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Wireless networks in next generation will provide users ubiquitous computing services with low delay by devices at the network edge, namely mobile edge computing (MEC). The intensive computation tasks can be partially offloaded to the MEC server via the wireless link and then processed through the MEC computation resources to cater for the delay demand. A parallel computation process is formed in the MEC network consists of local computation at MEC users (MUs) and MEC computation at MEC servers. However, the fluctuating wireless channel environment, changeable spatial distribution of MUs and the randomness of MEC servers’ locations make it hard to characterize and guarantee the end-to-end quality of service requirements. In this work, we are devoted to analyze and optimize the overall delay bound for MEC networks under two orthogonal frequency division multiple access (OFDMA) strategies via stochastic network calculus (SNC). Specifically, Poisson cluster process is utilized to capture the randomness of MEC servers’ and users’ spatial locations and to derive the Laplace transform of interference suffered by an MU of interest. The upper bounds for the delay violation probability of two OFDMA strategies are established by exploiting SNC with the Mellin transform of signal-to-interference ratio. Furthermore, we propose an optimal task offloading scheme by minimizing the overall delay, which balances the local computation delay and MEC delay. [ABSTRACT FROM AUTHOR]

In order to satisfy the requirement of extremely high data rate in traffic hotspot regions, millimeter wave (mmWave) has attracted significant attention in wireless communication networks. While the coverage performance of mmWave networks based on the distribution of signal-to-interference-plus-noise ratio (SINR) has been widely studied, it provides only very limited information on the link reliability. In this paper, we provide a fine-grained performance analysis of the mmWave networks with hotspots. Specifically, we first establish a general and tractable framework to investigate the performance of mmWave networks using the Poisson cluster process integrated with several features of the mmWave band. Both open and closed association strategies are considered. To show what fraction of users in the networks achieves target reliability when the SINR is given, we derive the tier association probability and the moments of the conditional SINR distribution, based on which the exact meta distributions of SINR are given. Interestingly, in clustered mmWave networks, the widely used standard and generalized beta approximations do not work well when the blockage effect is severe. To resolve this issue, we provide a modified approximation by scaling the standard beta distribution, which is shown to be closer to the exact results. We conduct extensive simulations to study the impact of mmWave and deployment features on the performance of clustered mmWave networks. Numerical results reveal that the optimal scattering variance of mmWave base stations scales with the cluster size to maximize the number of concurrent reliable links, and increasing the antenna directivity results in more reliable communications than elevating the transmit power of mmWave base stations. [ABSTRACT FROM AUTHOR]

Device-to-device (D2D) communication is a promising solution to meet rapidly growing demands for data services via spectrum reuse. This paper studies the physical layer security in a D2D underlay cellular network from a network-wide perspective, where the locations of D2D and cellular users are modeled as Poisson cluster processes (PCPs) to characterize the clustering feature of D2D users, the locations of eavesdroppers (Eves) and base stations (BSs) are modeled as a PCP and Poisson point process (PPP), respectively. We establish an analytical framework to assess the coverage and security performance of the network. Two scenarios are considered, i.e., one D2D pair scenario and multiple D2D pairs scenario, where in each cell there is one or multiple D2D users (DUs) sharing the frequency spectrum with the cellular users (CUs) in each time slot of the TDMA scheme adopted by BSs. In each considered scenario, we derive exact expressions for the coverage outage probabilities (COPs) and secrecy outage probabilities (SOPs), respectively, for both the CUs and DUs. Furthermore, the exact expression for the network-wide secrecy throughput (ST) is derived. Numerical results are presented to verify our theoretical derivations and reveal some insights into the impact of various parameters on the system performance. [ABSTRACT FROM AUTHOR]

Device-to-Device (D2D) communication has become a promising candidate in future cellular networks to improve spectrum efficiency and energy efficiency, while reducing the latency. As the capacity of D2D user equipments (DUEs) increases, it makes DUEs caching possible, and it can offload traffic from macro base stations, perform computation-intensive and latency-critical tasks. In this paper, in-band communication is considered, and the Poisson cluster process is utilized to model and analyze the clustered D2D networks under cluster-centric caching strategy. Firstly, we use the Thomas cluster process to model cellular user equipments (CUEs) and DUEs, and give a deployment scheme of clustered D2D caching networks. Secondly, the aggregated interference of the typical D2D receiver is analyzed in the clustered D2D networks. Then the Laplace transform of the aggregated interference is analyzed, and the expressions of coverage probability, average achievable rate and cache hit probability of the typical D2D receiver are deduced. The simulation results show that we can adjust the path loss exponent, densities of DUEs and CUEs, transmitting power of CUEs, mean of simultaneously active transmitters in each cluster and Zipf exponent to improve the performance of clustered D2D caching networks. [ABSTRACT FROM AUTHOR]

In order to satisfy the requirement of high throughput in most UAV applications, the potential of integrating millimeter wave (mmWave) communications with UAV networks is explored in this paper. A tractable three-dimensional (3D) spatial model is proposed for evaluating the average downlink performance of UAV networks at mmWave bands, where the locations of UAVs and users are randomly distributed with the aid of a Poisson cluster process. Moreover, an actual 3D antenna model with the uniform planar array is deployed at all UAVs to examine the impact of both azimuth and elevation angles. Based on this framework and two typical user selection schemes, closed-form approximation equations of the evaluated coverage probability and area spectral efficiency (ASE) are derived. In a noise-limited scenario, an exact expression is provided, which theoretically demonstrates that a large scale of antenna elements is able to enhance the coverage performance. Regarding the altitude of UAVs, there exists at least one optimal height for maximizing the coverage probability. Numerical results verify the proposed insight that non-line-of-sight transmission caused by obstacles have negligible effects on the proposed system. Another interesting result is that the ASE can be maximized by optimizing both the targeted data rate and the density of UAVs. [ABSTRACT FROM AUTHOR]

Deploying Sub-6GHz networks together with millimeter wave (mmWave) is a promising solution to achieve high data rates in traffic hotspots while guaranteeing sufficient coverage, where mmWave small cells are densely deployed to provide high quality of service. In this paper, we propose an analytical framework to investigate the integrated Sub-6GHz-mmWave cellular networks, in which the Sub-6GHz base stations (BSs) are modeled as a Poisson point process, and the mmWave BSs are clustered following a Poisson cluster process in traffic hotspots. We conduct stochastic geometry-based analysis and derive the performance metrics including the association probability, signal-to-interference-plus-noise ratio coverage probability and average achievable rate, which are validated to be accurate by Monte Carlo simulations. We analyze the impact of various deployment parameters on the network performance to give insights on the network design. In particular, it is shown that deploying mmWave small cells in traffic hotspots will outperform both traditional Sub-6GHz heterogeneous network and isolated mmWave system in terms of the coverage probability. It can also be shown that extremely high and extremely small association weight for mmWave BSs will deteriorate the performance for cell edge users and cell interior users, respectively. Moreover, there exists an optimal pre-decided dispersion parameter of mmWave BSs that contributes to the maximum coverage probability. [ABSTRACT FROM AUTHOR]

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated a variety of user and base station (BS) configurations to be considered for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models proposed by standardization bodies, such as the 3rd Generation Partnership Project (3GPP). Complementary to these simulation models, stochastic geometry-based approach, modeling the locations of the users, and the $K$ tiers of BSs as independent and homogeneous Poisson point processes (PPPs), has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based K$ -tier HetNet model is not rich enough to capture spatial coupling between user and BS locations that exists in real-world HetNet deployments and is included in 3GPP simulation models. In this paper, we demonstrate that modeling a fraction of users and arbitrary number of BS tiers alternatively with a Poisson cluster process (PCP) captures the aforementioned coupling, thus bridging the gap between the 3GPP simulation models and the PPP-based analytic model for HetNets. We further show that the downlink coverage probability of a typical user under maximum signal-to-interference-ratio ( \mathtt {SIR} ) association can be expressed in terms of the sum-product functionals over PPP, PCP, and its associated offspring point process, which are all characterized as a part of our analysis. We also show that the proposed model converges to the PPP-based HetNet model as the cluster size of the PCPs tends to infinity. Finally, we specialize our analysis based on general PCPs for Thomas and Matérn cluster processes. Special instances of the proposed model closely resemble the different configurations for BS and user locations considered in 3GPP simulations. [ABSTRACT FROM PUBLISHER]

This paper investigates the performance of millimeter wave (mmWave) communications in clustered device-to-device (D2D) networks. The locations of D2D transceivers are modeled as a Poisson Cluster Process. In each cluster, devices are equipped with multiple antennas, and the active D2D transmitter (D2D-Tx) utilizes mmWave to serve one of the proximate D2D receivers. Specifically, we introduce three user association strategies: 1) uniformly distributed D2D-Tx model; 2) nearest D2D-Tx model; and 3) closest line-of-site (LOS) D2D-Tx model. To characterize the performance of the considered scenarios, we derive new analytical expressions for the coverage probability and area spectral efficiency (ASE). Additionally, in order to efficiently illustrating the general trends of our system, a closed-form lower bound for the special case interfered by intra-cluster LOS links is derived. We provide Monte Carlo simulations to corroborate the theoretical results and show that: 1) the coverage probability is mainly affected by the intra-cluster interference with LOS links; 2) there exists an optimum number of simultaneously active D2D-Txs in each cluster for maximizing ASE; and 3) the closest LOS model outperforms the other two scenarios but at the cost of extra system overhead. [ABSTRACT FROM PUBLISHER]

This paper develops a comprehensive analytical framework with foundations in stochastic geometry to characterize the performance of cluster-centric content placement in a cache-enabled device-to-device (D2D) network. Different from device-centric content placement, cluster-centric placement focuses on placing content in each cluster, such that the collective performance of all the devices in each cluster is optimized. Modeling the locations of the devices by a Poisson cluster process, we define and analyze the performance for three general cases: 1) k -Tx case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at the k{\mathrm{ th}} closest device to the cluster center; 2) \ell $ -Rx case: the receiver of interest is the \ell {\mathrm{ th}} closest device to the cluster center and its content of interest is available at a device chosen uniformly at random from the same cluster; and 3) baseline case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at a device chosen independently and uniformly at random from the same cluster. Easy-to-use expressions for the key performance metrics, such as coverage probability and area spectral efficiency of the whole network, are derived for all three cases. Our analysis concretely demonstrates significant improvement in the network performance when the device on which content is cached or device requesting content from cache is biased to lie closer to the cluster center compared with the baseline case. Based on this insight, we develop and analyze a new generative model for cluster-centric D2D networks that allows to study the effect of intra-cluster interfering devices that are more likely to lie closer to the cluster center. [ABSTRACT FROM AUTHOR]