Edge computing (EC) is emerging as a key enabler for latency-sensitive applications such as Augmented Reality (AR), autonomous driving, and industrial IoT, by bringing computational resources closer to Wireless Devices (WDs). However, the limited computational capacity inherent to EC presents challenges in resource allocation and in designing pricing mechanisms that provide the right incentives and are aligned with the user-perceived service quality. This paper addresses these challenges by formulating a Stackelberg game that models WDs’ valuation of EC services based on their offloading rates and the service quality they receive. We prove the existence of Stackelberg equilibria and we propose a tractable approximation technique based on log-barrier functions for computing approximate equilibria. Furthermore, to overcome computational issues, we build on the concept of a Differential Stackelberg Equilibrium (DSE) and we propose Stackelberg Gradient Play (SGP), an implicit gradient-based algorithm that ensures convergence to DSE while maintaining efficiency. Extensive simulations show that our approach significantly outperforms existing methods, achieving up to 70% higher revenue for the edge operator while reducing computational overhead substantially. These results underscore the viability of our framework for use in EC systems that require fast, adaptive, and service-aware joint resource management and pricing.

Effective service deployment and orchestration will be essential to accommodate user workloads with diverse requirements in cloud-native beyond 5G Radio Access Networks (RAN). Orchestration will have to take into account individual service quality requirements, latency constraints, and dependencies, while leveraging unique characteristics of dominant workloads, such as machine learning (ML) models. In this work, we address the orchestration of ML-based services, considering users that request application services that rely on network services, such as localization, positioning, etc. Each service is composed of functions, at potentially different quality levels. The objective is to maximize the network operator's revenue by determining service deployment, quality selection and computational resource allocation. The resulting problem is a mixed-integer non-convex problem, which we show is NP-hard. We provide sufficient conditions for the problem to be submodular, and for the general case we propose JADES, which relies on linear relaxation and convexification to decompose the problem into two subproblems, which are solved iteratively until convergence, followed by dependent randomized rounding. Our evaluation based on synthetic workloads shows that JADES outperforms baselines in terms of operator revenue and computational efficiency.

The rapid advancement of Internet of Things (IoT), Augmented Reality (AR), autonomous systems, and intelligent automation is transforming daily life and revolutionizing industrial processes. These technologies demand significant computational resources while also imposing stringent latency requirements. A common approach to meet computational resource demand is leveraging Cloud Computing (CC), which offers scalable processing capabilities through centralized data centers. Nonetheless, this centralized approach often fails to meet stringent latency requirements due to communication delays caused by the geographical distance between cloud servers and end users. This limitation has led to the emergence of the novel paradigm of Edge Computing (EC), which addresses the latency issue by placing compute units closer to end users.

EC server clusters are expected to be smaller in scale and more geographically dispersed compared to CC data centers. This introduces new challenges, such as limited computational and storage capacity, making efficient resource allocation crucial. Additionally, the network operator managing edge infrastructure must maintain its financial sustainability under different workload characteristics and application requirements of users, necessitating joint and adaptable resource management and pricing strategies. Function-as-a-Service (FaaS) offers a promising approach in this regard, as its pay-as-you-go pricing model allows users to pay only for the resources they consume, while also enabling dynamic resource management by shifting the entire responsibility of application deployment to the operator. However, this flexibility also makes the choice of computation, memory, and bandwidth resources price-dependent, further complicating resource management and pricing.

The papers included in this thesis are organized into three parts, each addressing distinct challenges related to pricing, resource allocation, and system dynamics in EC. In the first part of the thesis, we first consider a setting where Wireless Devices (WDs) minimize energy and the monetary costs of computing tasks, while the operator maximizes revenue by optimizing pricing and application caching under memory constraints. We consider a dynamic setting where the operator has no prior knowledge of the varying availability of WDs over time. We model this interaction as a Stackelberg Game (SG) and demonstrate the existence of an equilibrium. To address information asymmetry, we use Bayesian optimization to learn pricing strategies, establish an upper bound on its asymptotic regret, and propose a greedy approximation algorithm for application caching. We then investigate the joint optimization of compute, communication, and memory resources in a static network setting, where WDs minimize the costs of executing the tasks of their applications, including monetary and energy expenses. We model this interaction as a SG, show the existence of an equilibrium, and prove that computing an equilibrium is NP-hard. We propose an efficient approximation algorithm with a bounded approximation ratio. An interesting feature of our solution is that the operator's revenue is maximized when the WDs maximize their energy savings through computation offloading. Furthermore, we investigate the rate-adaptation problem, where WDs adjust their offloading rates based on available compute resources and pricing. We model the interaction as a SG and propose a Stackelberg gradient play algorithm that computes the operator’s implicit revenue function with respect to the rate selection of the WDs.

The second part of this thesis explores a dynamic network and pricing setting where WDs arrive at the edge cell according to a non-homogeneous stochastic process, and the operator sets prices based on the availability of WDs and their heterogeneous workload characteristics. We formulate the problem of maximizing the revenue ofthe operator as a sequential decision-making problem under uncertainty, where the operator's price can be piecewise linear or non-linear and could vary over time. In a Markovian steady-state setting, we derive analytical results for the optimal pricing strategy, which also serve as a heuristic for the general case. To address the general case, we introduce a Generalized Hidden Parameter Markov Decision Process and propose a dual Bayesian neural network approximator that approximates the state transitions and the revenue to accelerate the learning of the optimal pricing policy. This approach enables pre-training on synthetic traces while adapting quickly to unseen workload patterns.

The third part addresses computational challenges by examining the impact of server contention on both operator revenue and application latency constraints. To address this, we propose a contention model validated through experiments across applications with varying compute demands, including L1/L2/L3 caches, I/O, and memory bus usage. We develop a novel model-based Bayesian optimization algorithm to maximize operator revenue while ensuring that latency and resource capacity constraints are met.

The algorithmic contributions of this thesis in pricing and resource management are intended to provide efficient, deployable, and scalable solutions that strengthen the robustness and efficiency of resource allocation and pricing in EC.

Den snabba utvecklingen av Internet of Things (IoT), Augmented Reality (AR), autonoma system och intelligent automation ger upphov till förändrade levnadsmönster och revolutionerar industriella processer. Dessa teknologier kräver betydande beräkningsresurser samtidigt som de ställer strikta krav på fördröjning (latens). Ett vanligt tillvägagångssätt för att möta behovet av beräkningsresurser är att utnyttja Cloud Computing (CC), som erbjuder skalbara bearbetningsmöjligheter genom centraliserade datacenter. Detta centraliserade tillvägagångssätt misslyckas dock ofta med att uppfylla strikta latenskrav på grund av kommunikationsfördröjningar orsakade av det geografiska avståndet mellan molnservrar och slutanvändare. Denna begränsning har lett till framväxten av det nya paradigmet Edge Computing (EC), som hanterar latensproblemet genom att placera beräkningsenheter närmare slutanvändarna.

EC-serverkluster förväntas vara mindre i skala och geografiskt mer spridda jämfört med CC-datacenter. Detta introducerar nya utmaningar, inklusive begränsad beräknings- och lagringskapacitet, vilket gör effektiv resursallokering avgörande. Dessutom måste nätverksoperatören som hanterar edge-infrastrukturen säkerställa en ekonomiskt hållbar drift, trots varierande arbetsbelastningar och applikationskrav från användare, vilket kräver gemensamma och anpassningsbara strategier för resursstyrning och prissättning. Function-as-a-Service (FaaS) är ett lovande tillvägagångssätt i detta avseende, eftersom dess betala-per-användning-prismodell gör det möjligt för användare att endast betala för de resurser de förbrukar, samtidigt som det möjliggör dynamisk resursstyrning genom att hela ansvaret för applikationsdistribution överförs till operatören. Denna flexibilitet gör dock att valet av beräkning, minne och bandbreddsresurser blir priskänsligt, vilket ytterligare komplicerar resursstyrning och prissättning.

Artiklarna som ingår i denna avhandling är organiserade i tre delar, där varje del behandlar olika utmaningar relaterade till prissättning, resursallokering och systemdynamik i edge computing. I den första delen av avhandlingen betraktar vi ett sammanhang där Wireless Devices (WD:er) minimerar energi- och penningkostnaderna för beräkningsuppgifter, medan operatören maximerar intäkterna genom att optimera prissättning och applikationscaching under minnesbegränsningar. Vi betraktar ett dynamiskt sammanhang där operatören inte har någon förkunskap om den varierande tillgängligheten av WD över tid. Vi modellerar detta som ett Stackelberg Game (SG) och visar att det finns ett jämviktsläge. För att hantera informationsasymmetri använder vi Bayesiansk optimering för att lära oss prissättningsstrategier, fastställer en övre gräns för dess asymptotiska ånger (en: regret), och föreslår en girig approximationsalgoritm för applikationscaching. Vi undersöker sedan att gemensamt optimera beräknings-, kommunikations- och minnesresurser i ett statiskt nätverkssammanhang, där WDs minimerar kostnaderna för att köra applikationsuppgifter, inklusive penning- och energikostnader. Vi modellerar denna interaktion som ett SG, visar existensen av ett jämviktsläge och bevisar att beräkningen av ett sådant är NP-svårt. Vi föreslår en effektiv approximationsalgoritm med en begränsad approximationskvot. En intressant egenskap hos vår lösning är att operatörens intäkter maximeras när WDs maximerar sina energibesparingar genom beräkningsavlastning. Vidare undersöker vi problemet med hastighetsanpassning, där WDs justerar sina avlastningshastigheter baserat på tillgängliga beräkningsresurser och prissättning. Vi modellerar interaktionen som ett SG och föreslår en Stackelberg gradient play-algoritm som beräknar operatörens implicita intäktsfunktion med avseende på WDs val av avlastningshastighet.

Den andra delen av denna avhandling undersöker en dynamisk nätverks- och prissättningsmodell där WDs anländer till edge-cellen enligt en icke-homogen stokastisk process. Operatören sätter priser baserat på tillgången på WDs och deras heterogena arbetsbelastningskarakteristiska. Vi formulerar problemet att maximera operatörens intäkter som ett sekventiellt beslutsproblem under osäkerhet, där operatörens pris kan vara styckvis linjära eller icke-linjära och kan variera över tid. I ett Markovskt stationärt tillstånd härleder vi analytiska resultat för den optimala prissättningsstrategin, denna fungerar också som en heuristik för det allmänna fallet. För att hantera det allmänna fallet introducerar vi en Generaliserad Markovbeslutsprocess med dolda parametrar och föreslår en dubbel Bayesiansk neurala nätverksapproximator som approximerar tillståndsövergångar och intäkter för att påskynda inlärningen av den optimala prissättningspolicyn. Detta tillvägagångssätt möjliggör förträning på syntetisk data samtidigt som det snabbt anpassar sig till nya belastningsmönster.

Den tredje delen tar upp förbisedda beräkningsutmaningar genom att undersöka påverkan av serverkonkurrens på både operatörens intäkter och applikationers latensbegränsningar. För att hantera detta föreslår vi en konkurrensmodell som valideras genom experiment över applikationer med varierande beräkningsbehov, inklusive L1/L2/L3-cache, I/O och minnesbussanvändning. Vi utvecklar en ny modellbaserad Bayesiansk optimeringsalgoritm för att maximera operatörens intäkter samtidigt som latens- och resurskapacitetskrav uppfylls. De algoritmiska bidragen inom området prissättning och resursstyrning är avsedda att fungera som effektiva, implementerbara och skalbara lösningar som förbättrar robustheten och effektiviteten i resursallokering och prissättning inom EC.

The commercial adoption of Edge Computing (EC) will require pricing schemes that cater to the financial interests of the operators and of the users. Pricing in EC is particularly challenging as it has to take into account the limited amount of edge resources as well as the stochasticity of user workloads due to location-specific workload characteristics and differences in user activity. We formulate the problem of maximizing the revenue of a serverless edge operator through dynamically pricing compute and memory resources under time varying workloads as a sequential decision making problem under uncertainty. We provide analytical results for the optimal pricing strategy in a Markovian setting in steady state. For the general case, we propose a novel Generalized Hidden Parameter Markov Decision Process (GHP-MDP) formulation of the revenue maximization problem, and we propose a dual Bayesian neural network approximator as a solution. The key novelty of the proposed solution is that it can be pre-trained on synthetic traces and adapts fast to previously unseen workload characteristics. We use simulations based on synthetic and real traffic traces to show that the proposed solution is sample-efficient thanks to effective transfer learning, and it outperforms state-of-the-art learning approaches in terms of revenue and learning rate by up to 50% on real traces.

We consider the problem of resource allocation, pricing and application caching for latency sensitive task offloading in serverless edge computing. We model the interaction between a profit-maximizing operator and cost-minimizing Wireless Devices (WDs) as a Stackelberg game where the operator is the leader and decides the price, resource allocation and set of applications to cache, while the WDs are the followers and decide whether to offload their tasks. We first show that the game has a Subgame Perfect Equilibrium (SPE), but computing it, is NP-hard. Importantly, we show that an SPE, which maximizes the operator's revenue, results in minimal energy consumption among the WDs. For computing an approximate SPE, we propose a linear time approximation algorithm with bounded approximation ratio for resource allocation and pricing, and we propose an efficient heuristic based on the utility density of individual applications for the joint optimization of caching, resource allocation and pricing. Our results show that the proposed algorithm outperforms state-of-the-art methods by up to an order of magnitude both in terms of revenue and total energy savings and has small computational overhead. An interesting feature of our results is that the utility of the operator is maximized by a solution that maximizes the WDs' energy savings through computation offloading, which makes it a promising candidate for energy efficient edge cloud deployments.

Motivated by the emergence of function-as-a-service (FaaS) as a programming abstraction for edge computing, we consider the problem of caching and pricing applications for edge computation offloading in a dynamic environment where (WDs) can be active or inactive at any point in time. We model the problem as a single leader multiple-follower Stackelberg game, where the service operator is the leader and decides what applications to cache and how much to charge for their use, while the WDs are the followers and decide whether or not to offload their computations. We show that the WDs' interaction can be modeled as a player-specific congestion game and show the existence and computability of equilibria. We then show that under perfect and complete information the equilibrium price of the service operator can be computed in polynomial time for any cache placement. For the incomplete information case, we propose a Bayesian Gaussian Process Bandit algorithm for learning an optimal price for a cache placement and provide a bound on its asymptotic regret. We then propose a Gaussian process approximation-based greedy heuristic for computing the cache placement. We use extensive simulations to evaluate the proposed learning scheme, and show that it outperforms state of the art algorithms by up to 50% at little computational overhead.

Edge computing (EC) is expected to provide low latency access to computing and storage resources to autonomous Wireless Devices (WDs). Pricing and resource allocation in EC thus have to cope with stochastic workloads, on the one hand offering resources at a price that is attractive to WDs, one the other hand ensuring revenue to the edge operator. In this paper, we formulate the strategic interaction between an edge operator and WDs as a Bayesian Stackelberg Markov game. We characterize the optimal strategy of the WDs that minimizes their costs. We then show that the operator's problem can be formulated as a Markov Decision Process and propose a model-based reinforcement learning approach, based on a novel approximation of the workload dynamics at the edge cell environment. The proposed approximation leverages two Bayesian Neural Networks (BNNs) to facilitate efficient policy learning, and enables sample efficient transfer learning from simulated environments to a real edge environment. Our extensive simulation results demonstrate the superiority of our approach in terms of sample efficiency, outperforming state-of-the-art methods 30 times in terms of learning rate and by 50% in terms of operator revenue.

We consider the interplay between latency constrained applications and function-level resource management in a serverless edge computing environment. We develop a game theoretic model of the interaction between rate adaptive applications and a load balancing operator under a function-oriented pay-as-you-go pricing model. We show that under perfect information, the strategic interaction between the applications can be formulated as a generalized Nash equilibrium problem, and use variational inequality theory to prove that the game admits an equilibrium. For the case of imperfect information, we propose an online learning algorithm for applications to maximize their utility through rate adaptation and resource reservation. We show that the proposed algorithm can converge to equilibria and achieves zero regret asymptotically, and our simulation results show that the algorithm achieves good system performance at equilibrium, ensures fast convergence, and enables applications to meet their latency constraints.

Motivated by the emergence of function-as-a-service (FaaS) as a programming abstraction for edge computing, we consider the problem of caching and pricing applications for edge computation offloading. We model the problem as a multiplefollower Stackelberg game, where the operator is the leader and decides what applications to cache and how much to charge for their use, while the wireless devices (WDs) are the followers and decide whether or not to offload their computations. We show that the WDs' interaction can be modeled as a player-specific congestion game and show the existence and computability of equilibria. We then show that the equilibrium price of the operator can be computed in polynomial time for any cache placement, and propose a greedy algorithm for computing the applications to be cached. We use extensive simulations to show that the proposed heuristic performs close to optimal at negligible computational overhead.

The commercial adoption of Edge Computingn (EC) will necessitate pricing schemes that align with the economic interests of Network Operator (NO), Service Providers (SPs) and mobile users. Pricing in EC is particularly challenging as it has to take into account resource constraints and contention among different workloads, which can lead to performance degradation and potentially to latency violations. We propose to model pricing subject to latency and resource constraints as an extensive game played between a NO that charges SP based on resource use, SP that charge their users a service specific price, and users that can decide to use the SP's services. We show that equilibria do exist, but computing an equilibrium is NP-hard even under complete information. We then propose an approximation algorithm for computing equilibrium prices for given application placement and we propose a novel, model-assisted Bayesian Optimization (BO) scheme combining probabilistic reparametrization and our approximation scheme. Extensive simulations show that our proposed approach achieves up to an order of magnitude higher revenue compared to state-of-the-art approaches, with a small computational overhead, and highlight the importance of taking into account contention among different workloads.