Mobile edge computing (MEC) is an emerging architecture for accommodating latency sensitive virtualized services (VSs). Many of these VSs are expected to be safety critical, and will have some form of reliability requirements. In order to support provisioning reliability to such VSs in MEC in an efficient and confidentiality preserving manner, in this paper we consider the joint resource dimensioning and placement problem for VSs with diverse reliability requirements, with the objective of minimizing the energy consumption. We formulate the problem as an integer programming problem, and prove that it is NP-hard. We propose a two-step approximation algorithm with bounded approximation ratio based on Lagrangian relaxation. We benchmark our algorithm against two greedy algorithms in realistic scenarios. The results show that the proposed solution is computationally efficient, scalable and can provide up to 30 percent reduction in energy consumption compared to greedy algorithms.

We consider the uplink of a single cell multi-user multiple input multiple output (MU-MIMO) system, in which the base station acquires channel state information at the receiver by means of uplink pilot signals. Since each mobile station has a sum power budget that is used to transmit pilot and data symbols, the pilot power ratio (PPR) has a large impact on the system performance in terms of spectral and energy efficiency. We formulate the problem of PPR setting as a non-cooperative game, in which each mobile station aims at minimizing the mean squared error of the uplink received data symbols at the base station. We show that in this game a unique Nash equilibrium exists, and propose an iterative decentralized algorithm-termed best PPR algorithm (BPA)-that is guaranteed to converge to that Nash equilibrium. Since BPA dynamically responds to the measured interference, it outperforms widely used schemes that use a predetermined PPR. BPA also performs close to the global optimum, especially when mobile stations with similar path loss values are co-scheduled in the MU-MIMO system. Based on these insights, we propose a practical signaling mechanism for implementing BPA in MU-MIMO systems.

Replacing hardware controllers with software-based virtual process control functions (VPFs) is a promising approach for improving the operational efficiency and flexibility of industrial control systems. VPFs can be executed in edge clouds in 5G mobile networks or in the wireless backhaul, which can further improve efficiency. Nonetheless, for the acceptance of virtualization in industrial control systems, a fundamental challenge is to ensure that the placement of VPFs be resilient to component failures and cyber-attacks, besides being efficient. In this paper we address this challenge by considering that VPF placement costs are incurred by reserving mobile edge computing (MEC) resources, executing VPF instances, and by data communication. We formulate the VPF placement problem as an integer programming problem, considering resilience as a constraint. We propose a solution based on generalized Benders decomposition and based on linear relaxation of the resulting sub-problems, which effectively reduces the number of integer variables to the number of MEC nodes. We evaluate the proposed solution with respect to operational cost, efficiency, and scalability in a simulated metropolitan area. Our results show that the proposed solution reduces the total cost significantly compared to a greedy baseline algorithm and a local search heuristic, and can scale to moderate problem instances.