The increasing reliance upon cloud services entails more flexible networks that are realized by virtualized network equipment and functions. When such advanced network systems face a massive failure by natural disasters or attacks, the recovery of the entire systems may be conducted in a progressive way due to limited repair resources. The prioritization of network equipment in the recovery phase influences the interim computation and communication capability of systems, since the systems are operated under partial functionality. Hence, finding the best recovery order is a critical problem, which is further complicated by virtualization due to dependency among network nodes and layers. This paper deals with a progressive recovery problem under limited resources in networks with VNFs, where some dependent network layers exist. We prove the NP-hardness of the progressive recovery problem and approach the optimum solution by introducing DeepPR, a progressive recovery technique based on deep reinforcement learning. Our simulation results indicate that DeepPR can obtain 98.4 of the theoretical optimum in certain networks. The results suggest the applicability of Deep RL to more general progressive recovery problems and similar intractable resource allocation problems.
Pioneering work @cite_11 on the progressive recovery problem focuses on determining the recovery order of communication links that maximizes the amount of flows on the recovered network with limited resources. As an extension, the work @cite_2 proposes node evaluation indices to decide the recovery order to maximize the number of virtual networks accommodated. Considering the necessity of monitoring to observe failure situations, the joint problem of progressive recovery and monitor placement is discussed in @cite_16 .
@cite_16 @cite_2 @cite_11
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A number of models have been proposed to analyze interdependent networks in recent years. However most of the models are unable to capture the complex interdependencies between such networks. To overcome the limitations, we have recently proposed a new model. Utilizing this model, we provide techniques for progressive recovery from failure. The goal of the progressive recovery problem is to maximize the system utility over the entire duration of the recovery process. We show that the problem can be solved in polynomial time in some special cases, whereas for some others, the problem is NP-complete. We provide two approximation algorithms with performance bounds of 2 and 4 respectively. We provide an optimal solution utilizing Integer Linear Programming and a heuristic. We evaluate the efficacy of our heuristic with both synthetic and real data collected from Phoenix metropolitan area. The experiments show that our heuristic almost always produces near optimal solution. A major disruption may affect many network components and significantly lower the capacity of a network measured in terms of the maximum total flow among a set of source-destination pairs. Since only a subset of the failed components may be repaired at a time due to e.g., limited availability of repair resources, the network capacity can only be progressively increased over time by following a recovery process that involves multiple recovery stages. Different recovery processes will restore the failed components in different orders, and accordingly, result in different amount of network capacity increase after each stage. This paper aims to investigate how to optimally recover the network capacity progressively, or in other words, to determine the optimal recovery process, subject to limited available repair resources. We formulate the optimization problem, analyze its computational complexity, devise solution schemes, and conduct numerical experiments to evaluate the algorithms. The concept of progressive network recovery proposed in this paper represents a paradigm-shift in the field of resilient and survivable networking to handle large-scale failures, and will motivate a rich body of research in network design and other applications. We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a computation strategy that leverages ideas from coding theory to design intermediate computations at the worker nodes, in order to optimally deal with straggling workers. The proposed strategy, named as , achieves the optimum recovery threshold, defined as the minimum number of workers that the master needs to wait for in order to compute the output. This is the first code that achieves the optimal utilization of redundancy for tolerating stragglers or failures in distributed matrix multiplication. Furthermore, by leveraging the algebraic structure of polynomial codes, we can map the reconstruction problem of the final output to a polynomial interpolation problem, which can be solved efficiently. Polynomial codes provide order-wise improvement over the state of the art in terms of recovery threshold, and are also optimal in terms of several other metrics including computation latency and communication load. Moreover, we extend this code to distributed convolution and show its order-wise optimality. After a massive scale failure, the assessment of damages to communication networks requires local interventions and remote monitoring. While previous works on network recovery require complete knowledge of damage extent, we address the problem of damage assessment and critical service restoration in a joint manner. We propose a polynomial algorithm called Centrality based Damage Assessment and Recovery (CeDAR) which performs a joint activity of failure monitoring and restoration of network components. CeDAR works under limited availability of recovery resources and optimizes service recovery over time. We modified two existing approaches to the problem of network recovery to make them also able to exploit incremental knowledge of the failure extent. Through simulations we show that CeDAR outperforms the previous approaches in terms of recovery resource utilization and accumulative flow over time of the critical services.