Probabilistic graphical models for resilience of all-optical networks under crosstalk attacks

Liu, G.; Ji, Chuanyi

doi:10.1109/ofc.2005.192560

Cited by 5 publications

(7 citation statements)

References 7 publications

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“…The graph is also known as a Random-Bond model [19], where dipoles are connected by random bonds which depend on node positions. The two-layer MRF (σ, X) can also be represented by a chain graph [21] of two MRF layers, one for X and the other for σ. The two-layer probabilistic graph thus maps the complex spatial dependence of a multihop wireless network to an explicit graphical representation.…”

Section: Two-layer Markov Random Fieldsmentioning

confidence: 99%

Randomized and Distributed Self-Configuration of Wireless Networks: Two-Layer Markov Random Fields and Near-Optimality

Jeon

2010

IEEE Trans. Signal Process.

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Distributed configuration management is imperative for wireless infrastructureless networks where each node adjusts locally its physical and logical configuration through information exchange with neighbors. Many algorithms have been developed with promising results in this area. However, two issues remain open. The first is the optimality, i.e., whether a distributed algorithm results in a near-optimal network configuration. The second is the complexity, i.e., whether a distributed algorithm scales gracefully with network size (N ). We study these issues through modeling, analysis, and randomized distributed algorithms.Modeling defines the optimality. We first derive a global probabilistic model for a network configuration which characterizes jointly the statistical spatial dependence of a physicaland a logical-configuration. The model is a Gibbs distribution that results from internal network properties on node positions, wireless channels and interference; and external management constraints on physical connectivity, signal quality and configuration costs. We then show that a local model which approximates the global model is a two-layer Markov Random Field or a random bond model. The complexity of the local model is the communication range among nodes. The local model is nearoptimal when the approximation error to the global model is within a given error bound. We analyze the trade-off between an approximation error and complexity, and derive sufficient conditions on the near-optimality of the local model. We show that when the power attenuation of a wireless channel is larger than 4, a node needs to communicate with more than O(1) neighbors for a local model to be near optimal. For a slowly decaying channel with power attenuation less than 4, a node may need to communicate with more than O( 3 √ N ) neighbors to result in a bounded approximation error. The two-layer Markov Random Fields enable a class of randomized distributed algorithms that allow a node to self-configure based on information from its neighbors. The distributed algorithms are applied to examples of (a) forming a 1-connected physical topology, (b) configuring a logical topology that maximizes the spatial channel reuse, and (c) reconfiguring from failures, both sequentially and jointly. We validate the model, the analysis and the randomized distributed algorithms also through simulation. Sung-eok Jeon received the B.S. degree from Yonsei University, Seoul, Korea, in 1996, the M.S. degree from KAIST, Daejeon, Korea, in 1999, the Ph.D degree from Georgia Institute of Technology, in 2007 He is now in Microsoft. His research interests are in statistical distributed management of large and complex networks, based on the probabilistic graphical models. PLACE PHOTO HEREChuanyi Ji 's research lies in the areas of networking, machine learning, and their interfaces. Her research interests are in understanding and managing complex networks, applications of machine learning to network management and security, large-scale measurements, learning theory a...

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Section: Two-layer Markov Random Fieldsmentioning

confidence: 99%

Randomized and Distributed Self-Configuration of Wireless Networks: Two-Layer Markov Random Fields and Near-Optimality

Jeon

2010

IEEE Trans. Signal Process.

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“…For clarity, we summarize the asymptotic results on M f sd in (19) and (20) for network resilience under various topologies in Table I. Assume that there is one link-shortest route between each pair of nodes in the network.…”

Section: B Impact Of Physical Topology On Network Resilience Lossmentioning

confidence: 99%

“…The network resilience loss M f sd does not always increase with ρ for arbitrary network with arbitrary route. For a counterexample, please refer to [19]. However, when practical route sets are considered, M f sd increases with ρ for several typical network topologies.…”

Section: A Impact Of Network Load On Network Resiliencementioning

confidence: 99%

Resilience of all-optical network architectures under in-band crosstalk attacks: a probabilistic graphical model approach

Liu

2007

IEEE J. Select. Areas Commun.

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An important question for secure all-optical networks (AONs) is how to incorporate security against attacks in the design and engineering of network architectures. In this work, we study the resilience of AON architectures under inband crosstalk attacks. Crosstalk attack propagation depends on both optical devices at the physical layer and wavelength usage at the network layer. This motivates us to employ probabilistic graphical models to model attack propagation. At the physical layer, we use a directed probabilistic graph (Bayesian Belief Network) to model the attack propagation under static network traffic and a given source of attack. At the network layer, we use an undirected probabilistic graph to represent the probability distribution of active connections in the network. The cross-layer model is obtained by combining the physical-and the networklayer models into a factor graph representation. Graphical models provide an explicit representation of interactions between the physical-and the network layer. Furthermore, graphical models facilitate derivations of analytical results on resilience with respect to physical-layer vulnerability, physical topology, and network load. Specifically, we derive bounds on the network resilience for regular topologies. For ring, star, and mesh-torus networks with link-shortest path routing and all-to-all traffic, we show that the average network resilience loss grows linearly with respect to the network load when the network load is small, and polynomially with respect to the probability of attack propagation from node to node along the attacker's route. In addition, numerical results suggest that the sum-product algorithm based on the factor graph representation can be used for computationally efficient evaluation of network resilience for irregular/large topologies.

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“…Then it suffices to focus on ( : ) propagation at the physical layer, where the values of ' i s are determined by physical layer parameters such as: nodal loss ratios, amplifier gain characteristics, and fiber attenuation ratios (see [5] for details). In the rest of the paper, we assume that …”

Section: A Physical-layer Modelmentioning

confidence: 99%

“…sd f Then the crosstalk attack may propagate along route sd r . Denote the signal power of flow sd f in the switching plane of node i V as a random variable , 1,2,... .i U i k The attenuation of the attacker's jamming power within the network can be captured using deterministic functions that depend on the characteristics of optical devices at the physical layer[5].Let the status of nodei V be a random variable i X , where 1 i Xif the level of crosstalk incurred by normal flows from the attacker's flow at the switching plane of node i V exceeds the threshold for a Quality of Service (QoS) constraint…”

mentioning

confidence: 99%

Resilient Architecture of All-Optical Networks: Probabilistic Graphical Models for Crosstalk Attack Propagation

Liu

2006

2006 IEEE International Symposium on Information Theory

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We study the resilience of all-optical network (AON) architectures under in-band crosstalk attacks. We first develop a cross-layer model that captures attack propagation based on probabilistic graphical models. At the physical layer, we use a directed probabilistic graph (Bayesian Belief Network) to model the attack propagation under static network traffic and a given source of attack. At the network layer, we use an undirected probabilistic graph (Random Field) to represent the probability distribution of active connections in the network. The cross-layer model is obtained by combining the physical-and the networklayer models into a factor graph representation. We then derive bounds on the network resilience for regular topologies. We show that for ring, star, and mesh-torus networks with link-shortest path routing and all-to-all traffic, the average network resilience loss grows linearly with respect to the network load when the network load is light; grows polynomially with respect to the probability of attack propagation from node to node along the attacker's route. We then show that the sum-product algorithm can be used for computationally efficient evaluation of network resilience for irregular topologies.1 Each bi-directional link is made up of two optical fibers, one for each direction. Throughout the paper, the term "connection" is used specifically for bi-directional traffic; the term "flow" is used for uni-directional traffic.

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Probabilistic graphical models for resilience of all-optical networks under crosstalk attacks

Cited by 5 publications

References 7 publications

Randomized and Distributed Self-Configuration of Wireless Networks: Two-Layer Markov Random Fields and Near-Optimality

Randomized and Distributed Self-Configuration of Wireless Networks: Two-Layer Markov Random Fields and Near-Optimality

Resilience of all-optical network architectures under in-band crosstalk attacks: a probabilistic graphical model approach

Resilient Architecture of All-Optical Networks: Probabilistic Graphical Models for Crosstalk Attack Propagation

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