Estimation and Coordination of Sequence Patterns for Frequency Hopping Dynamic Spectrum Access Networks

In 2010, the Shared Spectrum Company showed in a survey of Radio Frequency (RF) bands that underutilization of spectrum has resulted from current frequency management practices. Traditional frequency allocation allows large bands of licensed spectrum to remain vacant even under current high demands. Cognitive radio\u27s (CR) use of Dynamic Spectrum Access (DSA) enables better spectrum management by allowing usage in times of spectrum inactivity. This research presents the CR problem of rendezvous for fast Frequency Hopping Spread Spectrum (FHSS) networks, and examines protocols for disseminating RF environment information to coordinate spectrum usage. First, Gold\u27s algorithm is investigated as a rendezvous protocol for networks utilizing fast frequency hopping. A hardware implementation of Gold\u27s algorithm on a Virtex-5 Field Programmable Gate Array (FPGA) is constructed to determine the resource requirements and timing limitations for use in a CR. The resulting design proves functionality of the algorithm, and demonstrates a decrease in time-to-rendezvous over current methods. Once a CR network is formed, it must understand the changing environment in order to better utilize the available spectrum. This research addresses the costs a network incurs to coordinate such environment data. Three exchange protocols are introduced and evaluated via simulation to determine the best technique based on network size. The resulting comparison found that smaller networks function best with polled or timedivision based protocols where radios always share their environment information. Larger networks, on the other hand, function best when a dispute-based exchange protocol was utilized. These studies together conclude that the selection of a rendezvous algorithm or a protocol for the exchange of environment data in a CR network are determined by the characteristics of the network, and therefore their selection requires a cognitive decision

Spectrum sharing and management techniques in mobile networks

Το φάσμα συχνοτήτων αποδεικνύεται σπάνιο κομμάτι για τους πόρους ενός κινητού δικτύου το οποίο πρέπει να ληφθεί υπόψιν στη σχεδίαση τηλεπικοινωνιακών συστημάτων 5ης γενιάς. Επιπλέον οι πάροχοι κινητών δικτύων θα πρέπει να επαναπροσδιορίσουν επιχειρησιακά μοντέλα τα οποία μέχρι τώρα δεν θεωρούνταν αναγκαία (π.χ., γνωσιακά ραδιοδίκτυα), ή να εξετάσουν την υιοθέτηση νέων μοντέλων που αναδεικνύονται (π.χ., αδειοδοτούμενη από κοινού πρόσβαση) ώστε να καλύψουν τις ολοένα αυξανόμενες ανάγκες για εύρος ζώνης. Ο μερισμός φάσματος θεωρείται αναπόφευκτος για συστήματα 5G και η διατριβή παρέχει λύση για προσαρμοστικό μερισμό φάσματος με πολλαπλά καθεστώτα εξουσιοδότησης, βάσει ενός καινοτόμου αρχιτεκτονικού πλαισίου το οποίο επιτρέπει στα δικτυακά στοιχεία να λαμβάνουν αποφάσεις για απόκτηση φάσματος. Η προτεινόμενη διαδικασία λήψης αποφάσεων είναι μία καινοτόμα τεχνική προσαρμοστικού μερισμού φάσματος βασιζόμενη σε ελεγκτές ασαφούς λογικής που καθορίζονν το καταλληλότερο σχήμα μερισμού φάσματος και σε ενισχυμένη μάθηση που ρυθμίζει τους κανόνες ασαφούς λογικής, στοχεύοντας να βρει τη βέλτιστη πολιτική που πρέπει να ακολουθεί ο πάροχος ώστε να προσφέρει την επιθυμητή ποιότητα υπηρεσιών στους χρήστες, διατηρώντας πόρους (οικονομικούς ή ραδιοπόρους) όπου είναι εφικτό. Η τελευταία συνεισφορά της διατριβής είναι ένας μηχανισμός που εξασφαλίζει δίκαιη πρόσβαση σε φάσμα ανάμεσα σε χρήστες σε σενάρια στα οποία η εκχώρηση άδειας χρήσης φάσματος δεν είναι προαπαιτούμενη.Radio spectrum has loomed out to be a scarce resource that needs to be carefully considered when designing 5G communication systems and Mobile Network Operators (MNOs) will need to revisit business models that were not of their prior interest (e.g. Cognitive Radio) or consider adopting new business models that emerge (e.g. Licensed Shared Access) so as to cover the extended capacity needs. Spectrum sharing is considered unavoidable for 5G systems and this thesis provides a solution for adaptive spectrum sharing under multiple authorization regimes based on a novel architecture framework that enables network elements to proceed in decisions for spectrum acquisition. The decision making process for spectrum acquisition proposed is a novel Adaptive Spectrum Sharing technique that uses Fuzzy Logic controllers to determine the most suitable spectrum sharing option and reinforcement learning to tune the fuzzy logic rules, aiming to find an optimal policy that MNO should follow in order to offer the desirable Quality of Service to its users, while preserving resources (either economical, or radio) when possible. The final contribution of this thesis is a mechanism that ensures fair access to spectrum among the users in scenarios in which conveying spectrum license is not prerequisite

A new connectivity strategy for wireless mesh networks using dynamic spectrum access

The introduction of Dynamic Spectrum Access (DSA) marked an important juncture in the evolution of wireless networks. DSA is a spectrum assignment paradigm where devices are able to make real-time adjustment to their spectrum usage and adapt to changes in their spectral environment to meet performance objectives. DSA allows spectrum to be used more efficiently and may be considered as a viable approach to the ever increasing demand for spectrum in urban areas and the need for coverage extension to unconnected communities. While DSA can be applied to any spectrum band, the initial focus has been in the Ultra-High Frequency (UHF) band traditionally used for television broadcast because the band is lightly occupied and also happens to be ideal spectrum for sparsely populated rural areas. Wireless access in general is said to offer the most hope in extending connectivity to rural and unconnected peri-urban communities. Wireless Mesh Networks (WMN) in particular offer several attractive characteristics such as multi-hopping, ad-hoc networking, capabilities of self-organising and self-healing, hence the focus on WMNs. Motivated by the desire to leverage DSA for mesh networking, this research revisits the aspect of connectivity in WMNs with DSA. The advantages of DSA when combined with mesh networking not only build on the benefits, but also creates additional challenges. The study seeks to address the connectivity challenge across three key dimensions, namely network formation, link metric and multi-link utilisation. To start with, one of the conundrums faced in WMNs with DSA is that the current 802.11s mesh standard provides limited support for DSA, while DSA related standards such as 802.22 provide limited support for mesh networking. This gap in standardisation complicates the integration of DSA in WMNs as several issues are left outside the scope of the applicable standard. This dissertation highlights the inadequacy of the current MAC protocol in ensuring TVWS regulation compliance in multi-hop environments and proposes a logical link MAC sub-layer procedure to fill the gap. A network is considered compliant in this context if each node operates on a channel that it is allowed to use as determined for example, by the spectrum database. Using a combination of prototypical experiments, simulation and numerical analysis, it is shown that the proposed protocol ensures network formation is accomplished in a manner that is compliant with TVWS regulation. Having tackled the compliance problem at the mesh formation level, the next logical step was to explore performance improvement avenues. Considering the importance of routing in WMNs, the study evaluates link characterisation to determine suitable metric for routing purposes. Along this dimension, the research makes two main contributions. Firstly, A-link-metric (Augmented Link Metric) approach for WMN with DSA is proposed. A-link-metric reinforces existing metrics to factor in characteristics of a DSA channel, which is essential to improve the routing protocol's ranking of links for optimal path selection. Secondly, in response to the question of “which one is the suitable metric?”, the Dynamic Path Metric Selection (DPMeS) concept is introduced. The principal idea is to mechanise the routing protocol such that it assesses the network via a distributed probing mechanism and dynamically binds the routing metric. Using DPMeS, a routing metric is selected to match the network type and prevailing conditions, which is vital as each routing metric thrives or recedes in performance depending on the scenario. DPMeS is aimed at unifying the years worth of prior studies on routing metrics in WMNs. Simulation results indicate that A-link-metric achieves up to 83.4 % and 34.6 % performance improvement in terms of throughput and end-to-end delay respectively compared to the corresponding base metric (i.e. non-augmented variant). With DPMeS, the routing protocol is expected to yield better performance consistently compared to the fixed metric approach whose performance fluctuates amid changes in network setup and conditions. By and large, DSA-enabled WMN nodes will require access to some fixed spectrum to fall back on when opportunistic spectrum is unavailable. In the absence of fully functional integrated-chip cognitive radios to enable DSA, the immediate feasible solution for the interim is single hardware platforms fitted with multiple transceivers. This configuration results in multi-band multi-radio node capability that lends itself to a variety of link options in terms of transmit/receive radio functionality. The dissertation reports on the experimental performance evaluation of radios operating in the 5 GHz and UHF-TVWS bands for hybrid back-haul links. It is found that individual radios perform differently depending on the operating parameter settings, namely channel, channel-width and transmission power subject to prevailing environmental (both spectral and topographical) conditions. When aggregated, if the radios' data-rates are approximately equal, there is a throughput and round-trip time performance improvement of 44.5 - 61.8 % and 7.5 - 41.9 % respectively. For hybrid links comprising radios with significantly unequal data-rates, this study proposes an adaptive round-robin (ARR) based algorithm for efficient multilink utilisation. Numerical analysis indicate that ARR provides 75 % throughput improvement. These results indicate that network optimisation overall requires both time and frequency division duplexing. Based on the experimental test results, this dissertation presents a three-layered routing framework for multi-link utilisation. The top layer represents the nodes' logical interface to the WMN while the bottom layer corresponds to the underlying physical wireless network interface cards (WNIC). The middle layer is an abstract and reductive representation of the possible and available transmission, and reception options between node pairs, which depends on the number and type of WNICs. Drawing on the experimental results and insight gained, the study builds criteria towards a mechanism for auto selection of the optimal link option. Overall, this study is anticipated to serve as a springboard to stimulate the adoption and integration of DSA in WMNs, and further development in multi-link utilisation strategies to increase capacity. Ultimately, it is hoped that this contribution will collectively contribute effort towards attaining the global goal of extending connectivity to the unconnected

Self-organized backpressure routing for the wireless mesh backhaul of small cells

The ever increasing demand for wireless data services has given a starring role to dense small cell (SC) deployments for mobile networks, as increasing frequency re-use by reducing cell size has historically been the most effective and simple way to increase capacity. Such densification entails challenges at the Transport Network Layer (TNL), which carries packets throughout the network, since hard-wired deployments of small cells prove to be cost-unfeasible and inflexible in some scenarios. The goal of this thesis is, precisely, to provide cost-effective and dynamic solutions for the TNL that drastically improve the performance of dense and semi-planned SC deployments. One approach to decrease costs and augment the dynamicity at the TNL is the creation of a wireless mesh backhaul amongst SCs to carry control and data plane traffic towards/from the core network. Unfortunately, these lowcost SC deployments preclude the use of current TNL routing approaches such as Multiprotocol Label Switching Traffic Profile (MPLS-TP), which was originally designed for hard-wired SC deployments. In particular, one of the main problems is that these schemes are unable to provide an even network resource consumption, which in wireless environments can lead to a substantial degradation of key network performance metrics for Mobile Network Operators. The equivalent of distributing load across resources in SC deployments is making better use of available paths, and so exploiting the capacity offered by the wireless mesh backhaul formed amongst SCs. To tackle such uneven consumption of network resources, this thesis presents the design, implementation, and extensive evaluation of a self-organized backpressure routing protocol explicitly designed for the wireless mesh backhaul formed amongst the wireless links of SCs. Whilst backpressure routing in theory promises throughput optimality, its implementation complexity introduces several concerns, such as scalability, large end-to-end latencies, and centralization of all the network state. To address these issues, we present a throughput suboptimal yet scalable, decentralized, low-overhead, and low-complexity backpressure routing scheme. More specifically, the contributions in this thesis can be summarized as follows: We formulate the routing problem for the wireless mesh backhaul from a stochastic network optimization perspective, and solve the network optimization problem using the Lyapunov-driftplus-penalty method. The Lyapunov drift refers to the difference of queue backlogs in the network between different time instants, whereas the penalty refers to the routing cost incurred by some network utility parameter to optimize. In our case, this parameter is based on minimizing the length of the path taken by packets to reach their intended destination. Rather than building routing tables, we leverage geolocation information as a key component to complement the minimization of the Lyapunov drift in a decentralized way. In fact, we observed that the combination of both components helps to mitigate backpressure limitations (e.g., scalability,centralization, and large end-to-end latencies). The drift-plus-penalty method uses a tunable optimization parameter that weight the relative importance of queue drift and routing cost. We find evidence that, in fact, this optimization parameter impacts the overall network performance. In light of this observation, we propose a self-organized controller based on locally available information and in the current packet being routed to tune such an optimization parameter under dynamic traffic demands. Thus, the goal of this heuristically built controller is to maintain the best trade-off between the Lyapunov drift and the penalty function to take into account the dynamic nature of semi-planned SC deployments. We propose low complexity heuristics to address problems that appear under different wireless mesh backhaul scenarios and conditions..

Data Movement Challenges and Solutions with Software Defined Networking

With the recent rise in cloud computing, applications are routinely accessing and interacting with data on remote resources. Interaction with such remote resources for the operation of media-rich applications in mobile environments is also on the rise. As a result, the performance of the underlying network infrastructure can have a significant impact on the quality of service experienced by the user. Despite receiving significant attention from both academia and industry, computer networks still face a number of challenges. Users oftentimes report and complain about poor experiences with their devices and applications, which can oftentimes be attributed to network performance when downloading or uploading application data. This dissertation investigates problems that arise with data movement across computer networks and proposes novel solutions to address these issues through software defined networking (SDN). SDN is lauded to be the paradigm of choice for next generation networks. While academia explores use cases in various contexts, industry has focused on data center and wide area networks. There is a significant range of complex and application-specific network services that can potentially benefit from SDN, but introduction and adoption of such solutions remains slow in production networks. One impeding factor is the lack of a simple yet expressive enough framework applicable to all SDN services across production network domains. Without a uniform framework, SDN developers create disjoint solutions, resulting in untenable management and maintenance overhead. The SDN-based solutions developed in this dissertation make use of a common agent-based approach. The architecture facilitates application-oriented SDN design with an abstraction composed of software agents on top of the underlying network. There are three key components modern and future networks require to deliver exceptional data transfer performance to the end user: (1) user and application mobility, (2) high throughput data transfer, and (3) efficient and scalable content distribution. Meeting these key components will not only ensure the network can provide robust and reliable end-to-end connectivity, but also that network resources will be used efficiently. First, mobility support is critical for user applications to maintain connectivity to remote, cloud-based resources. Today\u27s network users are frequently accessing such resources while on the go, transitioning from network to network with the expectation that their applications will continue to operate seamlessly. As users perform handovers between heterogeneous networks or between networks across administrative domains, the application becomes responsible for maintaining or establishing new connections to remote resources. Although application developers often account for such handovers, the result is oftentimes visible to the user through diminished quality of service (e.g. rebuffering in video streaming applications). Many intra-domain handover solutions exist for handovers in WiFi and cellular networks, such as mobile IP, but they are architecturally complex and have not been integrated to form a scalable, inter-domain solution. A scalable framework is proposed that leverages SDN features to implement both horizontal and vertical handovers for heterogeneous wireless networks within and across administrative domains. User devices can select an appropriate network using an on-board virtual SDN implementation that manages available network interfaces. An SDN-based counterpart operates in the network core and edge to handle user migrations as they transition from one edge attachment point to another. The framework was developed and deployed as an extension to the Global Environment for Network Innovations (GENI) testbed; however, the framework can be deployed on any OpenFlow enabled network. Evaluation revealed users can maintain existing application connections without breaking the sockets and requiring the application to recover. Second, high throughput data transfer is essential for user applications to acquire large remote data sets. As data sizes become increasingly large, often combined with their locations being far from the applications, the well known impact of lower Transmission Control Protocol (TCP) throughput over large delay-bandwidth product paths becomes more significant to these applications. While myriads of solutions exist to alleviate the problem, they require specialized software and/or network stacks at both the application host and the remote data server, making it hard to scale up to a large range of applications and execution environments. This results in high throughput data transfer that is available to only a select subset of network users who have access to such specialized software. An SDN based solution called Steroid OpenFlow Service (SOS) has been proposed as a network service that transparently increases the throughput of TCP-based data transfers across large networks. SOS shifts the complexity of high performance data transfer from the end user to the network; users do not need to configure anything on the client and server machines participating in the data transfer. The SOS architecture supports seamless high performance data transfer at scale for multiple users and for high bandwidth connections. Emphasis is placed on the use of SOS as a part of a larger, richer data transfer ecosystem, complementing and compounding the efforts of existing data transfer solutions. Non-TCP-based solutions, such as Aspera, can operate seamlessly alongside an SOS deployment, while those based on TCP, such as wget, curl, and GridFTP, can leverage SOS for throughput improvement beyond what a single TCP connection can provide. Through extensive evaluation in real-world environments, the SOS architecture is proven to be flexibly deployable on a variety of network architectures, from cloud-based, to production networks, to scaled up, high performance data center environments. Evaluation showed that the SOS architecture scales linearly through the addition of SOS “agents†to the SOS deployment, providing data transfer performance improvement to multiple users simultaneously. An individual data transfer enhanced by SOS was shown to have increased throughput nearly forty times the same data transfer without SOS assistance. Third, efficient and scalable video content distribution is imperative as the demand for multimedia content over the Internet increases. Current state of the art solutions consist of vast content distribution networks (CDNs) where content is oftentimes hosted in duplicate at various geographically distributed locations. Although CDNs are useful for the dissemination of static content, they do not provide a clear and scalable model for the on demand production and distribution of live, streaming content. IP multicast is a popular solution to scalable video content distribution; however, it is seldom used due to deployment and operational complexity. Inspired from the distributed design of todays CDNs and the distribution trees used by IP multicast, a SDN based framework called GENI Cinema (GC) is proposed to allow for the distribution of live video content at scale. GC allows for the efficient management and distribution of live video content at scale without the added architectural complexity and inefficiencies inherent to contemporary solutions such as IP multicast. GC has been deployed as an experimental, nation-wide live video distribution service using the GENI network, broadcasting live and prerecorded video streams from conferences for remote attendees, from the classroom for distance education, and for live sporting events. GC clients can easily and efficiently switch back and forth between video streams with improved switching latency latency over cable, satellite, and other live video providers. The real world dep loyments and evaluation of the proposed solutions show how SDN can be used as a novel way to solve current data transfer problems across computer networks. In addition, this dissertation is expected to provide guidance for designing, deploying, and debugging SDN-based applications across a variety of network topologies

Smart Wireless Sensor Networks

The recent development of communication and sensor technology results in the growth of a new attractive and challenging area - wireless sensor networks (WSNs). A wireless sensor network which consists of a large number of sensor nodes is deployed in environmental fields to serve various applications. Facilitated with the ability of wireless communication and intelligent computation, these nodes become smart sensors which do not only perceive ambient physical parameters but also be able to process information, cooperate with each other and self-organize into the network. These new features assist the sensor nodes as well as the network to operate more efficiently in terms of both data acquisition and energy consumption. Special purposes of the applications require design and operation of WSNs different from conventional networks such as the internet. The network design must take into account of the objectives of specific applications. The nature of deployed environment must be considered. The limited of sensor nodes� resources such as memory, computational ability, communication bandwidth and energy source are the challenges in network design. A smart wireless sensor network must be able to deal with these constraints as well as to guarantee the connectivity, coverage, reliability and security of network's operation for a maximized lifetime. This book discusses various aspects of designing such smart wireless sensor networks. Main topics includes: design methodologies, network protocols and algorithms, quality of service management, coverage optimization, time synchronization and security techniques for sensor networks

one6G white paper, 6G technology overview:Second Edition, November 2022

6G is supposed to address the demands for consumption of mobile networking services in 2030 and beyond. These are characterized by a variety of diverse, often conflicting requirements, from technical ones such as extremely high data rates, unprecedented scale of communicating devices, high coverage, low communicating latency, flexibility of extension, etc., to non-technical ones such as enabling sustainable growth of the society as a whole, e.g., through energy efficiency of deployed networks. On the one hand, 6G is expected to fulfil all these individual requirements, extending thus the limits set by the previous generations of mobile networks (e.g., ten times lower latencies, or hundred times higher data rates than in 5G). On the other hand, 6G should also enable use cases characterized by combinations of these requirements never seen before, e.g., both extremely high data rates and extremely low communication latency). In this white paper, we give an overview of the key enabling technologies that constitute the pillars for the evolution towards 6G. They include: terahertz frequencies (Section 1), 6G radio access (Section 2), next generation MIMO (Section 3), integrated sensing and communication (Section 4), distributed and federated artificial intelligence (Section 5), intelligent user plane (Section 6) and flexible programmable infrastructures (Section 7). For each enabling technology, we first give the background on how and why the technology is relevant to 6G, backed up by a number of relevant use cases. After that, we describe the technology in detail, outline the key problems and difficulties, and give a comprehensive overview of the state of the art in that technology. 6G is, however, not limited to these seven technologies. They merely present our current understanding of the technological environment in which 6G is being born. Future versions of this white paper may include other relevant technologies too, as well as discuss how these technologies can be glued together in a coherent system

Radio Communications

In the last decades the restless evolution of information and communication technologies (ICT) brought to a deep transformation of our habits. The growth of the Internet and the advances in hardware and software implementations modified our way to communicate and to share information. In this book, an overview of the major issues faced today by researchers in the field of radio communications is given through 35 high quality chapters written by specialists working in universities and research centers all over the world. Various aspects will be deeply discussed: channel modeling, beamforming, multiple antennas, cooperative networks, opportunistic scheduling, advanced admission control, handover management, systems performance assessment, routing issues in mobility conditions, localization, web security. Advanced techniques for the radio resource management will be discussed both in single and multiple radio technologies; either in infrastructure, mesh or ad hoc networks

Resource Allocation for the Internet of Everything: From Energy Harvesting Tags to Cellular Networks

In the near future, objects equipped with heterogeneous devices such as sensors, actuators, and tags, will be able to interact with each other and cooperate to achieve common goals. These networks are termed the Internet of Things (IoT) and have applications in healthcare, smart buildings, assisted living, manufacturing, supply chain management, and intelligent transportation. The IoT vision is enabled by ubiquitous wireless communications and there are numerous resource allocation challenges to efficiently connect each device to the network. In this thesis, we study wireless resource allocation problems that arise in the IoT, namely in the areas of the energy harvesting tags, termed the Internet of Tags (IoTags), and in cellular networks (mobile and cognitive). First, we present our experience designing and developing Energy Harvesting Active Networked Tags (EnHANTs). The prototypes harvest indoor light energy using custom organic solar cells, communicate and form multihop networks using ultra-low-power Ultra- Wideband Impulse Radio (UWB-IR) transceivers, and dynamically adapt their communications and networking patterns to the energy harvesting and battery states. Using our custom designed small scale testbed, we evaluate energy-adaptive networking algorithms spanning the protocol stack (link, network, and flow control). Throughout the evaluation of experiments, we highlight numerous phenomena which are typically difficult to capture in simulations and nearly impossible to model in analytical work. We believe that these lessons would be useful for the designers of many different types of energy harvesters and energy harvesting adaptive networks. Based on the lessons learned from EnHANTs, we present Power Aware Neighbor Discovery Asynchronously (Panda), a Neighbor Discovery (ND) protocol optimized for networks of energy harvesting nodes. To enable object tracking and monitoring applications for IoTags, Panda is designed to efficiently identify nodes which are within wireless communication range of one another. By accounting for numerous hardware constraints which are typically ignored (i.e., energy costs for transmission/reception, and transceiver state switching times/costs), we formulate a power budget to guarantee perpetual ND. Finally, via testbed evaluation utilizing Commercial Off-The-Shelf (COTS) energy harvesting nodes, we demonstrate experimentally that Panda outperforms existing protocols by a factor of 2-3x. We then consider Proportional Fair (PF) cellular scheduling algorithms for mobile users, These users experience slow-fading wireless channels while traversing roads, train tracks, bus routes, etc. We leverage the predicable mobility on these routes and present the Predictive Finite-horizon PF Scheduling ((PF)2S) Framework. We collect extensive channel measurement results from a 3G network and characterize mobility-induced channel state trends. We show that a user’s channel state is highly reproducible and leverage that to develop a data rate prediction mechanism. Our trace-based simulations of the (PF)2S Framework indicate that the framework can increase the throughput by 15%–55% compared to traditional PF schedulers, while improving fairness. Finally, we study fragmentation within a probability model of combinatorial structures. Our model does not refer to any particular application. Yet, it is applicable to dynamic spectrum access networks which can be used as the wireless access technology for numerous IoT applications. In dynamic spectrum access networks, users share the wireless resource and compete to transmit and receive data, and accordingly have specific bandwidth and residence-time requirements. We prove that the spectrum tends towards states of complete fragmentation. That is, for every request for j > 1 sub-channels, nearly all size-j requests are allocated j mutually disjoint sub-channels. In a suite of four theorems, we show how this result specializes for certain classes of request-size distributions. We also show that the delays in reaching the inefficient states of complete fragmentation can be surprisingly long. The results of this chapter provide insights into the fragmentation process and, in turn, into those circumstances where defragmentation is worth the cost it incurs