Pricing network edges for heterogeneous selfish users

We study the degradation in network performance caused by the selfish behavior of noncooperative network users. We consider a directed network in which each edge possesses a latency function describing the common latency incurred by all traffic on the edge as a function of the edge congestion. Given a rate of traffic between each pair of nodes in the network, we aspire toward an assignment of traffic to paths in which the sum of all travel times (the total latency) is minimized; however, in many settings network users are free to route their traffic in a selfish manner, without regard to the total latency. We therefore assume that each network user routes its traffic on the minimum-latency path available to it, given the network congestion caused by the other users. In general such a selfishly motivated assignment of traffic to paths (a Nash equilibrium) will not minimize the total latency; hence, selfish behavior carries the cost of decreased network performance. We quantify this degradation in network performance via the price of anarchy, defined as the worst possible ratio between the total latency of a Nash equilibrium and of a minimum-latency routing of the traffic.In this paper, we show that the underlying network topology plays no role in the determination of the price of anarchy. Specifically, we show that under weak hypotheses on the class of allowable edge latency functions, the worst-case ratio between the total latency of a Nash equilibrium and of a minimum-latency routing for any multicommodity flow network is achieved by a single-commodity instance on a set of parallel links. In the special case where the class of allowable latency functions includes all of the constant functions, we prove that a network with only two parallel links suffices to achieve the worst-possible ratio. Informally, these results imply that the inefficiency inherent in a flow at Nash equilibrium stems from the inability of selfish users to discern which of two competing routes is superior and not from the topological complexity arising from the diverse intersections of many paths belonging to different commoditie.Our proof techniques also give powerful methods for computing the price of anarchy with respect to an arbitrary class of latency functions. We apply these methods to function classes that have been well studied in the literature (such as degree-bounded polynomials and functions of the form $\ell(x) = (u—x)—1} that are used to model edges with capacity u), thereby achieving the first tight analyses of the price of anarchy for significant classes of latency functions outside the class of linear functions.

We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times---the total latency---is minimized.In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimum-latency path available to it, given the network congestion caused by the other users. In general such a "selfishly motivated" assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance.In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total latency of the routes chosen by unregulated selfish network users may be arbitrarily larger than the minimum possible total latency; however, we prove that it is no more than the total latency incurred by optimally routingtwiceas much traffic.

We address the problem of crowd congestion at venues like theme parks, museums and world expos by providing route guidance to multiple selfish users (with budget constraints) moving through the venue simultaneously. To represent these settings, we introduce the Selfish Orienteering Problem (SeOP) that combines two well studied problems from literature, namely Orienteering Problem (OP) and Selfish Routing (SR). OP is a single agent routing problem where the goal is to minimize latency (or maximize reward) in traversing a subset of nodes while respecting budget constraints. SR is a game between selfish agents looking for minimum latency routes from source to destination along edges of a network available to all agents. Thus, SeOP is a multi-agent planning problem where agents have selfish interests and individual budget constraints. As with Selfish Routing, we employ Nash Equilibrium as the solution concept in solving SeOP. A direct mathematical program formulation to find a Nash equilibrium in SeOP cannot scale because the number of constraints is quadratic in the number of paths, which itself is an exponential quantity. To address scalability issues, we make two key contributions. First, we provide a compact non-pairwise formulation with linear number of constraints in the number of paths to enforce the equilibrium condition. Second, we introduce DIRECT, an incremental and iterative master-slave decomposition approach to compute an approximate equilibrium solution. Similar to existing flow based approaches, DIRECT is scale invariant in the number of agents. We also provide a theoretical discussion of our approximation quality and present extensive empirical results on synthetic and real-world graphs demonstrating the scalability of combining DIRECT with our non-pairwise formulation.

In this work, we study the combinatorial structure and the computational complexity of Nash equilibria for a certain game that models selfish routing over a network consisting of m parallel links. We assume a collection of n users, each employing a mixed strategy, which is a probability distribution over links, to control the routing of its own assigned traffic. In a Nash equilibrium, each user selfishly routes its traffic on those links that minimize its expected latency cost, given the network congestion caused by the other users. The social cost of a Nash equilibrium is the expectation, over all random choices of the users, of the maximum, over all links, latency through a link.We embark on a systematic study of several algorithmic problems related to the computation of Nash equilibria for the selfish routing game we consider. In a nutshell, these problems relate to deciding the existence of a Nash equilibrium, constructing a Nash equilibrium with given support characteristics, constructing the worst Nash equilibrium (the one with maximum social cost), constructing the best Nash equilibrium (the one with minimum social cost), or computing the social cost of a (given) Nash equilibrium. Our work provides a comprehensive collection of efficient algorithms, hardness results (both as \( \mathcal{N}\mathcal{P} \) -hardness and \( \# \mathcal{P} \) -completeness results), and structural results for these algorithmic problems. Our results span and contrast a wide range of assumptions on the syntax of the Nash equilibria and on the parameters of the system.

The current design of LTE is to deploy the EPC components in a core network, and the data traffic from UEs (User Equipment) is converged to these components. It will cause network congestion and inefficiencies with the increasing number of internet devices in the future. One distributed way to solve the network burden is to deploy the on demand EPC components close to the edge of network (near the base station; known as Edge-based EPC). At present, some researches directly use the current EPC components for edge deployment. However, it causes some problems. When a UE moves between two edge networks, it will face the inter-edge procedures to change of these serving edge components. The procedure involves many numbers of message exchanges between components for the re-establishment of the connection, which will affect the UE's experience. It represents that the current EPC architecture is not suitable for edge deployment. Based on our previous study, we had derived a Refactored EPC (R-EPC) architecture [1]. Then, we determine the deployment of the R-EPC components based on their responsibilities and call this architecture edge-based refactored EPC (abbreviated to E-R-EPC). In E-R-EPC, we deploy the common use of service triggering related components and the gateway responsible for data traffic to edge network, while deploying the components that record the location of UE to core network; thus, the UE can use the low-latency data traffic services in edge network, since the served recording location components are not changed, it can reduce the signaling cost to update the location information. Also, we propose a new handover procedure called inter-edge handover. Further, we compare the signaling cost and queuing delay of E-R-EPC with other architectures, the results of the proposed one showed good performance, especially in dealing with frequent movements of UE between two edge networks (e.g.: high-speed mobility); It proves E-R-EPC is a suitable reference for edge-designed networks.

With the explosive increase in mobile data traffic and stringent quality-of-experience requirements of users, mobile edge caching is a promising paradigm to reduce delivery latency and network congestions by serving content requests locally. However, it is extremely challenging to conduct cache replacement when the cache is full and the future request pattern is unknown subject to enormous content volume but limited cache capacity at the network edge. In this paper, we propose a cache replacement algorithm based on the oracle approximation named OA-Cache in an end-to-end manner to maximize the cache hit rate. Specifically, we construct a complex model that uses a temporal convolutional network to capture the long and short dependencies between content requests. Then, an attention mechanism is adopted to find out the correlations between the requests in the sliding window and cached contents. Instead of training a policy to mimic Belady that evicts the content with the longest reuse distance, we cast the learning task into a classification model to distinguish unpopular contents from popular ones. Finally, we apply the knowledge distillation approach to assist in transferring knowledge from a large pre-trained complex network to a lightweight network to readily accommodate to the network edge scenario. To validate the effectiveness of OA-Cache, we conduct extensive experiments on real-world datasets. The evaluation results demonstrate that OA-Cache can achieve the superior performance compared to candidate algorithms.

One of the most widely used solution concepts for strategic games is the concept of Nash equilibrium. A Nash equilibrium is a state in which no player can improve its objective by unilaterally changing its strategy. A Nash equilibrium is called pure if all players choose a pure strategy, and mixed if players choose probability distributions over strategies. Of special interest are fully mixed Nash equilibria where each player chooses each strategy with non-zero probability. Rosenthal [12] introduced a special class of strategic games, now widely known as congestion games. Here, the strategy set of each player is a subset of the power set of given resources. The players share a private objective function, defined as the sum (over their chosen resources) of functions in the number of players sharing this resource. In his seminal work, Rosenthal showed with help of a potential function that congestion games (in sharp contrast to general strategic games) always admit at least one pure Nash equilibrium. An extension to congestion games are weighted congestion games, in which the players have weights and thus different influence on the congestion of the resources. In (weighted) network congestion games the strategy sets of the players correspond to paths in a network. In order to measure the degradation of social welfare due to the selfish behavior of the players, Koutsoupias and Papadimitriou [8] introduced a global objective function, usually coined as social cost. They defined the price of anarchy, also called coordination ratio, as the worst-case ratio between the value of social cost in a Nash equilibrium and that of some social optimum. Thus the coordination ratio measures the extent to which non-cooperation approximates cooperation. As a starting point for studying the coordination ratio, Koutsoupias and Papadimitriou considered a very simple weighted network congestion game, now known as KP-model. Here, the network consists of a single source and a single destination which are connected by parallel links. The load on a link is the total weight of players assigned to this link. Associated with each link is a capacity representing the rate at which the link processes load. Each of the players selfishly routes from the source to the destination by choosing a probability distribution over the links. The private objective function of a player is defined as its expected latency. In the KP-model the social cost is defined as the expected maximum latency on a link, where the expectation is taken over all random choices of the players. In this paper, we give a thorough survey on the most exciting results on finite (weighted) congestion games and on special classes which are related to the KP-model. In particular, we review the findings on the existence and computational complexity of pure Nash equilibria. Furthermore, we discuss results on the price of anarchy. Last but not least, we survey known facts on fully mixed Nash equilibria.

Edge computing is proposed to solve the problem of centralized cloud computing caused by a large number of IoT (Internet of Things) devices. The IoT protocols need to be modified according to the edge computing paradigm, where the edge computing devices for analyzing IoT data are distributed to the edge networks. The MQTT (Message Queuing Telemetry Transport) protocol, as a data distribution protocol widely adopted in many international IoT standards, is suitable for cloud computing because it uses a centralized broker to effectively collect and transmit data. However, the standard MQTT may suffer from serious traffic congestion problem on the broker, causing long transfer delays if there are massive IoT devices connected to the broker. In addition, the big data exchange between the IoT devices and the broker decreases network capability of the edge networks. The authors in this paper propose a novel MQTT with a multicast mechanism to minimize data transfer delay and network usage for the massive IoT communications. The proposed MQTT reduces data transfer delays by establishing bidirectional SDN (Software Defined Networking) multicast trees between the publishers and the subscribers by means of bypassing the centralized broker. As a result, it can reduce transmission delay by 65% and network usage by 58% compared with the standard MQTT.

With the increase in Internet of Things (IoT) devices, data produced by these devices is also increasing. For its trusted use, security of the IoT data is very important. Nowadays, blockchain is a contemporary technology which is used in various fields for providing security. But the mining task of the blockchain is very computation intensive. So, there exist dependency on resource providers like near-by devices, edge network for providing resources to the miners for the task of computations. In our proposed framework, bidding of the resources is done by the miners from near-by devices and edge network. Reverse stackelberg game and auction mechanism are used to reach optimality of the decisions. Nash equilibrium is also achieved. Less storage is consumed by few blocks of the blockchain network as meta data is stored in some blocks. Experimental evaluation is done to compute average delay and net profit.

Joint optimization of UPF placement and traffic routing for 5G core network user plane

Mobile edge computing (MEC) is a key enabler for ultra-low latency in heterogeneous dense cellular networks in the 5G era and beyond, by deploying services at the network edge. Due to high user mobility, the services are usually migrated to follow the users by predicting the user trajectory to achieve a balance between energy consumption and service latency. However, service migration for multi-user heterogeneous dense cellular networks is challenging because (1) the user trajectory prediction, which is crucial for service migration, becomes intractable with a large number of users, and (2) making service migration decisions for each user independently is subjected to interference among the users. Therefore, in this study, we formulated the service migration of all the users in MEC-enabled heterogeneous dense cellular networks as an optimization problem, with the objective of minimizing the average energy consumption while satisfying the service latency requirements, taking into account the interference among different users. Next, we developed an efficient energy-efficient online algorithm based on the Lyapunov and particle swarm optimizations, called EGO, to resolve the original problem without predicting the trajectories of the users. Finally, a series of simulations based on real-world mobility traces of vehicles in Bologna were conducted to establish the superiority of the EGO algorithm over state-of-the-art solutions.

With the development of the Internet of Everything (IoE), huge amount of data is being generated at network edge and needs to be processed in real time, such as edge video analytics applications. However, limited computing resources and energy on edge devices make it challenging to efficiently perform the intensive computing tasks. Existing solutions of offloading tasks to edge servers depend on the availability of edge servers, and they are difficult to satisfy massive computation needs. Instead, this article proposes a novel offloading framework named EdgeBrain, which offloads computational tasks from one edge device (Producer of Computation, i.e., PCO) to other edge devices (Consumers of Computation, i.e., CCOs). We formulate this offloading problem as a multi-round non-cooperative Stackelberg game, prove the existence of unique Nash Equilibrium (NE) and Stackelberg Equilibrium (SE) in the game, and design the gradient search algorithm to calculate the optimal offloading decision. The performance evaluation based on a prototype implementation of EdgeBrain in the context of a video analytics application, face detection and recognition, shows that EdgeBrain outperforms several comparable techniques in terms of execution time, frame rate, transfer data volume, and power consumption.

The Metaverse, an expansive virtual universe blending physical and digital realities, demands sophisticated network infrastructures to deliver seamless and immersive user experiences. Network slicing and edge computing have emerged as pivotal technologies in meeting the stringent requirements of low latency, high bandwidth, and scalability essential for the Metaverse. This paper explores the synergistic role of network slicing and edge computing, examining their contributions to network efficiency, resource optimization, and user experience enhancement.

Mobile edge computing (MEC) has appeared as a promising solution to fill the gap between the growing computationally intensive applications and limited computation capability of mobile devices by providing powerful computing services at the edge of the wireless access network. To use the services provided by the MEC more effectively, making efficient and reasonable offloading decisions is crucial. In this paper, we study the computation offloading of tasks from multiple users to a single-cell edge server under a dynamic environment. We consider a practical case wherein a group of mobile users with random mobility patterns use a common set of time-varying stochastic transmission channels to perform computation offloading, and the number of active users in the system randomly changes. To reduce the mutual interference among users when accessing the wireless channels, we adopt game theory to formulate the users’ computation offloading decision process as a stochastic game model. Next, we prove the existence of the Nash Equilibrium (NE) for the proposed game model by showing its equivalency to a weighted potential game which has at least one pure-strategy NE point. Then, we present distributed computation offloading algorithms by adopting a payoff-based multi-agent reinforcement learning (MARL) approach to reach the NE of the game. Finally, through simulation, we validate the effectiveness of the proposed algorithms by comparing them with the results obtained from other previously studied multi-agent learning algorithms as well as conventional Q-learning and deep Q-learning algorithms.

Analyzing massive amounts of data using complex machine learning models requires significant computational resources. The conventional approach to such problems involves centralizing training data and inference processes in the cloud, i.e., in data centers. However, with the proliferation of mobile devices and increasing application of the Internet-of-Things (IoT) paradigm, very large amounts of data are collected at the edges of wireless networks, and due to privacy constraints and limited communication resources, it is undesirable or impractical to upload this data from mobile devices to the cloud for centralized learning. This problem can be solved by distributed learning at the network edge, by which edge devices collaboratively train a shared learning model using real-time mobile data. The avoidance of raw-data uploading not only helps to preserve privacy but may also alleviate network-traffic congestion and minimize latency. With that said, distributed training still requires a substantial amount of information exchange between devices and edge servers over wireless links. In the process, wireless impairments such as noise, interference, and imperfect knowledge of channel states can significantly slow down distributed learning (e.g., convergence speed) and degrades its performance (e.g., learning accuracy). This makes it crucial to optimize wireless network performance so as to support the efficient deployment of distributed learning algorithms. On the other hand, distributed learning algorithms provide a powerful tool-set for solving complex problems in wireless communication and networking. One important framework, called federated learning (FL), enables users to collaboratively learn a shared model while helping to preserve local data privacy. The application of FL can endow edge devices with capabilities of user behavior prediction, user identification, and wireless environment analysis. As another example, distributed reinforcement learning is capable of leveraging distributed computation power and data to solve complex optimization and control problems that arise in various use cases, such as network control, user clustering, resource management, and interference alignment. To cover this paradigm of distributed learning over wireless networks, this two-part Special Issue features papers dealing with two main research challenges: a) optimization of wireless network performance for efficient implementation of distributed learning in wireless networks, and b) distributed learning for solving communication problems and optimizing network performance.