Mobile edge computing makes available distributed computation and stor-age resources in close proximity to end users and allows to provide low-latencyand high-capacity services within mobile networks. Therefore, mobile edgecomputing is emerging as a promising architecture for hosting critical ser-vices with stringent latency and performance requirements, which otherwiseare challenging to be addressed in conventional cloud computing architectures.Notable use cases of mobile edge computing include real-time data analyticservices, industrial process control, and computation offloading for Internetof things devices. However, those services rely on efficient resource manage-ment, including resource dimensioning and service placement, and require tobe resilient to cyber-attacks, to faulty components and to operation mistakes.The work in this thesis proposes models of resilient resource management thatsupport rapid response to incidents in mobile edge computing and developsefficient algorithms for the resulting resource management problems.

In the first part of the thesis, we consider resilient resource managementfor edge computing systems in which failover is realized by restoring additionalservice instances in different mobile edge computing nodes in case of failures.We first develop a placement algorithm based on Benders decomposition andlinear relaxation to determine the mobile edge computing nodes to be openedand to compute the placement of the service instances with respect to a set ofconsidered failure scenarios, with the objective of minimizing operation costs.Upon the occurrence of a failure scenario, service migration is to be triggeredto migrate the service instances from one placement to another placement, forwhich we further develop service migration algorithms to schedule migrationunder time constraints, so as to minimize service interruptions.

In the second part of the thesis, we consider resilient resource manage-ment in mobile edge computing for services with different levels of resiliencerequirements. Resilience is achieved by synchronizing states of the servicesto two types of standby instances that maintain the trade-off between en-ergy consumption and activation time such that the standby instances cantake over the service seamlessly as an instantaneous failure response. We for-mulate the joint problem of resource dimensioning and service placement forminimizing energy consumption and prove that it is NP-hard. We propose anefficient approximation algorithm based on Lagrangian relaxation to decidethe type, amount, and locations of the computation resources and to com-pute the placement of service instances and their standby instances. We thenconsider the same resilience model but for hosting periodic services in mo-bile edge computing systems with resources portioned into availability zones,under schedulability constraints. We formulate the corresponding resilient re-source management problem as a non-linear programming problem and provethat it is NP-hard. We propose efficient solutions based on approximationprogramming and primal-dual approaches for resilient service placement.

By considering different models of resilient service placement in mobileedge computing, the results in this thesis provide effective, efficient, and scal-able resource management algorithms for emerging mobile edge computingsystems.

Databehandling i det mobila nätverkets utkant (mobile edge computing) innebär att distribuerade beräknings- och lagringsresurser tillgängliggörs direkt i infrastrukturen för det mobila nätverket. Den fysiska närheten till slutanvändarna gör det möjligt att tillhandahålla tjänster med liten fördröjning och hög kapacitet. Därför växer nu teknologin fram som ett lovande alternativ till molnberäkning, särskilt för att driva kritiska tjänster med strikta krav på fördröjning och prestanda som är svåra att uppfylla i traditionella molnberäkningssystem. Några exempel på viktiga tillämpningsområden är tjänster för dataanalys som måste köras i realtid, styrning av industriprocesser, samt avlastning av beräkningsintensiva uppgifter från sakernas-internet-enheter. Denna typ av system ställer dock höga krav på effektiv hantering av resurser, vilket innefattar att tilldela rätt mängd resurser och att avgöra var i nätverket en tjänst ska köras. Dessutom ställs höga krav på resiliens mot cyberattacker, felande komponenter, samt driftfel. Arbetet i denna avhandling lägger fram modeller för resilient resurshantering för databehandling i nätverkets utkant, som kan ställa om snabbt i händelse av fel, samt utvecklar effektiva algoritmer för att optimera hanteringen av resurser i dessa modeller.    I avhandlingens första del studeras en mekanism för resilient resurshantering i system för databearbetning i nätverkets utkant, som i händelse av fel initierar nya instanser av den felande tjänsten i andra beräkningsnoder och återställer tjänsten. En algoritm utvecklas, baserad på Benders dekomposition och relaxation, som tar hänsyn till flera olika felscenarier för att avgöra vilka beräkningsnoder som skall användas och var de nya tjänsteinstanserna skall köras, med målet att minimera driftskostnaderna. Därutöver utvecklas algoritmer för schemaläggning av migration av tjänster från en beräkningsnod till en annan, i den händelse att ett felscenario inträffar, som tar hänsyn till tidsbegränsningar och har som mål att minimera avbrott i aktiva tjänster.       

I avhandlingens andra del studeras resilient resurshantering då olika tjänster har olika krav på resiliensnivå. Resiliens uppnås genom att synkronisera tillstånden hos de tjänster som är i drift med två olika typer av ”standby”-instanser som är i viloläge och redo att ögonblickligen och sömlöst ta över efter en felande tjänsteinstans. Ett problem formuleras, samt bevisas vara NP-svårt, för att samtidigt optimera både tilldelning av resurser och av beräkningsnoder till tjänsterna, med målet att minimera energiåtgång.

En effektiv algoritm, baserad på Lagrangerelaxation, ges för att hitta en approximativ lösning till problemet, det vill säga för att avgöra typ, mängd och placering av de nödvändiga beräkningsresurserna, samt placering av tjänsteinstanser och deras respektive ”standby”-instanser. Dessutom utvidgas modellen till tjänster som måste köras periodiskt och för att inkludera resurser som är tillgängliga endast i vissa zoner, med begränsningar för schemaläggning av tjänster. Ett icke-linjärt optimeringsproblem formuleras för att lösa detta schemaläggningsproblem och bevisas vara NP-svårt. En effektiv lösningsmetod utvecklas, med hjälp av approximationsmetoder och primal-dual-metoder, för resilient nodplacering av tjänster.    

Avhandlingen överväger flera olika modeler för resilient resurshantering, det vill säga för att besluta hur tjänster ska delas upp mellan olika noder i nätverkets utkant, samt lägger fram effektiva och skalbara algoritmer för att optimera resurshantering i framtidens databearbetningssystem i det mobila nätverkets utkant.

In multi-user multiple-input-multiple-output (MU-MIMO) systems that employ pilot-symbol aided channel estimation, the pilot-to-data power ratio (PDPR) has a large impact on the system performance. In this paper, we consider the problem of setting the PDPR in multi-cell MU-MIMO systems in the presence of channel estimation errors, intercell interference and pilot contamination. To analyze and address this problem, we first develop a model of the multi-cell MU-MIMO system and derive a closed-form expression for the mean squared error of the uplink received data symbols. Building on this result, we then propose two decentralized PDPR-setting algorithms based on game theoretic approaches that are applicable in multi-cell systems. We find that both algorithms converge to a Nash equilibrium and provide performance improvements over systems that do not properly set the PDPR, while they maintain different levels of fairness.

Migrating virtualized services (VSs) in mobile edge clouds is essential for maintaining service quality under mobility, for optimizing resource utilization, and for responding to incidents. We consider migrating VSs with heterogeneous resource requirements from a source placement to a target placement under a time constraint, while maintaining service continuity as much as possible. We formulate the VS migration problem as an integer programming problem, and propose an efficient algorithm to compute sequences of migration actions. The algorithm is based on a graphical representation of the VS dependencies, and constructs a collection of acyclic directed hypergraphs with bounded length. We evaluate our algorithm in realistic scenarios and compare it to the optimal solution and to a baseline algorithm. Extensive simulations show that our algorithm achieves near-optimal performance, and is computationally efficient and scalable.

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.

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.

We consider the migration of virtualized services (VSs) in Mobile Edge Computing (MEC), so as to facilitate server maintenance, load balancing under mobility, improved energy efficiency and resource utilization, and incident response. We consider a set of VSs that has to be migrated from a source placement to a target placement, while maintaining service continuity as much as possible. We formulate the VS migration problem as an integer programming problem, and analyze its complexity. We propose an efficient iterative algorithm for computing when and in what order the VSs shall be migrated among the MEC nodes. We evaluate the proposed solution in terms of total service value, efficiency, and scalability. Extensive simulations show that our algorithm is computationally effective, and performs close to optimal.

Virtual Process Control Functions (VPFs) are a promising solution for replacing hardware controllers in industrial control processes in order to improve operational efficiency. With the introduction of Mobile Edge Computing (MEC) in 5G networks, VPFs could even be executed on cloud resources close to the mobile network edge to further improve operational efficiency. Nonetheless, for this to happen, it is fundamental to ensure that the placement of VPFs be resilient to potential cyber-attacks and component failures, besides being efficient. In this paper we address this problem by considering that VPF placement costs are incurred by reserving MEC resources, executing VPF instances, and by data transmission. We formulate the VPF placement problem as an integer programming (IP) problem, with resilience as a constraint. We propose a VPF placement algorithm based on generalized Benders decomposition and based on linear relaxation of the resulting sub-problems, which effectively reduces the number of integer variables to that of the number of MEC nodes. We evaluate the proposed solution with respect to operational cost, efficiency, and scalability, and compare it with a greedy baseline algorithm. Extensive simulations show that our algorithm performs well in realistic scenarios.