Optimal Offloading Decision Research Articles

DDQN-based online computation offloading and application caching for dynamic edge computing service management

Multi-access Edge Computing (MEC) reduces task service latency and energy consumption by offloading computing tasks to MEC servers. However, constrained by the limited bandwidth and computing resources, MEC servers often cannot parallelly process all computing tasks. Simultaneously, the high dynamism of service popularity necessitates MEC servers to dynamically update cached applications, under ensuring compliance with storage resource constraints and the system cache updating cost budget for service providers. In response to the above two issues, this paper firstly formulates computation offloading and application caching as a dual-timescale decision optimization problem, aiming to minimize the average service latency for users by obtaining optimal offloading decision, cache decision, transmission bandwidth, and computing resource. Then, we propose a Deep Reinforcement Learning (DRL)-based two-stage online computation offloading and application caching (DTSO2C) algorithm, effectively stabilizing application cache update costs and enhancing Quality of Service (QoS) for users. Furthermore, we utilize convex optimization algorithms to derive the optimal communication bandwidth and computing resource allocation strategy, further reducing the average service latency for users. Simulation results demonstrate that the DTSO2C algorithm outperforms the compared algorithms, achieving an average reduction in service latency of 66.2%, with an average cache update cost of only 0.15 USD per time frame.

Joint Optimization Algorithm for Latency-Energy and Privacy Combining Discrete Differential Evolution and Convex Optimization

A privacy protection task offloading algorithm combining discrete differential evolution and convex optimization is proposed to resolve the new position privacy leakage problem for mobile terminal due to transferring tasks to multiple edge servers for computation via wireless networks. First, the privacy cost of offloading decision is defined for the characteristics of the position privacy problem combined with the standard deviation theory. Second, the objective problem is modeled as a joint optimization of position privacy protection, offloading decision and transmission power, and the total cost of task offloading is an optimization objective. Finally, to handle the objective problem efficiently, offloading decision variable is decoupled from the transmission power variable to decrease the computational complexity of the problem; the discrete differential evolution algorithm is designed to accumulate the approximate optimal offloading decision, and the optimal transmission power is efficiently solved by variable substitution method and subgradient method. Simulations reveal that the algorithm has excellent convergence; it improves the position privacy protection level of mobile terminal and reduces the total cost of task offloading while maintaining lower energy consumption and latency.

A Novel intelligent SAV oriented QL-based task offloading in mobile edge environments

Edge computing is a novel and potential computing model which moves storage and computing capabilities to the network edge, substantially decreasing service latency and network traffic. The existing Internet of Things (IoT) network offloading algorithm faces limitations such as a fixed number of applications, high edge-to-edge delay, and reliance on a single Mobile Edge Computing (MEC) server, posing security and privacy concerns. Moreover, resource-constrained mobile devices need more effective data integration and compression strategies. Addressing these challenges, this study suggests an approach based on deep reinforcement learning (DRL), specifically the SAV (State Action Value) Oriented QL (Q-Learning) based Task Offloading method, to optimise task offloading and resource allocation in edge-cloud computing. The model aims to empower Mobile Devices (MDs) to develop optimal offloading decisions for long-term Quality Perception, utilising a neural network to establish the relationship between MD state and action value. The paper introduces a Recurrent Extended Memory Network (REMN) to capture dynamic workload behaviour at Edge nodes (ENs). It incorporates Quality Mapping, Quality Estimation, and a Quality-Aware DRL Task Offloading Algorithm to improve the accuracy and efficiency of the offloading procedure in MEC systems. This systematic approach improves overall system performance and enables MDs to leverage ENs for neural network training, reducing computational burdens. As a result, it can accomplish a more significant number of tasks, reducing latency from 0.74 ms to 7.168 ms and decreasing energy consumption from 270 J to 1820.39 J for tasks ranging from 10 to 50, respectively.

Cost-aware task offloading in vehicular edge computing: A Stackelberg game approach

With the popularity of vehicular communication systems and mobile edge vehicle networking, intelligent transportation applications arise in Internet of Vehicles (IoVs), which are latency-sensitive, computation-intensive, and requiring sufficient computing and communication resources. To satisfy the requirements of these applications, computation offloading emerges as a new paradigm to utilize idle resources on vehicles to cooperatively complete tasks. However, there exist several obstacles for realizing successful task offloading among vehicles. For one thing, extra cost such as communication overhead and energy consumption occurs when a task is offloaded on a service vehicle, it is unlikely to expect the service vehicle will contribute its resources without any reward. For another, since there are many vehicles around, both user vehicles and service vehicles are trying to strike a balance between cost and profit, through matching the perfect service/user vehicles and settled with optimal offloading plan that is beneficial to all parties. To solve these issues, this work focuses on the design of effective incentive mechanisms to stimulate vehicles with idle resources to actively participate in the offloading process. A fuzzy logic-based dynamic pricing strategy is proposed to accurately evaluate the cost of a vehicle for processing the task, which provides insightful guidance for finding the optimal offloading decision. Meanwhile, the competitive and cooperation relations among vehicles are thoroughly investigated and modeled as a two-stage Stackelberg game. Particularly, this work emphasizes the social attributes of vehicles and their effect on the offloading decision making process, multiple key properties such as the willingness of UV to undertake the task locally, the reputation of UV and the satisfaction of SV for the allocated task proportion, are carefully integrated in the design of the optimization problem. A distributed algorithm with applicable complexity is proposed to solve the problem and to find the optimal task offloading strategy. Extensive simulations are conducted on real-world scenarios and results show that the proposed mechanism achieves significant performance advantages in terms of vehicles' utilities, cost, completion delay under varied network and channel environment, which justifies the effectiveness and efficiency of this work.

Reliable and adaptive computation offload strategy with load and cost coordination for edge computing

There are several important factors to consider in edge computing systems including latency, reliability, power consumption, and queue load. Task replication requires additional energy costs in mobile edge offloading scenarios based on master-slave replication for fault tolerance. Excessive task offloading may lead to a sharp increase in the total energy consumption of the system including replication costs. Conversely, new tasks cannot enter the waiting queue and are lost, resulting in reliability issues. This paper proposes an adaptive task offloading strategy for balancing the edge node queue load and offloading cost (Lyapunov and Differential Evolution based Offloading schedule strategy, LDEO). The LDEO strategy innovatively customizes the Lyapunov drift-plus-penalty function by incorporating replication redundancy offloading costs to establish a balance model between the queue load and offloading cost. The LDEO strategy computes the optimal offloading decisions with dynamic adjustment characteristics by integrating a low-complexity differential evolution method, aiming to find the optimal balance point that minimizes the offloading cost while maintaining reliability performance. The experimental results show that compared with the existing strategies, LDEO strategy effectively reduces the redundancy of fault tolerance cost and the waiting time under the condition of ensuring that the task will not be discarded over time. It stabilizes the queue length in a reasonable range, controls the waiting time and loss rate of tasks, reduces the extra energy consumption paid by replication redundancy, and effectively realizes the optimal balance under multiple conditions.

Task offloading method based on CNN-LSTM-attention for cloud–edge–end collaboration system

Most of the existing task offloading methods in edge computing environments do not fully utilize the processing capabilities of cloud servers and have high computational complexity, making them unsuitable for real-time processing tasks. To address this problem, we propose a cloud–edge–end collaborative task offloading method based on deep learning methods, combining Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and attention mechanisms. This method models the total cost of the cloud–edge–end collaboration system as a weighted sum function of the time delay and energy consumption of task execution. Then, with the objective of minimizing the total cost of the system, the task offloading problem is formulated as a mixed-integer joint optimization problem with offloading decision and bandwidth allocation, and two subproblems are decomposed from the optimization problem: one focuses on offloading decision and the other on bandwidth allocation. A CNN-LSTM-Attention neural network-based method is proposed to solve the optimal offloading decision efficiently. Based on this, the differential evolution algorithm is used to generate the optimal bandwidth allocation, resulting in efficient task offloading. The simulation experiment results demonstrate that our method enhances system performance and reduces the overall cost of the system, which is significantly better than existing methods.

Joint DNN partitioning and task offloading in mobile edge computing via deep reinforcement learning

As Artificial Intelligence (AI) becomes increasingly prevalent, Deep Neural Networks (DNNs) have become a crucial tool for developing and advancing AI applications. Considering limited computing and energy resources on mobile devices (MDs), it is a challenge to perform compute-intensive DNN tasks on MDs. To attack this challenge, mobile edge computing (MEC) provides a viable solution through DNN partitioning and task offloading. However, as the communication conditions between different devices change over time, DNN partitioning on different devices must also change synchronously. This is a dynamic process, which aggravates the complexity of DNN partitioning. In this paper, we delve into the issue of jointly optimizing energy and delay for DNN partitioning and task offloading in a dynamic MEC scenario where each MD and the server adopt the pre-trained DNNs for task inference. Taking advantage of the characteristics of DNN, we first propose a strategy for layered partitioning of DNN tasks to divide the task of each MD into subtasks that can be either processed on the MD or offloaded to the server for computation. Then, we formulate the trade-off between energy and delay as a joint optimization problem, which is further represented as a Markov decision process (MDP). To solve this, we design a DNN partitioning and task offloading (DPTO) algorithm utilizing deep reinforcement learning (DRL), which enables MDs to make optimal offloading decisions. Finally, experimental results demonstrate that our algorithm outperforms existing non-DRL and DRL algorithms with respect to processing delay and energy consumption, and can be applied to different DNN types.

A deep reinforcement learning based research for optimal offloading decision

Currently, a concern about power resource constraints in the distribution environment is being voiced increasingly, where the increase of power consumption devices overwhelms the terminal load unaffordable and the quality of power consumption cannot be guaranteed. How to acquire the optimal offloading decision of power resources has become a problem that needs to be addressed urgently. To tackle this challenge, a novel reinforcement learning algorithm named Deep Q Network with a partial offloading strategy (DQNP) is proposed to optimize power resource allocation for high computational demands. In the DQNP, a coupled coordination degree model and Lyapunov algorithm are introduced, which trade-offs and decouples the relationships between local-edge and latency–energy consumption. To derive the optimal offloading decision, the resource computation utility function is selected as the objective function. In addition, model pruning is availed to further improve the training time and inference results. Results show that the proposed offloading mechanism can significantly decrease the function value and decline the weighted sum of latency and energy consumption by an average of 3.61%–7.31% relative to other state-of-the-art algorithms. Additionally, the energy loss in the power distribution process is successfully mitigated; furthermore, the effectiveness of the proposed algorithm is also verified.

CNN Partitioning and Offloading for Vehicular Edge Networks in Web3

Web3, an emerging blockchain-based decentralized network, grants users ownership and enhances the collaboration among devices under monitoring. Benefiting from decentralization and in-memory computing, vehicular edge networks can process tasks such as road object detection distributedly without being attacked. Recently, to provide intelligent service for Web3 users, artificial intelligence applications have been booming, thus generating enormous deep learning models. These models are supposed to be deployed in the edge due to their massive computation. Furthermore, edge servers may face overload and intolerable delay for the high concurrency of offloaded deep learning tasks. How to determine an optimal offloading decision in the highly dynamic and heterogeneous edge-cloud environment is still a challenge. To tackle the mentioned challenge, a dynamic offloading strategy based on game theory combined with convolutional neural network (CNN) partition for vehicular edge networks, named GPOV, is proposed. Specifically, CNN partition can utilize resources more efficiently and reduce the delay with parallelism. The game theoretic offloading decision strategy can determine the optimal offloading policy according to the realtime environment. The performance of our strategy is validated in the final part of this paper.

Optimizing task offloading and resource allocation in edge-cloud networks: a DRL approach

Edge-cloud computing is an emerging approach in which tasks are offloaded from mobile devices to edge or cloud servers. However, Task offloading may result in increased energy consumption and delays, and the decision to offload the task is dependent on various factors such as time-varying radio channels, available computation resources, and the location of devices. As edge-cloud computing is a dynamic and resource-constrained environment, making optimal offloading decisions is a challenging task. This paper aims to optimize offloading and resource allocation to minimize delay and meet computation and communication needs in edge-cloud computing. The problem of optimizing task offloading in the edge-cloud computing environment is a multi-objective problem, for which we employ deep reinforcement learning to find the optimal solution. To accomplish this, we formulate the problem as a Markov decision process and use a Double Deep Q-Network (DDQN) algorithm. Our DDQN-edge-cloud (DDQNEC) scheme dynamically makes offloading decisions by analyzing resource utilization, task constraints, and the current status of the edge-cloud network. Simulation results demonstrate that DDQNEC outperforms heuristic approaches in terms of resource utilization, task offloading, and task rejection.

Toward Heterogeneous Environment: Lyapunov-Orientated ImpHetero Reinforcement Learning for Task Offloading

Task offloading combined with reinforcement learning (RL) is a promising research direction in edge computing. However, the intractability in the training of RL and the heterogeneity of network devices have hindered the application of RL in large-scale networks. Moreover, traditional RL algorithms lack mechanisms to share information effectively in a heterogeneous environment, which makes it more difficult for RL algorithms to converge due to the lack of global information. This article focuses on the task offloading problem in a heterogeneous environment. First, we give a formalized representation of the Lyapunov function to normalize both data and virtual energy queue operations. Subsequently, we jointly consider the computing rate and energy consumption in task offloading and then derive the optimization target leveraging Lyapunov optimization. A Deep Deterministic Policy Gradient(DDPG)-based multiple continuous variable decision model is proposed to make the optimal offloading decision in edge computing. Considering the heterogeneous environment, we improve Hetero Federated Learning (HFL) by introducing Kullback-Leibler (KL) divergence to accelerate the convergence of our DDPG based model. Experiments demonstrate that our algorithm accelerates the search for the optimal task offloading decision in heterogeneous environment.

Computation Offloading and Resource Allocation in C-RAN Supporting Wireless Charging

In this paper, we consider a Cloud-Radio Access Network (C-RAN) with multiple enhanced remote radio heads (RRHs), which support for wireless charging, computation offloading and information transmission. The employment of enhanced RRHs requires a redesign for efficient resource allocation. Our goal is to minimize the weighted sum of energy transfer time and computation time by jointly optimizing energy transmission time, energy beamforming vectors, offloading factors, information transmission time, and combining vectors, while satisfying the communication performance requirements of terminal nodes. The problem is formulated as a mixed-integer nonlinear programming, which can be solved by alternating optimization (AO) utilizing semidefinite relaxation (SDR) and nonlinear transformation. To reduce the online computation delay of AO algorithm, we propose an optimization method based on deep learning framework, which can determine optimal solution with trained neural network in real-time application. To improve the performance of learning algorithm, we use two methods to set labels for training deep neural network to obtain the optimal offloading decision: pre-optimization and self-evolution. Simulation results show that with trained neural network, the algorithms based on deep learning can achieve similar performance to AO algorithm with less computation time.

Resource optimization for UAV-assisted mobile edge computing system based on deep reinforcement learning

Computational efficiency is a direction worth considering in moving edge computing (MEC) systems. However, the computational efficiency of UAV-assisted MEC systems is rarely studied. In this paper, we maximize the computational efficiency of the MEC network by optimizing offloading decisions, UAV flight paths, and allocating users’ charging and offloading time reasonably. The method of deep reinforcement learning is used to optimize the resources of UAV-assisted MEC system in complex urban environment, and the user’s computation-intensive tasks are offloaded to the UAV-mounted MEC server, so that the overloaded tasks in the whole system can be alleviated. We study and design a framework algorithm that can quickly adapt to task offload decision making and resource allocation under changing wireless channel conditions in complex urban environments. The optimal offloading decisions from state space to action space is generated through deep reinforcement learning, and then the user’s own charging time and offloading time are rationally allocated to maximize the weighted sum computation rate. Finally, combined with the radio map to optimize the UAC trajectory to improve the overall weighted sum computation rate of the system. Simulation results show that the proposed DRL+TO framework algorithm can significantly improve the weighted sum computation rate of the whole MEC system and save time. It can be seen that the MEC system resource optimization scheme proposed in this paper is feasible and has better performance than other benchmark schemes.

Double Deep Q-Network Based Dynamic Framing Offloading in Vehicular Edge Computing

With the rapid development of Artificial Intelligence (AI) and the Internet of Vehicles (IoV), there is an increasing demand for deploying various intelligent applications on vehicles. Vehicular Edge Computing (VEC) is receiving extensive attention from both the industry and academia due to its benefits from the edge computing paradigm, which pushes computing tasks from the core of the network to the edge of the network. However, in the VEC environment considering vehicles to Road Side Units (RSUs), due to the mobility of vehicles, it is still a challenge to make dynamic and efficient offloading decisions for compute-intensive tasks, especially in the congestion situation. In order to minimize the total delay and waiting time of tasks from moving vehicles, we establish a dynamic offloading model for multiple moving vehicles whose tasks can be divided into sequential subtasks, so that the offloading decisions are more refined. Moreover, the proposed model is frame-based to avoid unnecessary waiting time, which makes offloading decisions when the subtasks of each vehicle are generated rather than offloading subtasks after gathering subtasks of vehicles for a time slot. Aiming to find the optimal offloading decision for sequential subtasks, we propose a Dynamic Framing Offloading algorithm based on Double Deep Q-Network (DFO-DDQN). Extensive experimental results demonstrate the effectiveness and superiority of the proposed DFO-DDQN when compared with other DRL-based methods and greedy-based methods.

Cooperative Task Offloading and Block Mining in Blockchain-Based Edge Computing With Multi-Agent Deep Reinforcement Learning

The convergence of mobile edge computing (MEC) and blockchain is transforming the current computing services in mobile networks, by offering task offloading solutions with security enhancement empowered by blockchain mining. Nevertheless, these important enabling technologies have been studied separately in most existing works. This article proposes a novel cooperative task offloading and block mining (TOBM) scheme for a blockchain-based MEC system where each edge device not only handles data tasks but also deals with block mining for improving the system utility. To address the latency issues caused by the blockchain operation in MEC, we develop a new Proof-of-Reputation consensus mechanism based on a lightweight block verification strategy. A multi-objective function is then formulated to maximize the system utility of the blockchain-based MEC system, by jointly optimizing offloading decision, channel selection, transmit power allocation, and computational resource allocation. We propose a novel distributed deep reinforcement learning-based approach by using a multi-agent deep deterministic policy gradient algorithm. We then develop a game-theoretic solution to model the offloading and mining competition among edge devices as a potential game, and prove the existence of a pure Nash equilibrium. Simulation results demonstrate the significant system utility improvements of our proposed scheme over baseline approaches.

Energy Consumption and QoS-Aware Co-Offloading for Vehicular Edge Computing

By deploying computing, storage, and bandwidth resources at the user side, vehicular edge computing (VEC) provides low-delay services for vehicle users. However, due to the limited resources of edge servers, how to efficiently meet the Quality-of-Service (QoS) requirements of multiple tasks and save the total energy consumption in a dynamic environment is an important issue in VEC. In this article, we first propose an energy consumption and QoS-aware co-offloading model. Unlike most previous studies, our goal is to minimize the total energy consumption while guaranteeing the QoS constraints of tasks, thus avoiding the overallocation of resources and high energy consumption caused by the one-sided pursuit of delay minimization. Then, without the requirements for domain experts, we propose Bayesian optimization-based computation offloading (BOCO) method to find the optimal offloading decision. To the best of our knowledge, this work is the first to apply Bayesian optimization to computation offloading in VEC. Furthermore, we conduct a series of experiments and comparisons with other offloading methods to analyze the effectiveness and performance of the proposed algorithm. Experimental results verify that our proposed BOCO outperforms counterparts.

WiEdge: Edge Computing for Audio Sensing Applications With Accurate Wireless Link Prediction

Audio sensing applications on embedded and mobile devices have recently enjoyed increasing popularity. Their performance can be significantly improved by edge computing which offloads computation-intensive tasks to edge servers through wireless links. The quality of wireless links is essential to offloading performance. However, existing edge computing solutions can hardly predict the link quality accurately and efficiently in a dynamic wireless environment, resulting in less optimal offloading decisions and unsatisfied user-perceived Quality of Experience (QoE). In this article, we present WiEdge, a distributed edge computing framework for audio sensing applications with accurate wireless link prediction. By combining cross-layer information extracted from recently received WiFi beacons, TCP-level statistics, and the past throughput observations, WiEdge can predict the throughput of wireless links accurately and efficiently in the near future. Based on the prediction, WiEdge makes optimal offloading decisions for QoE maximization. We formulate the offloading decision problem as a stochastic optimal control problem and propose an efficient solution based on model predictive control from the control-theoretic perspective. We implement WiEdge and evaluate its performance extensively in three representative real-world scenarios. Results show that WiEdge achieves high prediction accuracy and improves average normalized QoE by 2%, 11%, and 40% in three different scenarios, compared with state-of-the-art approaches.

MR-DRO: A Fast and Efficient Task Offloading Algorithm in Heterogeneous Edge/Cloud Computing Environments

With the rapid development of Internet of Things (IoT) and next-generation communication technologies, resource-constrained mobile devices (MDs) fail to meet the demand of resource-hungry and compute-intensive applications. To cope with this challenge, with the assistance of mobile-edge computing (MEC), offloading complex tasks from MDs to edge cloud servers (CSs) or central CSs can reduce the computational burden of devices and improve the efficiency of task processing. However, it is difficult to obtain optimal offloading decisions by conventional heuristic optimization methods, because the decision-making problem is usually NP-hard. In addition, there are shortcomings in using intelligent decision-making methods, e.g., lack of training samples and poor ability of migration under different MEC environments. To this end, we propose a novel offloading algorithm named meta reinforcement-deep reinforcement learning-based offloading, consisting of a meta-reinforcement learning (meta-RL) model, which improves the migration ability of the whole model, and a deep reinforcement learning (DRL) model, which combines multiple parallel deep neural networks (DNNs) to learn from historical task offloading scenarios. Simulation results demonstrate that our approach can effectively and efficiently generate near-optimal offloading decisions in IoT environments with edge and cloud collaboration, which further improves the computational performance and has strong portability when making offloading decisions.

Deep Reinforcement Learning Based Computation Offloading and Trajectory Planning for Multi-UAV Cooperative Target Search

Unmanned aerial vehicles (UAVs) are widely used for surveillance and monitoring to complete target search tasks. However, the short battery life and moderate computational capability hinder UAVs to process computation-intensive tasks. The emerging edge computing technologies can alleviate this problem by offloading tasks to the ground edge servers. How to evaluate the search process so as to make optimal offloading decisions and make optimal flying trajectories represent fundamental research challenges. In this paper, we propose to utilize the concept of uncertainty to evaluate the search process, which reflects the reliability of the target search results. Thereafter, we propose a deep reinforcement learning (DRL) technique to jointly make optimal computation offloading decisions and flying orientation choices for multi-UAV cooperative target search. Specifically, we first formulate an uncertainty minimization problem based on the established system model. By introducing a reward function, we prove that the uncertainty minimization problem is equivalent to a reward maximization problem, which is further analyzed by a Markov decision process (MDP). To obtain the optimal task offloading decisions and flying orientation choices, a deep Q-network (DQN) based DRL architecture with a separated Q-network is then proposed. Finally, extensive simulations validate the effectiveness of the proposed techniques, and comprehensive discussions on how different parameters affect the search performance are given.

Collaborative and Intelligent Resource Optimization for Computing and Caching in IoV With Blockchain and MEC Using A3C Approach

Recently, the rise of the Internet of Vehicles (IoV) has driven the broad development of intelligent transportation and smart cities. In order to promote the computing power of mobile vehicles and decrease the content delivery latency of suppliers, mobile edge computing (MEC) is recognized as a promising computational paradigm and used in vehicular networks. However, there are some essential issues to be considered: 1) privacy and authenticity of data transmission in IoV, and 2) reasonable resource allocation for collaborative computing and caching. In this paper, to solve above issues, blockchain technology is introduced and adopted to ensure the accuracy and reliability of data transmission and interaction. Meanwhile, we develop an intelligent framework of resource allocation about computing and caching for blockchain-enabled MEC systems in IoV. Through jointly considering and optimizing offloading decision of computation task carried by vehicle, caching decision, the number of offloaded consensus nodes, block interval and block size, the weighted consumption costs of energy consumption and computation overheads can be decreased, and the transactional throughput of the blockchain can be increased. Moreover, due to the continuity and dynamic of the available resources of mobile vehicles and computing servers, the optimization problem is modeled as a Markov decision process (MDP). Facing the large-scale and dynamic characteristics of the system, the asynchronous advantage actor-critic (A3C) approach is introduced to deal with the optimization problem. Simulation results show that our proposed scheme achieves significant advantages over other comparison schemes, such as the total reward of the proposed scheme is about 14% higher than that of the deep <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -network based scheme.