay-rate of the tail probability that the HOL (head-of-line) delay exceeds athreshold. is delay metric is important when the packets require stringent delivery deadlines.Working with this system model, in Section 2.3 we show that the classical MaxWeight policies,although known to be throughput-optimal in our multi-channel setting, exhibit very poor delayperformance. Using simple examples, we demonstrate in Sections 2.4 and 2.5, respectively, thata queue-length-based iterative scheduling policy can significantly improve the delay performanceand that a delay-based counterpart can further reduce the delay by orders of magnitude. eseexamples motivate us to develop a rigorous and systematic framework for designing schedulingpolicies that can achieve good performance in all three dimensions of throughput, delay, and com-plexity. We first discuss the intuitions of achieving delay optimality and throughput optimality inSection 2.6. Employing a divide-and-conquer approach, we will present the sufficient conditionsfor delay optimality and throughput optimality in Sections 2.7 and 2.8, respectively. en, in Sec-tion 2.9 we will discuss several important scheduling policies, including a class of low-complexityhybrid policies that intelligently combine different policies satisfying the sufficient conditions andachieve both optimality of delay and throughput. Further, in Section 2.10 we show how a simple,greedy algorithm can dramatically reduce the complexity with only a minimal drop in the delayperformance. While most of Chapter 2 focuses on analytical results for a simple channel model,we will present the simulation results for more general system models too in Section 2.11. In Sec-tion 2.12, we will conclude Chapter 2 by summarizing the key results presented in this chapterand discuss how the useful insights we obtained can be utilized for more general scenarios.

en, in Chapter 3, we will study network-side scheduling for a larger system with mul-tiple interference domains. Here, the additional source of difficulty comes from the complex in-terference relationship governing simultaneous transmissions. As we will survey in Section 3.2,most of the existing single-channel resource-allocation algorithms have some relationship to theMaxWeight algorithm, which incurs exponential complexity. Due to this inherent difficulty, ex-isting algorithms that attempt to reduce this exponential complexity suffer either much lowerthroughput guarantees, or exponentially large delay. In contrast, we will show in the rest of Chap-ter 3 how the availability of mutliple channels can be exploited to overcome this difficulty. Here,our delay metrics of interest are the average packet delay and the tail distribution of the HOLwaiting time at each link.² In Section 3.3, we will introduce a new formulation of the resourceallocation problem tailored to multi-channel systems, which then results in a new Multi-Channel(MC-)CSMA algorithm in Section 3.4. In Section 3.5, we will show that the new MC-CSMAalgorithm can provably achieve near-optimal system utility, with complexity that grows only log-arithmically with the network size. Further, under certain conditions, the delay of each link willnot grow with the network size. We will discuss further implementation issues in Section 3.6,

²Note that different delay metrics are used in Chapter 3 compared to Chapter 2, partly due to the higher complexity of thenetwork-wide resource allocation problem.

6 1. OVERVIEW

especially when the notion of virtual channels must be used for systems with only one physicalchannel. While most of Chapter 3 focuses on a simpler protocol interference model, in Sec-tion 3.7 we will also demonstrate how the key ideas of MC-CSMA can be used for SINR-basedinterference models to solve the inter-cell coordination problem in multi-cell OFDM systems.

7

C H A P T E R 2

Intra-Cell Scheduling2.1 INTRODUCTION

Today’s wireless networks are witnessing a significant increase in the volume of traffic. For in-stance, according to theCiscoVisual Networking Index (VNI) white paper [4], globalmobile datatraffic grew 74% in 2015 and is forecasted to reach 2.3 zettabytes (i.e., 2.3 billion terabytes) peryear by 2020. In order to accommodate this deluge of traffic, the network must be able to providesignificantly larger capacity and deliver substantially higher throughput. However, not only hasthe volume of traffic increased over the years, but the types of traffic have dramatically changed.For instance, mobile data traffic exceeded mobile voice traffic for the first time in 2009; mobilevoice service is being shifted from circuit-switched networks to IP networks; mobile video trafficgrew to 55% of total mobile data traffic by the end of 2015 and is forecasted to account for nearlythree-fourths of total mobile data traffic by the end of 2020 [4]. A common feature of voice andvideo applications is their requirement of stringent delay-guarantees. Hence, this integration ofdata/voice/video traffic requires that the network must not only provide high throughput, but alsoguarantee low delay. Moreover, current and next-generation wireless cellular systems are typicallybased on Orthogonal Frequency Division Multiplexing (OFDM) (e.g., LTE [1] and WiMAX[2]) and have a large bandwidth that can be divided into multiple narrow frequency subcarriers(or channels). A given user can be served by multiple channels simultaneously, and the channelsneed to be allocated to a large number of users in every scheduling cycle, which could be as shortas one millisecond. us, for actual implementation to occur, the scheduling policies must be oflow computational complexity while satisfying the above requirements of high throughput andlow delay. erefore, in such multi-channel wireless networks it is critical to develop schedulingpolicies that meet all three dimensions of performance.

In this chapter, we focus on single-cell multi-channel cellular systems. To motivate thescheduling problem in such systems, we consider the downlink scenario of a single-cell OFDM-based LTE system [1] as an application scenario. An illustration of the system is presented inFig. 2.1a. In a typical LTE system, during peak times there could be hundreds of users (calledUser Equipments or UEs) that are simultaneously connected to a base-station (called eNodeB).e arriving packets for the users get buffered in separate data queues at the base-station beforethey are transmitted to the users. e wide-band can be divided into a large number of subcar-riers that can be allocated to possibly different users in each scheduling cycle (i.e., TransmissionTime Interval or TTI, which could be as short as one millisecond). For example, in the currentLTE system a 20MHz band can be divided into 100 Physical Resource Blocks (PRBs) in each

8 2. INTRA-CELL SCHEDULING

scheduling cycle. A PRB consists of 12 consecutive subcarriers and is the smallest element ofresource allocation assigned by the base-station scheduler. An example of the PRBs allocation isillustrated in Fig. 2.1b.

Hundreds of UEs

LTE eNodeB

UE 1

UE 2

UE n

Q1

Q2

Qn

(a) LTE base-station (eNodeB)

PRBs Allocation

PRB

TimeScheduling Cycle

Fre

quen

cy

(b) PRBs allocation

Figure 2.1: A motivating example: the downlink scenario of a single-cell LTE system.

e scheduling problem here is to decide which PRBs are allocated to which users in eachscheduling cycle. Note that in each scheduling cycle, a PRB is the smallest scheduling unit andcan only be allocated to one user, but a user can get multiple PRBs at the same time. Due tofading and user mobility, the channel condition between the user and the base-station could betime-varying. For a given user, it typically experiences flat fading on the channel of each individualPRB, but across PRBs the channel conditions are different due to multi-path fading. us, whenthe overall channel condition of the user is good, it will see a larger number of PRBs in goodconditions. However, even if the overall channel condition is poor, the user will still likely seegood channel conditions on a few PRBs. Hence, this channel diversity offers a great opportunityof designing high-performance scheduling policies that can achieve low delay without sacrificingany throughput. On the other hand, this also substantially increases the design space, whichmakesthe scheduling problem much more challenging. In addition to this major research goal, anothersignificant challenge in the LTE system is that the scheduling cycles are very short (e.g., onemillisecond), and hundreds of orthogonal channels and hundreds of users need to be scheduled atthe same time. erefore, as discussed in Chapter 1 the goal of the scheduling problem is threefold: (1) tomaximize the throughput, (2) to minimize the amount of time that any packet spends in the buffer at thebase-station, and (3) to ensure that the designed scheduling policies are of low computational complexity.

2.2 A SIMPLE SYSTEM MODELIn this section, we present a simple model of a multi-queue multi-server system with stochasticconnectivity, as shown in Fig. 2.2. e key issues of the single-cell multi-channel system we de-

2.2. A SIMPLE SYSTEM MODEL 9

scribed in the previous section can be captured in this model. We assume that there are n channels,each of which is represented by a server. We also assume that there are n users, each of whichis associated with a separate First-In First-Out (FIFO) data queue. For ease of presenting the keyideas, the number of users is assumed to be equal to the number of channels. e approaches we presentin this chapter will similarly carry through if the number of users scales linearly with the number ofchannels (e.g., see [110]). We assume a simple binary channel model. If the channel state is above acertain quality threshold (e.g., a signal-to-interference-plus-noise ratio or SINR threshold) thenwe say that the channel is ON, otherwise the channel is assumed to be OFF. roughout therest of this chapter, we will interchangeably use the terms “user” and “queue”; similarly for theterms “channel” and “server.” We assume a time-slotted system. In each time-slot, a server can beallocated to only one queue, but a queue can get service from multiple servers. e connectivitybetween queues and servers is time-varying, i.e., it can change between ON and OFF from timeto time. We assume that perfect channel state information (i.e., whether each channel is ON orOFF for each user in each time-slot) is known at the base-station.

Q1

Q2 S2

Sn

S1

Qn

q

Figure 2.2: System model. e connectivity between each pair of queue Qi and server Sj is ON(denoted by a solid edge) with probability q, and OFF (denoted by a dashed edge) otherwise.

e basic notations used in this chapter are as follows. We let Qi denote the FIFO queue(at the base-station) associated with the i-th user and let Sj denote the j -th server. We assumean infinite buffer for all the queues. Let Ai .t/ denote the number of packet arrivals to queue Qi intime-slot t . Other technical assumptions on the arrival processes that are specifically needed fordelay analysis and throughput analysis will be presented later in Sections 2.7 and 2.8, respectively.For concreteness we assume that packet arrivals occur at the beginning of each time-slot and thatpacket departures occur at the end of each time-slot. By slightly abusing the notations, we useQi .t/ to denote the length of queue Qi at the beginning of time-slot t immediately after packetarrivals. Also, let Zi;l.t/ denote the delay (i.e., waiting time in the queue) of the l-th packet ofqueue Qi at the beginning of time-slot t , which is measured since the time when the packetarrived to queue Qi until the beginning of time-slot t . Note that at the end of each time-slot,the packets still present in the system will have their delays increased by one due to the elapsed

10 2. INTRA-CELL SCHEDULING

time. We then let Wi .t/ D Zi;1.t/ denote the HOL packet delay of queue Qi at the beginningof time-slot t .

We next describe our channel model. Let Ci;j .t/ denote the capacity of the link betweenqueue Qi and server Sj in time-slot t , i.e., the maximum number of packets that can be served byserver Sj from queue Qi in time-slot t . We model Ci;j .t/ as an i.i.d. Bernoulli random variablewith a parameter q 2 .0; 1/, called the channel ON probability:

Ci;j .t/ D

�1; with probability q;

0; with probability 1 � q:(2.1)

All the variables Ci;j .t/ are assumed to be mutually independent across all the variables i , j , andt . Under this assumption, variable Ci;j .t/ also denotes the connectivity between queue Qi andserver Sj in time-slot t . is i.i.d. Bernoulli ON-OFF fading channel model has been used inmany studies (e.g., [14, 15, 54–56, 68, 110, 111]). Although this channel model is a simplification,we believe that the obtained insights will also be useful for more general channel models. Undersome additional conditions, many of the analytical results for delay analysis can be extended tomore general channels that are potentially multi-rate (e.g., [13, 16]) or time-correlated (e.g., [97]).

2.3 PITFALLS OF THE CLASSICAL MAXWEIGHT POLICYAs discussed in Section 2.1, our goal is to design low-complexity scheduling policies that can pro-vide high throughput and low delay. Note that the throughput performance of scheduling policieshas been extensively studied since the seminal work of Tassiulas and Ephremides [118] and is nowconsidered to be well understood. e celebrated MaxWeight policy developed in [118] and itsvariants have been shown to be throughput-optimal in a variety of settings (e.g., see [38, 85]and reference therein), including the multi-channel setting we consider. We say that a schedulingpolicy is throughput-optimal, if it can stabilize the system (i.e., all the queues in the system donot blow up to infinity¹) under any feasible traffic load. Hence, as a first step it makes sense toexamine the delay performance in the multi-channel system for the classical MaxWeight policy.

In our multi-channel setting, the MaxWeight policy makes scheduling decisions accordingto the following procedure: in each time-slot, theMaxWeight policy assigns each server to a queuethat has the largest weight among all the queues connected to this server. e weight of a queuecould be either the queue length or the HOL delay, and the resultant MaxWeight schedulingpolicy is then called Q-MWS or D-MWS, respectively. An example of the schedules generatedby Q-MWS and D-MWS is provided in Fig. 2.3, where there are three queues (Q1, Q2, and Q3)and three servers (S1, S2, and S3). We use a solid edge to denote an ON channel between theservers and the queues and omit theOFF channels in the figure. In this example, servers S1 and S3

are connected to both Q1 and Q2, and server S2 is connected to all the queues. e queue lengthsof the three queues are Œ2; 3; 1�.e delay of each packet is labeled above the corresponding packet.

¹A more precise definition of stability (using the notion of positive recurrence) can be found in [118].