Brian L. Mark

Bio: Brian L. Mark is an academic researcher from George Mason University. The author has contributed to research in topics: Cognitive radio & Markov process. The author has an hindex of 32, co-authored 151 publications receiving 3411 citations. Previous affiliations of Brian L. Mark include NEC & University of Waterloo.

A quantitative trust establishment framework for reliable data packet delivery in MANETs

Abstract: In mobile ad hoc networks (MANETs), a source node must rely on other nodes to forward its packets on multi-hop routes to the destination. Secure and reliable handling of packets by the intermediate nodes is difficult to ensure in an ad hoc environment. We propose a trust establishment scheme for MANETs which aims to improve the reliability of packet forwarding over multi-hop routes in the presence of potentially malicious nodes. Each node forms an "opinion" about each of the other nodes based on both first and second-hand observation data collected from the network. The opinion metric can be incorporated into ad hoc routing protocols to achieve reliable packet delivery even when a portion of the network exhibits malicious behavior. We present numerical results which demonstrate the effectiveness of the proposed trust establishment scheme.

Large capacity, multiclass core ATM switch architecture

Abstract: A large capacity ATM core switch architecture is disclosed, which supports multiple traffic classes and quality-of-service (QoS) guarantees. The switch supports both real-time traffic classes with strict QoS requirements, e.g., CBR and VBR, and non-real-time traffic classes with less stringent requirements, e.g., ABR and UBR. The architecture also accommodates real-time and non-real-time multicast flows in an efficient manner. The switch consists of a high-speed core module that interconnects input/output modules with large buffers and intelligent scheduling/buffer management mechanisms. The scheduling can be implemented using a novel dynamic rate control, which controls internal congestion and achieves fair throughput performance among competing flows at switch bottlenecks. In the dynamic rate control scheme, flows are rate-controlled according to congestion information observed at bottleneck points within the switch. Each switch flow is guaranteed a minimum service rate plus a dynamic rate component which distributes any unused bandwidth in a fair manner.

Dynamic rate control scheduler for ATM networks

Abstract: A Dynamic Rate Control (DRC) scheduler for scheduling cells for service in a generic Asynchronous Transfer Mode (ATM) switch is disclosed. According to the inventive DRC, each traffic stream associated with an internal switch queue is rate-shaped according to a rate which consists of a minimum guaranteed rate and a dynamic component computed based on congestion information within the switch. While achieving high utilization, DRC guarantees a minimum throughput for each stream and fairly distributes unused bandwidth. The distribution of unused bandwidth in DRC can be assigned flexibly, i.e., the unused bandwidth need not be shared in proportion to the minimum throughput guarantees, as in weighted fair share schedulers. Moreover, an effective closed-loop QoS control can be built into DRC by dynamically updating a set of weights based on observed QoS. Another salient feature of DRC is its ability to control congestion internal congestion at bottleneck points within a multistage switch. DRC can also be extended beyond the local switch in a hop-by-hop fashion.

Real-time mobility tracking algorithms for cellular networks based on Kalman filtering

Abstract: We propose two algorithms for real-time tracking of the location and dynamic motion of a mobile station in a cellular network using the pilot signal strengths from neighboring base stations. The underlying mobility model is based on a dynamic linear system driven by a discrete command process that determines the mobile station's acceleration. The command process is modeled as a semi-Markov process over a finite set of acceleration levels. The first algorithm consists of an averaging filter for processing pilot signal, strength measurements and two Kalman filters, one to estimate the discrete command process and the other to estimate the mobility state. The second algorithm employs a single Kalman filter without prefiltering and is able to track a mobile station even when a limited set of pilot signal measurements is available. Both of the proposed tracking algorithms can be used to predict future mobility behavior, which can be, useful in resource allocation applications. Our numerical results show that the proposed tracking algorithms perform accurately over a wide range of mobility parameter values.

Modeling and analysis of opportunistic spectrum sharing with unreliable spectrum sensing

Abstract: We analyze the performance of a wireless system consisting of a set of secondary users opportunistically sharing bandwidth with a set of primary users over a coverage area. The secondary users employ spectrum sensing to detect channels that are unused by the primary users and hence make use of the idle channels. If an active secondary user detects the presence of a primary user on a given channel, it releases the channel and switches to another idle channel, if one is available. In the event that no channel is available, the call waits in a buffer until either a channel becomes available or a maximum waiting time is reached. Spectrum sensing errors on the part of a secondary user cause false alarm and mis-detection events, which can potentially degrade the quality-of-service experienced by primary users. We derive system performance metrics of interest such as blocking probabilities. Our results suggest that opportunistic spectrum sharing can significantly improve spectrum efficiency and system capacity, even under unreliable spectrum detection. The proposed model and analysis method can be used to evaluate the performance of future opportunistic spectrum sharing systems.

Laplacian Eigenmaps for dimensionality reduction and data representation

Abstract: One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.

A survey of spectrum sensing algorithms for cognitive radio applications

Abstract: The spectrum sensing problem has gained new aspects with cognitive radio and opportunistic spectrum access concepts. It is one of the most challenging issues in cognitive radio systems. In this paper, a survey of spectrum sensing methodologies for cognitive radio is presented. Various aspects of spectrum sensing problem are studied from a cognitive radio perspective and multi-dimensional spectrum sensing concept is introduced. Challenges associated with spectrum sensing are given and enabling spectrum sensing methods are reviewed. The paper explains the cooperative sensing concept and its various forms. External sensing algorithms and other alternative sensing methods are discussed. Furthermore, statistical modeling of network traffic and utilization of these models for prediction of primary user behavior is studied. Finally, sensing features of some current wireless standards are given.

Convergence of probability measures

Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

A Survey of Dynamic Spectrum Access

Abstract: Compounding the confusion is the use of the broad term cognitive radio as a synonym for dynamic spectrum access. As an initial attempt at unifying the terminology, the taxonomy of dynamic spectrum access is provided. In this article, an overview of challenges and recent developments in both technological and regulatory aspects of opportunistic spectrum access (OSA). The three basic components of OSA are discussed. Spectrum opportunity identification is crucial to OSA in order to achieve nonintrusive communication. The basic functions of the opportunity identification module are identified

Fundamentals of Queueing Theory

Abstract: Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.