Lyapunov Stochastic Optimization Research Articles

Dynamic Service Chaining for Ultra-Reliable Services in Softwarized Networks

Network softwarization is a paradigm shift for the next generation of network. Network Function Virtualization (NFV) softwarizes network functions as virtual network function (VNF) instances on top of a network infrastructure. Along with the merits of flexibility, programmability and reduced function provisioning cost, softwarization of network functions introduces new challenges of service’s reliability due to possible hardware failures, software bugs and hacker attacks. Currently reliable service provisioning schemes based on first-order statistics fails in accounting for the ultra-reliable needs of mission-critical services. In this paper, we propose a dynamic service chaining (DSC) framework to provision ultra-reliable services where the reliability is characterized by the probability distribution using extreme value theory. Our design objective is to minimize the number of backup VNF modules subject to reliability and resource constraints. Due to the dynamic nature of network, primary and backup VNFs are re-mapped to higher reliable physical machines in order to provide ultra-reliable services. Using Lyapunov stochastic optimization, primary VNF mapping and backup VNF selection are performed in the large and small timescales respectively. Numerical results show that the proposed DSC framework can guarantee ultra-reliable network services efficiently.

Satisfying strict deadlines for cellular Internet of Things through hybrid multiple access

AbstractLatency‐constrained aspects of cellular Internet of Things (IoT) applications rely on Ultra‐Reliable and Low Latency Communications (URLLC), which highlight research on satisfying strict deadlines. In this study, we address the problem of latency‐constrained communications with strict deadlines under average power constraint using Hybrid Multiple Access (MA), which consists of both Orthogonal MA (OMA) and power domain Non‐Orthogonal MA (NOMA) as transmission scheme options. We aim to maximize the timely throughput, which represents the average number of successfully transmitted packets before deadline expiration, where expired packets are dropped from the buffer. We use Lyapunov stochastic optimization methods to develop a dynamic power assignment algorithm for minimizing the packet drop rate while satisfying time average power constraints. Moreover, we propose a flexible packet dropping mechanism called Early Packet Dropping (EPD) to detect likely to become expired packets and drop them immediately. Numerical results show that Hybrid MA improves the timely throughput compared to conventional OMA by up to and on average by more than . With EPD, these timely throughput gains improve to and , respectively.

Lyapunov-Based Optimization of Edge Resources for Energy-Efficient Adaptive Federated Learning

The aim of this paper is to propose a novel dynamic resource allocation strategy for energy-efficient adaptive federated learning at the wireless network edge, with latency and learning performance guarantees. We consider a set of devices collecting local data and uploading processed information to an edge server, which runs stochastic gradient-based algorithms to perform continuous learning and adaptation. Hinging on Lyapunov stochastic optimization tools, we dynamically optimize radio parameters (e.g., set of transmitting devices, transmit powers, bits, and rates) and computation resources (e.g., CPU cycles at devices and at server) in order to strike the best trade-off between power, latency, and performance of the federated learning task. The framework admits both a model-based implementation, where the learning performance metrics are available in closed-form, and a data-driven approach, which works with online estimates of the learning performance of interest. The method is then customized to the case of federated least mean squares (LMS) estimation, and federated training of deep convolutional neural networks. Numerical results illustrate the effectiveness of our strategy to perform energy-efficient, low-latency, adaptive federated learning at the wireless network edge.

Adaptive resource optimization for edge inference with goal-oriented communications

Goal-oriented communications represent an emerging paradigm for efficient and reliable learning at the wireless edge, where only the information relevant for the specific learning task is transmitted to perform inference and/or training. The aim of this paper is to introduce a novel system design and algorithmic framework to enable goal-oriented communications. Specifically, inspired by the information bottleneck principle and targeting an image classification task, we dynamically change the size of the data to be transmitted by exploiting banks of convolutional encoders at the device in order to extract meaningful and parsimonious data features in a totally adaptive and goal-oriented fashion. Exploiting knowledge of the system conditions, such as the channel state and the computation load, such features are dynamically transmitted to an edge server that takes the final decision, based on a proper convolutional classifier. Hinging on Lyapunov stochastic optimization, we devise a novel algorithmic framework that dynamically and jointly optimizes communication, computation, and the convolutional encoder classifier, in order to strike a desired trade-off between energy, latency, and accuracy of the edge learning task. Several simulation results illustrate the effectiveness of the proposed strategy for edge learning with goal-oriented communications.

Offloading Cost Optimization in Multiserver Mobile Edge Computing Systems with Energy Harvesting Devices

In mobile edge computing (MEC) systems with energy harvesting, edge devices are powered by unstable energy harvested from the environment. To prolong the lifetime of edge devices, some computing tasks should be offloaded to MEC servers. However, computing services offered by MEC servers may be very costly. In this work, we aim to minimize total costs caused by computing services and dropping tasks while avoiding the devices running out energy. With the consideration of the unpredictability of the harvestable energy, we adopt the stochastic Lyapunov optimization framework to jointly manage energy and make task execution decisions (i.e., local executing, offloading, or dropping tasks) and develop an online algorithm which could help asymptotically obtain the optimal results for the whole system. The algorithm does not require any knowledge of the harvestable energy and the statistics of task arriving processes and can be easily implemented in a distributed manner. Numerical results corroborate that the proposed algorithm can try its best to push battery energy of edge devices to a preset parameter and effectively reduce the service costs and task drops.

Discontinuous Computation Offloading for Energy-Efficient Mobile Edge Computing

We propose a novel strategy for energy-efficient dynamic computation offloading, in the context of edge-computing-aided beyond 5G networks. The goal is to minimize the energy consumption of the overall system, comprising multiple User Equipment (UE), an access point (AP), and an edge server (ES), under constraints on the end-to-end service delay and the packet error rate performance over the wireless interface. To reduce the energy consumption, we exploit low-power sleep operation modes for the users, the AP and the ES, shifting the edge computing paradigm from an always on to an always available architecture, capable of guaranteeing an on-demand target service quality with the minimum energy consumption. To this aim, we propose an online algorithm for dynamic and optimal orchestration of radio and computational resources called Discontinuous Computation Offloading (DisCO). In such a framework, end-to-end delay constraints translate into constraints on overall queueing delays, including both the communication and the computation phases of the offloading service. DisCO hinges on Lyapunov stochastic optimization, does not require any prior knowledge on the statistics of the offloading traffic or the radio channels, and satisfies the long-term performance constraints imposed by the users. Several numerical results illustrate the advantages of the proposed method.

A Non-Cooperative Game-Based Distributed Beam Scheduling Framework for 5G Millimeter-Wave Cellular Networks

This paper studies the problem of distributed beam scheduling for 5G millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging to different operators share the same spectrum without centralized coordination among them. Our goal is to design efficient distributed scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to the average and instantaneous power consumption constraints of the BSs. We propose a Media Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lyapunov stochastic optimization framework and non-cooperative games. In particular, we first decompose the original utility maximization problem into two sub-optimization problems for each time frame, which are a convex optimization problem and a non-convex optimization problem, respectively. By formulating the distributed scheduling problem as a non-cooperative game where each BS is a player attempting to optimize its own utility, we provide a distributed solution to the non-convex sub-optimization problem via finding the Nash Equilibrium (NE) of the game whose weights are determined optimally by the Lyapunov optimization framework. Finally, we conduct simulation under various network settings to show the effectiveness of the proposed game-based beam scheduling algorithm in comparison to that of several reference schemes.

Real-Time Energy Management for Microgrid With EV Station and CHP Generation

A microgrid scenario that consists of electric vehicle (EV) station, combined heat and power (CHP) co-generation, main power grid, and external natural gas station, as well as thermal energy storage water tank is considered in this paper. By jointly considering the uncertainty of real-time electricity price, electricity and heat demands and EVs' behaviours, the EVs' batteries are used as energy storage adjusters to reduce the time-averaged operation cost, which includes energy acquiring cost from main power grid, the natural gas cost for CHP generation and heat only generation. We propose a real-time energy management algorithm for EV based microgrid by adopting Lyapunov stochastic optimization technique which optimizes the microgrid average cost without knowing future price, demands and other system information. Furthermore, our approach can accommodate a wide spectrum of characteristics of EVs, including the independent charging/discharging action, dynamic charging energy limits, and lifetime-guaranteed battery. Lastly, extensive simulations are provided to demonstrate that our proposed algorithm can outperform the other three alternatives.

Intelligent task offloading and collaborative computation over D2D communication

In this paper, the problem of computation offloading in the edge server is studied in a mobile edge computation (MEC)-enabled cell networks that consists of a base station (BS) integrating edge servers, several terminal devices and collaborators. In the considered networks, we develop an intelligent task offloading and collaborative computation scheme to achieve the optimal computation offloading. First, a distance-based collaborator screening method is proposed to get collaborators within the distance threshold and with high power. Second, based on the Lyapunov stochastic optimization theory, the system stability problem is transformed into a queue stability issue, and the optimal computation offloading is obtained by solving these three sub-problems: task allocation control, task execution control and queue update, respectively. Moreover, rigorous experimental simulation shows that our proposed computation offloading algorithm can achieve the joint optimization among the system efficiency, energy consumption and time delay compared to the mobility-aware and migration-enabled approach, Full BS and Full local.

Wireless Edge Machine Learning: Resource Allocation and Trade-Offs

The aim of this paper is to propose a resource allocation strategy for dynamic training and inference of machine learning tasks at the edge of the wireless network, with the goal of exploring the trade-off between energy, delay and learning accuracy. The scenario of interest is composed of a set of devices sending a continuous flow of data to an edge server that extracts relevant information running online learning algorithms, within the emerging framework known as Edge Machine Learning (EML). Taking into account the limitations of the edge servers, with respect to a cloud, and the scarcity of resources of mobile devices, we focus on the efficient allocation of radio (e.g., data rate, quantization) and computation (e.g., CPU scheduling) resources, to strike the best trade-off between energy consumption and quality of the EML service, including service end-to-end (E2E) delay and accuracy of the learning task. To this aim, we propose two different dynamic strategies: (i) The first method aims to minimize the system energy consumption, under constraints on E2E service delay and accuracy; (ii) the second method aims to optimize the learning accuracy, while guaranteeing an E2E delay and a bounded average energy consumption. Then, we present a dynamic resource allocation framework for EML based on stochastic Lyapunov optimization. Our low-complexity algorithms do not require any prior knowledge on the statistics of wireless channels, data arrivals, and data probability distributions. Furthermore, our strategies can incorporate prior knowledge regarding the model underlying the observed data, or can work in a totally data-driven fashion. Several numerical results on synthetic and real data assess the performance of the proposed approach.

Enabling Optimal Control Under Demand Elasticity for Electric Vehicle Charging Systems

Recent years have witnessed the proliferation of electric vehicles (EVs) that enable environment-friendly commuting and traveling. However, the increasing number of EVs inevitably create massive charging demands that are challenging to satisfy. Oftentimes in practice, EVs have to wait in queues for a long time outside charging stations before chargers become available. To address this challenge, we fully capture the elasticity of EVs' charging demands in response to the charging prices, and propose a dynamic charging pricing mechanism that jointly controls the lengths of the demand queues at multiple charging stations and maximizes the charging platform's long-term profit for offering charging services. Clearly, such an approach is more feasible than the financially and temporally expensive way of constructing extra charging facilities. Technically, we augment the Lyapunov stochastic optimization technique to decompose the challenging long-term decision-making problem into a series of single-time-slot optimization programs which require zero knowledge of future system parameters. However, due to the correlation of charging demands among different stations, the aforementioned optimization program in each time slot is non-convex. We handle the non-convexity by jointly constructing independent sets of charging stations and adapting the block coordinate descent method to iteratively obtain approximately optimal charging prices.

Stochastic Cooperative Optimization for Multicast Scheduling in Heterogeneous and Green 5G Networks

Multicast is able to satisfy multiple identical requests by a multicast stream, which can effectively reduce network energy consumption and service delay. Combined with edge caching, multicast can fully exploit its advantages and is becoming one of the most promising technologies to realize tremendous data transmission in 5G networks. As an important theme of multicast technology, multicast scheduling has attracted extensive attention. However, most of them only consider the scheduling in a single base station and ignore the different delay requirement of services. In this paper, we consider cooperative multicast scheduling between multiple base stations in cache-enabled 5G networks, aiming to satisfy user demands while minimizing energy consumption. We propose a novel pending request queue model related to delay requirement, based on which we formulate the cooperative multicast scheduling problem. Then we transform the problem into Lyapunov stochastic optimization and propose an on-line centralized algorithm to obtain the optimal strategy. Considering some scenarios where global information is unavailable, we further propose a distributed algorithm which has close performance but much lower complexity. Extensive simulations have been conducted to verify that our algorithms have better performance than several state-of-art algorithms, including both energy consumption and service delay.

DREAM: Online Control Mechanisms for Data Aggregation Error Minimization in Privacy-Preserving Crowdsensing

Nowadays, by integrating the smart devices carried by users with existing communication infrastructures to provide large-scale, fine-grained and complex sensing services, crowdsensing as a novel sensing paradigm has significantly enriched the applications of smart city and promoted the development of Internet of Things (IoT). However, privacy has become skyrocketing concern for crowdsensing and gravely affected the deployment of crowdsensing. In this paper, we present a framework to make the tradeoff between minimizing data aggregation error and guaranteeing system stability by jointly considering the privacy of participants, the randomness of sensing task arrival and the cost of platform. We propose an online control mechanism by exploiting Lyapunov stochastic optimization technique. Additionally, considering that, in reality, it always take different time for different tasks to make sensing decisions, we extend standard Lyapunov stochastic optimization technique to make separate decisions for different types of sensing tasks in consecutive time. Through rigorous theoretical analysis, we prove that our time-average data aggregation error is approximately optimal while still maintaining system stability. By carrying out extensive simulations, we demonstrate the superiority of our proposed mechanisms.

Taming the Tail of Maximal Information Age in Wireless Industrial Networks

In wireless industrial networks, the information of time-sensitive control systems needs to be transmitted in an ultra-reliable and low-latency manner. This letter studies the resource allocation problem in finite blocklength transmission, in which the information freshness is measured as the age of information (AoI) whose maximal AoI is characterized using extreme value theory (EVT). The considered system design is to minimize the sensors' transmit power and transmission blocklength subject to constraints on the maximal AoI's tail behavior. The studied problem is solved using Lyapunov stochastic optimization, and a dynamic reliability and age-aware policy for resource allocation and status updates is proposed. Simulation results validate the effectiveness of using EVT to characterize the maximal AoI. It is shown that sensors need to send larger-size data with longer transmission blocklength at lower transmit power. Moreover, the maximal AoI's tail decays faster at the expense of higher average information age.

Energy-Efficient Service Provisioning in Inter-Data Center Elastic Optical Networks

We investigate the problem of energy-efficient transponder configuration constrained to quality of service and physical requirements in orthogonal frequency division multiplexing-based software-defined inter-data center elastic optical networks. We consider two types of services which are called delay-sensitive and delay-tolerant. A deterministic and a stochastic mixed-integer nonlinear program with a target of minimizing the total transponder power consumption are formulated which their solutions provide a long-term and a short-term configuration for delay-sensitive service and delay-tolerant service transponders, respectively. We use geometric and stochastic Lyapunov optimization techniques to convert the complex mixed-integer nonlinear formulations to their equivalent convex forms that can be solved more than 1 order of magnitude faster. We demonstrate that total power consumption of delay-tolerant service transponders is reduced by more than 29% when average traffic load is 30% and transponder parameters are stochastically reconfigured rather than fixed configuration. Furthermore, we show that there is an adjustable tradeoff between transmission delay and transponder power consumption in the proposed scheme. We also incorporate transmit optical power as a tunable parameter in the transponder configuration process and use simulation results to demonstrate its impact on power consumption reduction.

Ultra-Reliable and Low-Latency Vehicular Transmission: An Extreme Value Theory Approach

Considering a Manhattan mobility model in vehicle-to-vehicle networks, this work studies a power minimization problem subject to second-order statistical constraints on latency and reliability, captured by a network-wide maximal data queue length. We invoke results in extreme value theory to characterize statistics of extreme events in terms of the maximal queue length. Subsequently, leveraging Lyapunov stochastic optimization to deal with network dynamics, we propose two queue-aware power allocation solutions. In contrast with the baseline, our approaches achieve lower mean and variance of the maximal queue length.

Fronthaul-Aware Software-Defined Wireless Networks: Resource Allocation and User Scheduling

Software-defined networking (SDN) provides an agile and programmable way to optimize radio access networks via a control-data plane separation. Nevertheless, reaping the benefits of wireless SDN hinges on making optimal use of the limited wireless fronthaul capacity. In this work, the problem of fronthaul-aware resource allocation and user scheduling is studied. To this end, a two-timescale fronthaul-aware SDN control mechanism is proposed in which the controller maximizes the time-averaged network throughput by enforcing a coarse correlated equilibrium in the long timescale. Subsequently, leveraging the controller's recommendations, each base station schedules its users using Lyapunov stochastic optimization in the short timescale, i.e., at each time slot. Simulation results show that significant network throughput enhancements and up to 40% latency reduction are achieved with the aid of the SDN controller. Moreover, the gains are more pronounced for denser network deployments.

Joint Admission Control and Resource Allocation in Edge Computing for Internet of Things

The IoT is a novel platform for making objects more intelligent by connecting to the Internet. However, mass connections, big data processing, and huge power consumption restrict the development of IoT. In order to address these challenges, this article proposes a novel ECIoT architecture. To further enhance the system performance, radio resource and computational resource management in ECIoT are also investigated. According to the characteristics of the ECIoT, we mainly focus on admission control, computational resource allocation, and power control. To improve the performance of ECIoT, cross-layer dynamic stochastic network optimization is studied to maximize the system utility, based on the Lyapunov stochastic optimization approach. Evaluation results are provided which demonstrate that the proposed resource allocation scheme can improve throughput, reduce end-to-end delay, and also achieve an average throughput and delay trade-off. Finally, the future research topics of resource management in ECIoT are discussed.

Q*: Energy and delay-efficient dynamic queue management in TCP/IP virtualized data centers

The emerging utilization of Software-as-a-Service (SaaS) Fog computing centers as an Internet virtual computing commodity is raising concerns over the energy consumptions of networked data centers for the support of delay-sensitive applications. In addition to the energy consumed by the servers, the energy wasted by the network devices that support TCP/IP reliable inter-Virtual Machines (VMs) connections is becoming a significant challenge. In this paper, we propose and develop a framework for the joint characterization and optimization of TCP/IP SaaS Fog data centers that utilize a bank of queues for increasing the fraction of the admitted workload. Our goal is two-fold: (i) we maximize the average workload admitted by the data center; and, (ii) we minimize the resulting networking-plus-computing average energy consumption. For this purpose, we exploit the Lyapunov stochastic optimization approach, in order to design and analyze an optimal (yet practical) online joint resource management framework, which dynamically performs: (i) admission control; (ii) dispatching of the admitted workload; (iii) flow control of the inter-VM TCP/IP connections; (iv) queue control; (v) up/down scaling of the processing frequencies of the instantiated VMs; and, (vi) adaptive joint consolidation of both physical servers and TCP/IP connections. The salient features of the resulting scheduler (e.g., the Q* scheduler) are that: (i) it admits distributed and scalable implementation; (ii) it provides deterministic bounds on the instantaneous queue backlogs; (iii) it avoids queue overflow phenomena; and, (iv) it effectively tracks the (possibly unpredictable) time-fluctuations of the input workload, in order to perform joint resource consolidation without requiring any a prioriinformation and/or forecast of the input workload. Actual energy and delay performances of the proposed scheduler are numerically evaluated and compared against the corresponding ones of some competing and state-of-the-art schedulers, under: (i) Fast - Giga - 10Giga Ethernet switching technologies; (ii) various settings of the reconfiguration-consolidation costs; and, (iii) synthetic, as well as real-world workloads. The experimental results support the conclusion that the proposed scheduler can achieve over 30% energy savings.

MATCH for the Prosumer Smart Grid The Algorithmics of Real-Time Power Balance

Prosumers or proactive consumers are steadily on the rise in emerging Smart Grid systems. These consumers, apart from their traditonal role of using energy from the grid, also are actively involved in individually transferring stored energy from renewable sources such as wind and solar, to the grid. The large-scale integration of renewable generation in the emerging grid will re-define ways of meeting consumer energy demands, and more importantly drive greener and cost-effective utility operations. In this paper, we investigate the problem of matching consumer demand with the grid supply in real-time, and in the presence of renewables. We formulate this problem as a stochastic optimization problem and propose MATCH, a fast distributed real-time algorithm that accounts for the uncertainties in (i) renewable generation, (ii) the latter's transmission through the grid network, (iii) loads, and (iv) energy prices, and balances power in the Smart Grid at all times. MATCH is based on the Lyapunov stochastic optimization framework and scales to localities with a large number of networked renewable generation sources. We validate the efficacy of MATCH through experiments conducted using data modelled on proprietary data obtained from two public utilities. As part of the main results of this work, we show that (a) MATCH outputs unique approximate-optimal grid parameter configuration vectors in real-time that ensure perennial supply-demand balance in the grid at a minimum cost, and (b) mesh transmission network topologies lead to better MATCH outputs when compared to other existing transmission network topologies.