The convergence of computing and networking heralds a promising paradigm for future sixth-generation (6G) systems, enabling low-latency services for end users by deploying modern applications, which typically consist of multiple interdependent functions, at the network edge. However, unstable and short-range Device-to-Device (D2D) links often restrict offloading options, forcing users to either face limited access to nearby devices or rely on distant cloud resources, thereby underutilizing edge resources and diminishing user experience. To address this challenge, we propose utilizing base stations to relay traffic between unconnected edge devices. Additionally, we strategically reuse historical function placements to balance re-deployment costs against dynamic request adaptation. Then, aiming to minimize storage, computation, and transmission resource consumption costs along with function replacement costs, we formulate the Dependent Function Scheduling (DFS) problem as a Mixed Integer Non-Linear Programming (MINLP) problem, which is NP-hard even in single-slot scenarios. We introduce a random rounding-based approach to derive high-quality integer solutions for the single-slot DFS problem. Building on this, we further develop an efficient online algorithm for the general multi-slot DFS problem, which is proved to achieve near-optimal performance with high probability. Extensive real-trace simulations demonstrate that our proposed method significantly outperforms state-of-the-art baselines, achieving up to a 68.22% reduction in total cost.

In decentralized edge computing environments, user devices need to perceive the status of neighboring devices, including computational availability and communication delays, to optimize task offloading decisions. However, probing the real-time status of all devices introduces significant overhead, and probing only a few devices can lead to suboptimal decision-making, considering the massive connectivity and non-stationarity of edge networks. Aiming to balance the status probing cost and task offloading performance, we study the joint transmission and computation status probing problem, where the status and offloading delay on edge devices are characterized by general, bounded, and non-stationary distributions. The problem is proved to be NP-hard, even with known offloading delay distributions. To handle this case, we design an efficient offline method that guarantees a$(1-1/e)$approximation ratio via leveraging the submodularity of the expected offloading delay function. Furthermore, for scenarios with unknown and non-stationary offloading delay distributions, we reformulate the problem using the piecewise-stationary combinatorial multi-armed bandit framework and develop a change-point detection-based online status probing (CD-OSP) algorithm. CD-OSP can timely detect environmental changes and update probing strategies via using the proposed offline method and estimating offloading delay distributions. We prove that CD-OSP achieves a regret of$\mathcal {O}(NV\sqrt{T\ln T})$, with$N$,$V$, and$T$denoting the numbers of stationary periods, edge devices, and time slots, respectively. Extensive simulations and testbed experiments demonstrate that CD-OSP significantly outperforms state-of-the-art baselines, which can reduce the probing cost by up to 16.18X with a 2.14X increase in the offloading delay.

Real-time video analytics services aim to provide users with accurate recognition results timely. However, existing studies usually fall into the dilemma between reducing delay and improving accuracy. The edge computing scenario imposes strict transmission and computation resource constraints, making balancing these conflicting metrics under dynamic network conditions difficult. In this regard, we introduce the age of processed information (AoPI) concept, which quantifies the time elapsed since the generation of the latest accurately recognized frame. AoPI depicts the integrated impact of recognition accuracy, transmission, and computation efficiency. We derive closed-form expressions for AoPI under preemptive and non-preemptive computation scheduling policies w.r.t. the transmission/computation rate and recognition accuracy of video frames. We then investigate the joint problem of edge server selection, video configuration adaptation, and bandwidth/computation resource allocation to minimize the long-term average AoPI over all cameras. We propose an online method, i.e., Lyapunov-based block coordinate descent (LBCD), to solve the problem, which decouples the original problem into two subproblems to optimize the video configuration/resource allocation and edge server selection strategy separately. We prove that LBCD achieves asymptotically optimal performance. According to the testbed experiments and simulation results, LBCD reduces the average AoPI by up to 10.94X compared to state-of-the-art baselines.

Real-time video analytics services are expected to deliver accurate recognition results to users timely. However, existing studies usually fail in the dilemma between reducing delay and improving accuracy. Balancing such conflicting metrics is extremely hard under dynamic network conditions. In this regard, we introduce the age of processed information (AoPI) concept, i.e., the time elapsed since the generation of the latest accurately recognized frame. As a systematic metric, AoPI depicts the integrated impact of recognition accuracy, transmission, and computation efficiency. We derive the closed-form expressions of AoPI under preemptive and non-preemptive computation scheduling policies w.r.t. the transmission/computation rate and recognition accuracy of video frames, which are validated using prototype experiments. Based on the derived results, we study the joint video configuration selection, bandwidth, and computation resource allocation problem to minimize the long-term average AoPI among all cameras. An efficient method is proposed to solve the problem, which utilizes Lyapunov optimization and block coordinate descent to make decisions online without requiring future information about network variations and video content. We prove that our method achieves asymptotically optimal performance. Extensive simulations show that our method reduces the AoPI by up to 4.06X compared with the state-of-the-art baselines.

Accommodating services at the network edge is favorable for time-sensitive applications. However, maintaining service usability is resource consuming in terms of pulling service images to the edge, synchronizing databases of service containers, and hot updates of service modules. Accordingly, it is critical to determine which service to place based on the received user requests and service refreshing (maintaining) cost, which is usually neglected in existing studies. In this work, we study how to cooperatively place timely refreshing services and offload user requests among edge servers to minimize the backhaul transmission costs. We formulate an integer nonlinear programming problem and prove its NP-hardness. This problem is highly nontractable due to the complex spatial-and-temporal coupling effect among service placement, offloading, and refreshing costs. We first decouple the problem in the temporal domain by transforming it into a Markov shortest path problem. We then propose a lightweighted discounted value approximation (DVA) method, which further decouples the problem in the spatial domain by estimating the offloading costs among edge servers. The worst performance of DVA is proved to be bounded. 5G service placement testbed experiments and real-trace simulations show that DVA reduces the total transmission cost by up to 59.1% compared with the state-of-the-art baselines.

In this work, we aim to maintain the timeliness of a multipath-based real-time video analytics system by analyzing the age of processed information (AoPI) at the receiver side. In the system, a camera consistently uploads captured frames to different edge servers for processing via corresponding wireless channels. To measure the timeliness of the system, a novel metric named AoPI is proposed, which is the time elapsed since the generation of the latest successfully recognized frame. Hence, AoPI is impacted by the transmission/computation delay on different paths and whether the frames are successfully recognized. We derive the closed-form average AoPI at the receiver side of the system, which is inversely proportional to the recognition probability. Moreover, we prove that adding an identical path can reduce the average AoPI by 37.5% to 50% compared with using a single path. Nevertheless, numerical results show that utilizing a secondary path to access an available edge node will increase the average AoPI in the case of low spectrum efficiency and constrained bandwidth.