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.
Modern society depends on the operations of civil infrastructure systems, such as transportation, energy, telecommunications, and water. These systems have become so interconnected, one relying on another, that disruption of one may lead to disruptions in all. The approach taken in this research is to model these systems by explicitly identifying these interconnections or interdependencies. Definitions of five types of infrastructure inter-dependencies are presented and incorporated into a network flows mathematical representation, i.e., an interdependent layer network model. Using the lower Manhattan region of New York, for illustrative purposes, the implementation of the model is shown. First, the data requirements are presented with realistic data on the interdependent infrastructure systems of power, telecommunications, and subways. Next, a scenario is given that causes major disruption in the services provided by these infrastructures and demonstrates the use of the model in guiding restoration of services. The paper concludes with a discussion of accomplishments and opportunities for future work. This paper studies how to determine an optimal order of recovering interdependent Cyber Physical Systems (CPS) after a large scale failure. In such a CPS, some failed devices must be repaired first before others can. In addition, such failed devices require a certain amount of repair resources and may take multiple stages to repair. We consider two scenarios: 1) reserved model where all the required repair resources should be prepared at the beginning of repairing a device; and 2) opportunistic model where we can partially repair a device with only part of the required resources. For each scenario, we model it using an Integer Linear Programming (ILP) and use a relaxation and rounding method to design an ILP based algorithm. In addition, we also design a Dynamic Programming (DP) based algorithm. Simulation results show that ILP based algorithm outperforms DP based algorithm by 10 -20 in systems with less than 200 failed devices, but DP based algorithm can support extreme large size systems with more than 5000 failed devices. 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. 