As augmented and virtual reality evolve, achieving seamless synchronization between physical and digital realms remains a critical challenge, especially for real-time applications where delays affect the user experience. This paper presents MetaLore, a Deep Reinforcement Learning (DRL) based framework for joint communication and computational resource allocation in Metaverse or digital twin environments. MetaLore dynamically shares the communication bandwidth and computational resources among sensors and mobile devices to optimize synchronization, while offering high throughput performance. Special treatment is given in satisfying end-to-end delay guarantees. A key contribution is the introduction of two novel Age of Information (AoI) metrics: Age of Request Information (AoRI) and Age of Sensor Information (AoSI) — integrated into the reward function to enhance synchronization quality. An open source simulator has been extended to incorporate and evaluate the approach. The DRL solution is shown to achieve the performance of full-enumeration brute-force solutions by making use of a small, task-oriented observation space of two queue lengths at the network side. This allows the DRL approach the flexibility to effectively and autonomously adapt to dynamic traffic conditions.

Measuring the influence of users in social networks is key for numerous applications. A recently proposed influence metric, coined as Ψ-score, allows to go beyond traditional centrality metrics, which only assess structural graph importance, by further incorporating the rich information provided by the posting and re-posting activity of users. The Ψ-score is shown in fact to generalize PageRank for non-homogeneous node activity. Despite its significance, it scales poorly to large datasets; for a network of$N$users, it requires to solve$N$linear systems of equations of size$N$. To address this problem, this work introduces a novel scalable algorithm for the fast approximation of Ψ- score, named Power-Ψ. The proposed algorithm is based on a novel equation indicating that it suffices to solve one system of equations of size$N$to compute the Ψ-score. Then, our algorithm exploits the fact that such a system can be recursively and distributedly approximated to any desired error. This permits the Ψ-score, summarizing both structural and behavioral information for the nodes, to run as fast as PageRank. We validate the effectiveness of the proposed algorithm, which we release as an open source Python library, on several real-world datasets.

Network inference is the process of deciding what is the true unknown graph underlying a set of interactions between nodes. There is a vast literature on the subject, but most known methods have an important drawback: the inferred graph is not guaranteed to explain every interaction from the input trace. We consider this an important issue since such inferred graph cannot be used as input for applications that require a reliable estimate of the true graph. On the other hand, a graph having trace feasibility guarantees can help us better understand the true (hidden) interactions that may have taken place between nodes of interest. The inference of such graph is the goal of this paper. Firstly, given an activity log from a social network, we introduce a set of constraints that take into consideration all the hidden paths that are possible between the nodes of the trace, given their timestamps of interaction. Then, we develop a nontrivial modification of the Expectation-Maximization algorithm by Newman [1], that we call Constrained-EM, which incorporates the constraints and a set of auxiliary variables into the inference process to guide it towards the feasibility of the trace. Experimental results on real-world data from Twitter confirm that Constrained-EM generates a posterior distribution of graphs that explains all the events observed in the trace while presenting the desired properties of a scale-free, small-world graph. Our method also outperforms established methods in terms of feasibility and quality of the inferred graph.

We formulate and analyze a generic sequential resource access problem arising in a variety of engineering fields, where a user disposes a number of heterogeneous computing, communication, or storage resources, each characterized by the probability of successfully executing the user's task and the related access delay and cost, and seeks an optimal access strategy to maximize her utility within a given time horizon, defined as the expected reward minus the access cost. We develop an algorithmic framework on the (near-)optimal sequential resource access strategy. We first prove that the problem of finding an optimal strategy is NP-hard in general. Given the hardness result, we present a greedy strategy implementable in linear time, and establish the closed-form sufficient condition for its optimality. We then develop a series of polynomial-time approximation algorithms achieving (ϵ, δ)-optimality. The key components in our design include a pruning process eliminating dominated strategies, thus maintaining polynomial time and space overhead, and a comprehensive scheme allowing flexibly trading-off time and space overhead against performance guarantee.

Caching content over CDNs or at the network edge has been solidified as a means to improve network cost and offer better streaming experience to users. Furthermore, nudging the users towards low-cost content has recently gained momentum as a strategy to boost network performance. We focus on the problem of optimal policy design for Network Friendly Recommendations (NFR). We depart from recent modeling attempts, and propose a Markov Decision Process (MDP) formulation. MDPs offer a unified framework that can model a user with random session length. As it turns out, many state-of-the-art approaches can be cast as subcases of our MDP formulation. Moreover, the approach offers flexibility to model users who are reactive to the quality of the received recommendations. In terms of performance, for users consuming an arbitrary number of contents in sequence, we show theoretically and using extensive validation over real traces that the MDP approach outperforms myopic algorithms both in session cost as well as in offered recommendation quality. Finally, even compared to optimal state-of-art algorithms targeting specific subcases, our MDP framework is significantly more efficient, speeding the execution time by a factor of 10, and enjoying better scaling with the content catalog and recommendation batch sizes.

Influencer marketing has become in the recent years a thriving industry that includes more than 1120 agencies worldwide and with a global market value expected to reach 15 billion dollars by 2022. The advertising problem that such agencies face is the following: given a monetary budget find a set of appropriate influencers on a social platform and recruit them to create a number of posts for the promotion of a certain product. The objective of the campaign is to maximize some impact metric, e.g. the number of impressions, the sales, or the audience reach. In this work, we present an original formulation of the budgeted campaign orchestration problem as a convex program, and further derive a near-optimal algorithm to solve it efficiently. The proposed algorithm has low computational complexity and can scale well for problems with large numbers (millions) of social users, encountered in real-world platforms. We apply our algorithm to a Twitter data set and illustrate the optimal campaign performance for various metrics of interest.

As mobile traffic is dominated by content services (e.g., video), which typically use recommendation systems, the paradigm of network-friendly recommendations (NFR) has been proposed recently to boost the network performance by promoting content that can be efficiently delivered (e.g., cached at the edge). NFR increase the network performance, however, at the cost of being unfair towards certain contents when compared to the standard recommendations. This unfairness is a side effect of NFR that has not been studied in literature. Nevertheless, retaining fairness among contents is a key operational requirement for content providers. This paper is the first to study the fairness in NFR, and design fair-NFR. Specifically, we use a set of metrics that capture different notions of fairness, and study the unfairness created by existing NFR schemes. Our analysis reveals that NFR can be significantly unfair. We identify an inherent trade-off between the network gains achieved by NFR and the resulting unfairness, and derive bounds for this trade-off. We show that existing NFR schemes frequently operate far from the bounds, i.e., there is room for improvement. To this end, we formulate the design of Fair-NFR (i.e., NFR with fairness guarantees compared to the baseline recommendations) as a linear optimization problem. Our results show that the Fair-NFR can achieve high network gains (similar to non-fair-NFR) with little unfairness.

We introduce an original mathematical model to analyze the diffusion of posts within a generic online social platform. The main novelty is that each user is not simply considered as a node on the social graph, but is further equipped with his/her own Wall and Newsfeed, and has his/her own individual self-posting and re-posting activity. As a main result using our developed model, we derive in closed form the probabilities that posts originating from a given user are found on the Wall and Newsfeed of any other. These are the solution of a linear system of equations, which can be resolved iteratively. In fact, our model is very flexible with respect to the modeling assumptions. Using the probabilities derived from the solution, we define a new measure of per-user influence over the entire network, the$\Psi $-score, which combines the user position on the graph with user (re-)posting activity. In the homogeneous case where all users have the same activity rates, it is shown that a variant of the$\Psi $-score is equal to PageRank. Furthermore, we compare the new model and its$\Psi $-score against the empirical influence measured from very large data traces (Twitter, Weibo). The results illustrate that these new tools can accurately rank influencers with asymmetric (re-)posting activity for such real world applications.

We introduce an original mathematical model to analyze the diffusion of posts within a generic online social platform. Each user of such a platform has his own Wall and Newsfeed, as well as his own self-posting and re-posting activity. As a main result, using our developed model, we derive in closed form the probabilities that posts originating from a given user are found on the Wall and Newsfeed of any other. These probabilities are the solution of a linear system of equations. Conditions of existence of the solution are provided, and two ways of solving the system are proposed, one using matrix inversion and another using fixed-point iteration. Comparisons with simulations show the accuracy of our model and its robustness with respect to the modeling assumptions. Hence, this article introduces a novel measure which allows to rank users by their influence on the social platform, by taking into account not only the social graph structure, but also the platform design, user activity (self-and re-posting), as well as competition among posts.

Caching popular content at the wireless edge is recently proposed as a means to reduce congestion at the backbone of cellular networks. The two main actors involved are Mobile Network Operators (MNOs) and Content Providers (CPs). In this work, we consider the following arrangement: an MNO pre-installs memory on its wireless equipment (e.g. Base Stations) and invites a unique CP to use them, with monetary cost. The CP will lease memory space and place its content; the MNO will associate network users to stations. For a given association policy, the MNO may help (or not) the CP to offload traffic, depending on whether the association takes into account content placement. We formulate an optimization problem from the CP perspective, which aims at maximizing traffic offloading with minimum leasing costs. This is a joint optimization problem that can include any association policy, and can also derive the optimal one. We present a general exact solution using Benders decomposition. It iteratively updates decisions of the two actors separately and converges to the global optimum. We illustrate the optimal CP leasing/placement strategy and hit probability gains under different association policies. Performance is maximised when the MNO association follows CP actions.

Caching popular content at the wireless edge promises performance benefits as well as business perspectives. In this paper, we study the following arrangement: a mobile network operator (MNO) pre-installs memory on its wireless equipment, sets a price, and invites a unique content provider (CP) to invest. The CP leases memory space and places its content; the MNO then associates network users to stations, aiming for offloading CP traffic or not. We formulate an optimization problem, which maximizes offloading with minimum leasing costs for the CP. This is an NP-hard mixed-integer non-linear optimization problem. We present an iterative exact solution using Generalized Benders decomposition into a content-related master problem and a user-association slave problem. Master is integer linear. Slave is convex for various association policies, including: 1) join-the-closest cache and 2) cache-aware association. For slave, we introduce a distributed exact solution, named generalized bucket-filling. Extensive simulations illustrate the performance benefits under different association policies. The solution helps to determine the optimal leasing price for the MNO, and the optimal investment budget for the CP. As a general conclusion, both actors profit when the MNO association supports CP decisions.

Base station cooperation is a promising scheme to improve network performance for next generation cellular networks. Up to this point research has focused on station grouping criteria based solely on geographic proximity. However, for the cooperation to be meaningful, each station participating in a group should have sufficient available resources to share with others. In this work we consider an alternative grouping criterion based on a distance that considers both geographic proximity and available resources of the stations. When the network is modelled by a Poisson Point Process, we derive analytical formulas on the proportion of cooperative pairs or single stations, and the expected sum interference from each of the groups. The results illustrate that cooperation gains strongly depend on the distribution of available resources over the network.

Caching of popular content on wireless nodes is recently proposed as a means to reduce congestion in the backbone of cellular networks and to improve Quality of Service. From a network point of view, the goal is to offload as many users as possible from the backbone network to the wireless caches while at the same time offering good service to cache-unrelated users. Aggressive offloading can lead to an unbalanced user association. Some wireless nodes can be overloaded by cache-related traffic while the resources of others remain underused. Given a fixed content placement, this work proposes an efficient distributed algorithm to control and balance the association of cache-related traffic among cellular cache memories. The algorithm allows the network to achieve the globally optimal solution and can be executed on base stations using a limited amount of information exchange between them. It is based on a novel algorithm we call Bucket-filling. The solution limits the cache-users per node by balancing the total load among the nodes in a fair way. The improvement compared to common user assignment policies is highlighted for single-as well as for multi-tier random networks.

Cooperation in cellular networks has been recently suggested as a promising scheme to improve system performance. In this work, clusters are formed based on the Mutually Nearest Neighbour relation, which defines which stations cooperate in pair and which do not. When node positions follow a Poisson Point Process (PPP) the performance of the original clustering model can be approximated by another one, formed by the superposition of two PPPs (one for the singles and one for the pairs) equipped with adequate marks. This allows to derive exact expressions for the network coverage probability under two user-cluster association rules. Numerical evaluation shows coverage gains from different signal cooperation schemes that can reach up to 15% compared to the standard non- cooperative network coverage. The analysis is general and can be applied to any type of cooperation or coordination between pairs of transmitting nodes.

This article introduces a novel family of decentralised caching policies for wireless networks, referred to as spatial multi-LRU. Based on these, cache inventories are updated in a way that provides content diversity to users that are covered by, and thus have access to, more than one station. Two variations are proposed, the multi-LRU-One and -All, which differ in the number of replicas inserted in the involved edge caches. Che-like approximations are proposed to accurately predict their hit probability under the Independent Reference Model (IRM). For IRM traffic multi-LRU-One outperforms multi-LRU-All, whereas when the traffic exhibits temporal locality the -All variation can perform better.

A device-to-device (D2D) wireless network is considered, where user devices also have the ability to cache content. In such networks, users are mobile and communication links can be spontaneously activated and dropped depending on the users' relative position. Receivers request files from transmitters, these files having a certain popularity and file-size distribution. In this work a new performance metric is introduced, namely the Service Success Probability, which captures the specificities of D2D networks. For the Poisson Point Process case for node distribution and the SNR coverage model, explicit expressions are derived. Simulations support the analytical results and explain the influence of mobility and file-size distribution on the system performance, while providing intuition on how to appropriately cache content on mobile storage space. Of particular interest is the investigation on how different file-size distributions (Exponential, Uniform, or Heavy-Tailed) influence the performance.

In this work we consider the problem of an optimal geographic placement of content in wireless cellular networks modelled by Poisson point processes. Specifically, for the typical user requesting some particular content and whose popularity follows a given law (e.g. Zipf), we calculate the probability of finding the content cached in one of the base stations. Wireless coverage follows the usual signal-to-interference-and noise ratio (SINR) model, or some variants of it. We formulate and solve the problem of an optimal randomized content placement policy, to maximize the user's hit probability. The result dictates that it is not always optimal to follow the standard policy “cache the most popular content, everywhere”. In fact, our numerical results regarding three different coverage scenarios, show that the optimal policy significantly increases the chances of hit under high-coverage regime, i.e., when the probabilities of coverage by more than just one station are high enough.

The problem of base station cooperation has recently been set within the framework of Stochastic Geometry. Existing works consider that a user dynamically chooses the set of stations that cooperate for his/her service. However, this assumption often does not hold. Cooperation groups could be predefined and static, with nodes connected by fixed infrastructure. To analyse such a potential network, in this work we propose a grouping method based on proximity. It is a variation of the so called Nearest Neighbour Model. We restrict ourselves to the simplest case where only singles and pairs of base stations are allowed to be formed. For this, two new point processes are defined from the dependent thinning of a Poisson Point Process, one for the singles and one for the pairs. Structural characteristics for the two are provided, including their density, Voronoi surface, nearest neighbour, empty space and J-function. We further make use of these results to analyse their interference fields and give explicit formulas to their expected value and their Laplace transform. The results constitute a novel toolbox towards the performance evaluation of networks with static cooperation.

Cooperation in cellular networks is a promising scheme to improve system performance, especially for cell-edge users. In this work, stochastic geometry is used to analyze cooperation models where the positions of base stations follow a Poisson point process distribution and where Voronoi cells define the planar areas associated with them. For the service of each user, either one or two base stations are involved. If two, these cooperate by exchange of user data and channel related information with conferencing over some backhaul link. Our framework generally allows for variable levels of channel information at the transmitters. This paper is focused on a case of limited information based on Willems' encoding. The total per-user transmission power is split between the two transmitters and a common message is encoded. The decision for a user to choose service with or without cooperation is directed by a family of geometric policies, depending on its relative position to its two closest base stations. An exact expression of the network coverage probability is derived. Numerical evaluation shows average coverage benefits of up to 17% compared to the non-cooperative case. Various other network problems of cellular cooperation, like the fully adaptive case, can be analyzed within our framework.

Base station cooperation in the downlink of cellular systems has been recently suggested as a promising concept towards a better exploitation of the communication system's physical resources. It may offer a high gain in capacity through interference mitigation. This however, comes at a cost of high information exchange between cooperating entities and a high computational burden. Clustering of base stations into subgroups is an alternative to guarantee such cooperation benefits in a lower scale. The optimal definition of clusters, however, and a systematic way to find a solution to such problem is not yet available. In this work, we highlight the combinatorial nature of the problem, exploit this to describe the system of users and base stations as a graph and formulate a pure 0-1 program. Its solution suggests a cost optimal way to form clusters and assign user subsets to them.

In the current work the effects of hop-by-hop packet loss and retransmissions via ARQ protocols are investigated within a Mobile Ad-hoc NET-work (MANET). A success probability function is related to each link, which can be controlled by power and rate allocation. The expression for the network's stability region is initially derived where the success function plays a critical role. The investigation considers functions with specific properties which are shown to be satisfied for various expressions of the success probability related to different modulation and coding schemes as well as outage events. A Network Utility Maximization problem (NUM) with stability constraints is further formulated which decomposes into the input rate control and the scheduling problem. Under certain assumptions the latter is relaxed to a simpler form. This allows application of supermodular game theory and the algorithmic approach in is adapted to include the family of success functions of interest. It is shown finally that interference measurements per node drastically reduce the amount of information exchange required for solving the scheduling problem.

In the current work the effects of hop-by-hop packet loss and retransmissions via ARQ protocols are investigated within a Mobile Ad-hoc NET-work (MANET). Errors occur due to outages and a success probability function is related to each link, which can be controlled by power and rate allocation. We first derive the expression for the network's capacity region. A Network Utility Maximization problem (NUM) with stability constraints is further formulated which decomposes into (a) the input rate control problem and (b) the scheduling problem. The NUM problem can be solved in a fully decentralized manner if (b) is solved distributedly. Use of supermodular game theory suggests a price based algorithm that requires minimum information exchange between interfering nodes and converges to a power allocation which satisfies the necessary optimality conditions of (b). Simulations illustrate that the suggested algorithm brings near optimal results.

A single queue incorporating a retransmission protocol is investigated, assuming that the sequence of per effort success probabilities in the Automatic Retransmission reQuest (ARQ) chain is a priori defined and no channel state information at the transmitter is available. A Markov Decision Problem with an average cost criterion is formulated where the possible actions are to either continue the retransmission process of an erroneous packet at the next time slot or to drop the packet and move on to the next packet awaiting for transmission. The cost per slot is a linear combination of the current queue length and a penalty term in case dropping is chosen as action. The investigation seeks policies that provide the best possible average packet delay-dropping trade-off for Quality of Service guarantees. An optimal deterministic stationary policy is shown to exist, several structural properties of which are obtained. Based on that, a class of suboptimal-policies is introduced. These suggest that it is almost optimal to use a K-truncated ARQ protocol as long as the queue length is lower than L, else send all packets in one shot. The work concludes with an evaluation of the optimal delay-dropping tradeoff using dynamic programming and a comparison between the optimal and suboptimal policies.

The problem of optimal power allocation for a single user in an OFDMA system is considered for uplink, under the assumption that the total power is divided equally to a selected subset of subcarriers. This scenario suggests reduced feedback information for power control from base station to the user since only the information over modulation on each subcarrier is necessary. Assuming knowledge of the instantaneous users' channel gains, the rate optimization problem reduces to a subcarrier allocation problem, described by a discrete function with the set of possible allocated subcarriers as domain and the set of achievable sum rates as range. A continuous equivalent of the function is used to derive properties that also hold in the discrete case. The function is in general not concave and concavity holds only for high CNR regions - over a specified bound. In all cases however it is proved that the maximum is unique and a simple and efficient algorithm is proposed for subcarrier allocation which always provides the optimal solution concerning the subcarriers to be loaded. The cost in achievable capacity from the use of equal-power compared to actual waterfilling is calculated, which is shown to be small while the gain in frequency resources and feedback reduction is important.

In this paper, strategies for dynamic user grouping and shared frequency resource assignments for OFDMA systems are proposed. The users are grouped based on their modulation type and a metric for this purpose is introduced which considers tradeoffs between maximum rate and minimum allocated resources per user. The available resources are distributed through the modulation groups based on fairness criteria. Equal power allocation on the loaded subcarriers of each user is further incorporated. Simulations show that under equal power assumptions the algorithm proposed in the following can bring a better exploitation of the available bandwidth and can provide good QoS to an increased number of users simultaneously.