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This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that share them. The algorithm is divided into three phases. The first phase consists of labeling each edge and triangle of the input triangulation according to its size; the second phase builds polygons (simple or not) from terminal-edges regions using the label system; and the third phase transforms each non simple polygon into simple ones. The final mesh contains polygons with convex and nonconvex shape. Since Voronoi based meshes are currently the most used polygonal meshes, we compare some geometric properties of our meshes against constrained Voronoi meshes. Several experiments are run to compare the shape and size of polygons, the number of final mesh points and polygons. Finally, we validate these polygonal meshes by solving a Laplace equation on an L-shaped domain using the Virtual Element Method (VEM) and show the optimal convergence rate of the numerical solution.

We study private classical communication over quantum multiple-access channels. For an arbitrary number of transmitters, we derive a regularized expression of the capacity region. In the case of degradable channels, we establish a single-letter expression for the best achievable sum-rate and prove that this quantity also corresponds to the best achievable sum-rate for quantum communication over degradable quantum multiple-access channels. In our achievability result, we decouple the reliability and privacy constraints, which are handled via source coding with quantum side information and universal hashing, respectively. Hence, we also establish that the multi-user coding problem under consideration can be handled solely via point-to-point coding techniques. As a by-product of independent interest, we derive a distributed leftover hash lemma against quantum side information that ensures privacy in our achievability result.

Energy efficiency (EE) plays a key role in future wireless communication network and it is easily to achieve high EE performance in low SNR regime. In this paper, a new high EE scheme is proposed for a MIMO wireless communication system working in the low SNR regime by using two dimension resource allocation. First, we define the high EE area based on the relationship between the transmission power and the SNR. To meet the constraint of the high EE area, both frequency and space dimension are needed. Besides analysing them separately, we decided to consider frequency and space dimensions as a unit and proposed a two-dimension scheme. Furthermore, considering communication in the high EE area may cause decline of the communication quality, we add quality-of-service(QoS) constraint into the consideration and derive the corresponding EE performance based on the effective capacity. We also derive an approximate expression to simplify the complex EE performance. Finally, our numerical results demonstrate the effectiveness of the proposed scheme.

Low-Latency IoT applications such as autonomous vehicles, augmented/virtual reality devices and security applications require high computation resources to make decisions on the fly. However, these kinds of applications cannot tolerate offloading their tasks to be processed on a cloud infrastructure due to the experienced latency. Therefore, edge computing is introduced to enable low latency by moving the tasks processing closer to the users at the edge of the network. The edge of the network is characterized by the heterogeneity of edge devices forming it; thus, it is crucial to devise novel solutions that take into account the different physical resources of each edge device. In this paper, we propose a resource representation scheme, allowing each edge device to expose its resource information to the supervisor of the edge node through the mobile edge computing application programming interfaces proposed by European Telecommunications Standards Institute. The information about the edge device resource is exposed to the supervisor of the EN each time a resource allocation is required. To this end, we leverage a Lyapunov optimization framework to dynamically allocate resources at the edge devices. To test our proposed model, we performed intensive theoretical and experimental simulations on a testbed to validate the proposed scheme and its impact on different system's parameters. The simulations have shown that our proposed approach outperforms other benchmark approaches and provides low latency and optimal resource consumption.

In this paper, we address the resource provisioning problem for service function chaining (SFC) in terms of the placement and chaining of virtual network functions (VNFs) within a multi-access edge computing (MEC) infrastructure to reduce service delay. We consider the VNFs as the main entities of the system and propose a mean-field game (MFG) framework to model their behavior for their placement and chaining. Then, to achieve the optimal resource provisioning policy without considering the system control parameters, we reduce the proposed MFG to a Markov decision process (MDP). In this way, we leverage reinforcement learning with an actor-critic approach for MEC nodes to learn complex placement and chaining policies. Simulation results show that our proposed approach outperforms benchmark state-of-the-art approaches.

Fog computing is emerging as a new paradigm to deal with latency-sensitive applications, by making data processing and analysis close to their source. Due to the heterogeneity of devices in the fog, it is important to devise novel solutions which take into account the diverse physical resources available in each device to efficiently and dynamically distribute the processing. In this paper, we propose a resource representation scheme which allows exposing the resources of each device through Mobile Edge Computing Application Programming Interfaces (MEC APIs) in order to optimize resource allocation by the supervising entity in the fog. Then, we formulate the resource allocation problem as a Lyapunov optimization and we discuss the impact of our proposed approach on latency. Simulation results show that our proposed approach can minimize latency and improve the performance of the system.

Performance assessment and optimization for networks jointly performing caching, computing, and communication (3C) has recently drawn significant attention because many emerging applications require 3C functionality. However, studies in the literature mostly focus on the particular algorithms and setups of such networks, while their theoretical understanding and characterization has been less explored. To fill this gap, this paper conducts the asymptotic (scaling-law) analysis for the delay-outage tradeoff of noise-limited wireless edge networks with joint 3C. In particular, assuming the user requests for different tasks following a Zipf distribution, we derive the analytical expression for the optimal caching policy. Based on this, we next derive the closed-form expression for the optimum outage probability as a function of delay and other network parameters for the case that the Zipf parameter is smaller than 1. Then, for the case that the Zipf parameter is larger than 1, we derive the closed-form expressions for upper and lower bounds of the optimum outage probability. We provide insights and interpretations based on the derived expressions. Computer simulations validate our analytical results and insights.

Iterative distributed optimization algorithms involve multiple agents that communicate with each other, over time, in order to minimize/maximize a global objective. In the presence of unreliable communication networks, the Age-of-Information (AoI), which measures the freshness of data received, may be large and hence hinder algorithmic convergence. In this paper, we study the convergence of general distributed gradient-based optimization algorithms in the presence of communication that neither happens periodically nor at stochastically independent points in time. We show that convergence is guaranteed provided the random variables associated with the AoI processes are stochastically dominated by a random variable with finite first moment. This improves on previous requirements of boundedness of more than the first moment. We then introduce stochastically strongly connected (SSC) networks, a new stochastic form of strong connectedness for time-varying networks. We show: If for any $p \ge0$ the processes that describe the success of communication between agents in a SSC network are $\alpha$-mixing with $n^{p-1}\alpha(n)$ summable, then the associated AoI processes are stochastically dominated by a random variable with finite $p$-th moment. In combination with our first contribution, this implies that distributed stochastic gradient descend converges in the presence of AoI, if $\alpha(n)$ is summable.

The interconnection of vehicles in the future fifth generation (5G) wireless ecosystem forms the so-called Internet of vehicles (IoV). IoV offers new kinds of applications requiring delay-sensitive, compute-intensive and bandwidth-hungry services. Mobile edge computing (MEC) and network slicing (NS) are two of the key enabler technologies in 5G networks that can be used to optimize the allocation of the network resources and guarantee the diverse requirements of IoV applications. As traditional model-based optimization techniques generally end up with NP-hard and strongly non-convex and non-linear mathematical programming formulations, in this paper, we introduce a model-free approach based on deep reinforcement learning (DRL) to solve the resource allocation problem in MEC-enabled IoV network based on network slicing. Furthermore, the solution uses non-orthogonal multiple access (NOMA) to enable a better exploitation of the scarce channel resources. The considered problem addresses jointly the channel and power allocation, the slice selection and the vehicles selection (vehicles grouping). We model the problem as a single-agent Markov decision process. Then, we solve it using DRL using the well-known DQL algorithm. We show that our approach is robust and effective under different network conditions compared to benchmark solutions.

This paper studies the problem of online user grouping, scheduling and power allocation in beyond 5G cellular-based Internet of things networks. Due to the massive number of devices trying to be granted to the network, non-orthogonal multiple access method is adopted in order to accommodate multiple devices in the same radio resource block. Different from most previous works, the objective is to maximize the number of served devices while allocating their transmission powers such that their real-time requirements as well as their limited operating energy are respected. First, we formulate the general problem as a mixed integer non-linear program (MINLP) that can be transformed easily to MILP for some special cases. Second, we study its computational complexity by characterizing the NP-hardness of different special cases. Then, by dividing the problem into multiple NOMA grouping and scheduling subproblems, efficient online competitive algorithms are proposed. Further, we show how to use these online algorithms and combine their solutions in a reinforcement learning setting to obtain the power allocation and hence the global solution to the problem. Our analysis are supplemented by simulation results to illustrate the performance of the proposed algorithms with comparison to optimal and state-of-the-art methods.