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The efficacy of Network Function Virtualization (NFV) depends critically on (1) where the virtual network functions (VNFs) are placed and (2) how the traffic is routed. Unfortunately, these aspects are not easily optimized, especially under time-varying network states with different quality of service (QoS) requirements. Given the importance of NFV, many approaches have been proposed to solve the VNF placement and traffic routing problem. However, those prior approaches mainly assume that the state of the network is static and known, disregarding real-time network variations. To bridge that gap, in this paper, we formulate the VNF placement and traffic routing problem as a Markov Decision Process model to capture the dynamic network state transitions. In order to jointly minimize the delay and cost of NFV providers and maximize the revenue, we devise a customized Deep Reinforcement Learning (DRL) algorithm, called A-DDPG, for VNF placement and traffic routing in a real-time network. A-DDPG uses the attention mechanism to ascertain smooth network behavior within the general framework of network utility maximization (NUM). The simulation results show that A-DDPG outperforms the state-of- the-art in terms of network utility, delay, and cost., Accepted Author Manuscript, Embedded and Networked Systems

Spatially-close network fibers have a significant chance of failing simultaneously in the event of man-made or natural disasters within their geographic area. Network operators are interested in the proper detection and grouping of any existing spatially-close fiber segments, to avoid service disruptions due to simultaneous fiber failures. Moreover, spatially-close fibers can further be differentiated by computing the intervals over which they are spatially close. In this paper, we propose (1) polynomial-time algorithms for detecting all the spatially-close fiber segments of different fibers, (2) a polynomial-time algorithm for finding the spatially-close intervals of a fiber to a set of other fibers, and (3) a fast exact algorithm for grouping spatially-close fibers using the minimum number of distinct risk groups. All of our algorithms have a fast running time when simulated on three real-world network topologies., Network Architectures and Services

Forming, in a decentralized fashion, an optimal network topology while balancing multiple, possibly conflicting objectives like cost, high performance, security and resiliency to viruses is a challenging endeavor. In this paper, we take a game-formation approach to network design where each player, for instance an autonomous system in the Internet, aims to collectively minimize the cost of installing links, of protecting against viruses, and of assuring connectivity. In the game, minimizing virus risk as well as connectivity costs results in sparse graphs. We show that the Nash Equilibria are trees that, according to the Price of Anarchy (PoA), are close to the global optimum, while the worst-case Nash Equilibrium and the global optimum may significantly differ for small infection rate and link installation cost. Moreover, the types of trees, in both the Nash Equilibria and the optimal solution, depend on the virus infection rate, which provides new insights into how viruses spread: for high infection rate τ, the path graph is the worst- and the star graph is the best-case Nash Equilibrium. However, for small and intermediate values of τ, trees different from the path and star graphs may be optimal., Network Architectures and Services

Due to their importance to society, communication networks should be built and operated to withstand failures.However, cost considerations make network providers less inclined to take robustness measures against failures that are unlikely to manifest, like several failures coinciding simultaneously in different geographic regions of their network. Considering networks embedded in a two-dimensional plane, we study the problem of finding a critical region - a part of the network that can be enclosed by a given elementary figure of predetermined size - whose destruction would lead to the highest network disruption.We determine that only a polynomial,in the input, number of non-trivial positions for such a figure need to be considered and propose a corresponding polynomialtime algorithm. In addition, we consider region-aware network augmentation to decrease the impact of a regional failure. We subsequently address the region-disjoint paths problem, which asks for two paths with minimum total weight between a source (s) and a destination (d) that cannot both be cut by a single regional failure of diameter D (unless that failure includes s or d). We prove that deciding whether region-disjoint paths exist is NP-hard and propose a heuristic region-disjoint paths algorithm., Network Architectures & Services (NAS), Electrical Engineering, Mathematics and Computer Science

Due to the importance of communication networks to society, it is pertinent that these networks can withstand failures. Improving the robustness of a network usually requires installing redundant resources, which is very costly. Network providers are consequently less inclined to take robustness measures against failures that are unlikely to manifest, like several failures coinciding simultaneously in different geographic regions of their network. Protecting against single regional failures is more realistic. Network robustness, in terms of connectivity properties, also requires survivability algorithms to quickly reroute traffic affected by a network failure. In this paper, we consider a network embedded in a plane and study the problem of finding a circular region with radius r in that plane that would cause the biggest network degradation if all nodes within that particular region were to be destroyed. We propose a polynomial time algorithm for finding such critical regions. In addition, we develop a region-aware network augmentation technique to decrease the impact of a critical region failure. We subsequently consider the region-disjoint paths problem, which asks for two paths with minimum total weight between a source (s) and a destination (d) that cannot both be cut by a single circular regional failure of radius r (unless that failure includes s and d). We prove that the region-disjoint paths problem is NP-hard and propose and evaluate a heuristic algorithm for it., Intelligent Systems, Electrical Engineering, Mathematics and Computer Science

It is important that our vital networks (e.g., infrastructures) are robust to more than single-link failures. Failures might for instance affect a part of the network that resides in a certain geographical region. In this paper, considering networks embedded in a two-dimensional plane, we study the problem of finding a critical region - that is, a part of the network that can be enclosed by a given elementary figure (a circle, ellipse, rectangle, square, or equilateral triangle) with a predetermined size - whose removal would lead to the highest network disruption. We determine that there is a polynomial number of non-trivial positions for such a figure that need to be considered and, subsequently, we propose a polynomial-time algorithm for the problem. Simulations on realistic networks illustrate that different figures with equal area result in different critical regions in a network., Intelligent Systems, Electrical Engineering, Mathematics and Computer Science