Low-latency computational-task execution can be achieved by leveraging device-to-device offloading and parallel processing over nearby extreme edge devices (EEDs), a paradigm known as extreme edge computing (EEC). However, EEC performance is challenged by device spatial randomness with intermittent wireless connectivity, limited device computing power, time-varying availability, and device failures. This paper introduces a novel spatiotemporal analytical framework for EEC by integrating stochastic geometry with an absorbing continuous-time Markov chain (ACTMC) to capture the interplay between communication and computation. Modeling a large-scale millimeter-wave network, we derive tractable expressions for the average task response delay and the task completion probability under both random and location-aware EED selection. Numerical results quantify the impact of location-awareness and unveil the existence of an optimal task segmentation that minimizes delay, which depends on network parameters and EED capabilities. We also demonstrate that device failures and EED scarcity exacerbate delay, which can be mitigated through a collaborative load-balancing approach between EEC and Multi-Access Edge Computing (MEC) schemes. Simulations and sensitivity analyses validate the proposed framework and offer design insights for optimizing system performance.

This paper characterizes integration and coordination gains in dense millimeter-wave ISAC networks through a dual-mode framework that combines monostatic and multistatic sensing. A comprehensive system-level analysis is conducted, accounting for base station (BS) density, power allocation, antenna misalignment, radar cross-section (RCS) fluctuations, clutter, bistatic geometry, channel fading, and self-interference cancellation (SIC) efficiency. Using stochastic geometry, coverage probabilities and ergodic rates for sensing and communication are derived, revealing trade-offs among BS density, beamwidth, and power allocation. It is shown that the communication performance sustained reliable operation despite the overlaid sensing functionality. In addition, the results reveal the foundational role of spatial sensing diversity, driven by the dual-mode operation, to compensate for the weak sensing reflections and vulnerability to imperfect SIC along with interference and clutter. To this end, we identify a system transition from monostatic to multistatic-dominant sensing operation as a function of the SIC efficiency. In the latter case, using six multistatic BSs instead of a single bistatic receiver improved sensing coverage probability by over 100%, highlighting the coordination gain. Moreover, comparisons with pure communication networks confirm substantial integration gain. Specifically, dual-mode networked sensing with four cooperative BSs can double throughput, while multistatic sensing alone improves throughput by over 50%.

In this paper, a novel stochastic geometry-based mathematical model is constructed to examine the performance of a millimeter-wave band joint radar communication (JRC) system. The proposed system comprises two sub-systems: the sensing sub-system, in which radar detects mobile users (MUs), and the communication sub-system, in which directional antennas establish communication with the detected users. Both function-alities operate simultaneously to reduce delay and accelerate beam alignment. The system is modeled under realistic fading channel conditions with distributed scatterers and interferers. Several system parameters are considered in the analytical model, including the density of MUs and clutter from surrounding scatterers, the radar cross section (RCS) fluctuations of the target and clutter, radar search time duration, antenna directivity, and bandwidth. The results reveal that the radar sensing sub-system has the greatest impact on the overall system performance, with radar search duration being a crucial parameter for maximizing the average system throughput.

This article studies data aggregation in large-scale regularly deployed Internet of Things (IoT) networks. The data granularity, in terms of information content and temporal resolution, is parameterized by the sizes of the generated packets and the average interpacket generation time. The generated data packets at the devices are aggregated through static terrestrial gateways. Universal frequency reuse is adopted across all gateways and randomized scheduling is utilized for the IoT devices associated with each gateway. Such network model finds applications in environmental sensing, precision agriculture, and geological seismic sensing to name a few. To this end, we develop a novel spatiotemporal mathematical model to characterize the interplay between data granularity, transmission reliability, and delay. The developed model accounts for several IoT design parameters, which include packet sizes, average generation duty cycle, devices and gateways spatial densities, transmission rate adaptation, power control, and antenna directivity. For tractable analysis, we propose two accurate approximations, based on the Poisson point process (PPP), to characterize the signal-to-interference-plus-noise-ratio (SINR)-based transmission reliability. For the delay analysis, we propose a phase-type arrival/departure (PH/PH/1) queueing model that accounts for packet generation, transmission scheduling, and rate-sensitive SINR-based packet departure. The developed model is utilized to obtain the optimal transmission rate for the IoT devices that minimizes delay. The numerical results delineate the joint feasibility range of packet sizes and interarrival times for data aggregation and reveal significant gains when deploying directional antennas.