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.
The vulnerability of interdependent networks has recently drawn much attention, especially in the key infrastructure networks such as power and communication networks. However, the existing works mainly considered a single cascade model across the networks and there is a need for more accurate models and analysis. In this paper, we focus on the interdependent power communication networks to accurately analyze their vulnerability by considering heterogeneous cascade models. Accurately analyzing interdependent networks is challenging as the cascades are heterogeneous yet interdependent. Also, including multiple timescales into the context can further increase the complexity. To better depict the vulnerability of interdependent networks, we first propose a method to learn a threshold model from historical data to characterize the cascades in the power network and alleviate the need of calculating complicated power network dynamics. Next, we introduce message passing equations to generalize the threshold model in the power network and the percolation model in the communication network, based on which we derive efficient solution for finding the most critical nodes in the interdependent networks. Removing the most critical nodes can cause the largest cascade and thus characterizes the vulnerability. We evaluate the performance of the proposed methods in various datasets and discuss how network parameters, such as the timescales, can impact the vulnerability. This paper treats the problem of optimal resource allocation over time in a finite-horizon setting, in which the resource become available only sequentially and in incremental values, and the utility function is concave and can freely vary over time. Such resource allocation problems have direct applications in data communication networks (e.g., energy harvesting systems). This problem is studied extensively for special choices of the concave utility function (time invariant and logarithmic) in which case the optimal resource allocation policies are well-understood. This paper treats this problem in its general form and analytically characterizes the structure of the optimal resource allocation policy and devises an algorithm for computing the exact solutions analytically. An observation instrumental to devising the provided algorithm is that there exist time instances at which the available resources are exhausted, with no carryover to future. This algorithm identifies all such instances, which in turn, facilitates breaking the original problem into multiple problems with significantly reduced dimensions. Furthermore, some widely used special cases in which the algorithm takes simpler structures are characterized, and the application to the energy harvesting systems is discussed. Numerical evaluations are provided to assess the key properties of the optimal resource allocation structure and to compare the performance with the generic convex optimization algorithms. Today's cloud system are composed of geographically distributed datacenter interconnected by high-speed optical networks. Disaster failures can severely affect both the communication network as well as datacenters infrastructure and prevent users from accessing cloud services. After large-scale disasters, recovery efforts on both network and datacenters may take days, and, in some cases, weeks or months. Traditionally, the repair of the communication network has been treated as a separate problem from the repair of datacenters. While past research has mostly focused on network recovery, how to efficiently recover a cloud system jointly considering the limited computing and networking resources has been an important and open research problem. In this work, we investigate the problem of progressive datacenter recovery after a large-scale disaster failure, given that a network-recovery plan is made. An efficient recovery plan is explored to determine which datacenters should be recovered at each recovery stage to maximize cumulative content reachability from any source considering limited available network resources. We devise an Integer Linear Program (ILP) formulation to model the associated optimization problem. Our numerical examples using the ILP show that an efficient progressive datacenter-recovery plan can significantly help to increase reachability of contents during the network recovery phase. We succeeded in increasing the number of important contents in the early stages of recovery compared to a random-recovery strategy with a slight increase in resource consumption.