Time Average Cost Research Articles

Credit-Based Distributed Real-Time Energy Storage Sharing Management

In this paper, energy storage sharing among a group of cooperative households with integrated renewable generations in a grid-connected microgrid is studied. In such a microgrid, a group of households, who are willing to cooperatively operate a shared energy storage via a central coordinator, aims to minimize their long term time-averaged costs, by jointly taking into account the operational constraints of the shared energy storage, the stochastic solar power generations and the time-varying load demands from all households, as well as the fluctuating electricity prices. This energy management problem, which comprises storage management and load control, is first formulated as a constrained stochastic programming problem. Based on the Lyapunov optimization theory, a distributed real-time sharing control algorithm is proposed to solve the constrained stochastic programming problem without requiring any statistical knowledge of the stochastic renewable energy generations and the uncertain power loads. The credit-based distributed sharing algorithm, in which each household independently solves a simple convex optimization problem without requiring any statistics of the system, is designed to quickly adapt to the system dynamics while facilitating a fair allocation of the shared energy storage with respect to individual households’ energy contributions. The performance of the proposed low-complexity distributed sharing algorithm is evaluated via theoretical analysis. Numerical simulations using a practical system setup are conducted to investigate the effectiveness of the proposed sharing control algorithm in terms of energy cost saving and fairness. The simulation results show that the proposed credit-based distributed sharing algorithm can save power consumption cost by coordinating the use of the shared battery among households in a fair manner while improving the utilization of renewable energy generation.

Multi-Timescale Decentralized Online Orchestration of Software-Defined Networks

Decentralized orchestration of the control plane is critical to the scalability and reliability of software-defined network (SDN). However, existing orchestrations of SDN are either one-off or centralized, and would be inefficient the presence of temporal and spatial variations in traffic requests. In this paper, a fully distributed orchestration is proposed to minimize the time-average cost of SDN, adapting to the variations. This is achieved by stochastically optimizing the on-demand activation of controllers, adaptive association of controllers and switches, and real-time request processing and dispatching. The proposed approach is able to operate at multiple timescales for activation and association of controllers, and request processing and dispatching, thereby alleviating potential service interruptions caused by orchestration. A new analytic framework is developed to confirm the asymptotic optimality of the proposed approach in the presence of non-negligible signaling delays between controllers. Corroborated from extensive simulations, the proposed approach can save up to 73% the time-average operational cost of SDN, as compared to the existing static orchestration.

Optimal-Cost Scheduling of Electrical Vehicle Charging Under Uncertainty

Electric vehicle (EV) charging stations are increasingly set up to meet the recharge demand of EVs, and the stations equipped with local renewable energy generation need to optimize their charging. A basic challenge for the optimization stems from inherent uncertainties such as intermittent renewable generation that is hard to predict accurately. In this paper, we consider a charging station for EVs that have deadline constraints for their requests and aim to minimize its supply cost. We use Lyapunov optimization to minimize the time-average cost under unknown renewable supply, EV mobility, and grid electricity prices. We model the unfulfilled energy requests as a novel system of queues, based on whose evolution we define the Lyapunov drift and minimize it asymptotically. We prove that our algorithm achieves at most ${O({1}/{V})}$ more than the optimal cost, where the parameter ${V}$ trades off cost against unfulfilled requests by their deadlines, and its time complexity is linear in the number of EVs. Simulation results driven by real-world traces of wind power, EV mobility, and electricity prices show that, compared with a state-of-the-art scheduling algorithm, our algorithm reduces the respective charging costs by 12.48% and 51.98% for two scenarios.

Online Energy Management and Heterogeneous Task Scheduling for Smart Communities with Residential Cogeneration and Renewable Energy

With the development of renewable energy technology and communication technology in recent years, many residents now utilize renewable energy devices in their residences with energy storage systems. We have full confidence in the promising prospects of sharing idle energy with others in a community. However, it is a great challenge to share residents’ energy with others in a community to minimize the total cost of all residents. In this paper, we study the problem of energy management and task scheduling for a community with renewable energy and residential cogeneration, such as residential combined heat and power system (resCHP) to pay the least electricity bill. We take elastic and inelastic load demands into account which are delay intolerant and delay tolerant tasks in the community. The minimum cost problem of a non-cooperative community is extracted into a random non-convex optimization problem with some physical constraints. Our objective is to minimize the time-average cost for each resident in the community, including the cost of the external grid and natural gas. The Lyapunov optimization theory and a primal-dual gradient method are adopted to tackle this problem, which needs no future data and has low computational complexity. Furthermore, we design a cooperative renewable energy sharing algorithm based on State-action-reward-state-action (Sarsa) Algorithm, in the condition that each residence in the community is able to communicate with its neighbors by a central controller. Finally, extensive simulations are presented to validate the proposed algorithms by using practical data.

Distributed Optimization of Collaborative Regions in Large-Scale Inhomogeneous Fog Computing

Fog computing enables resource-limited network devices to help each other with computationally demanding tasks, but has yet to be implemented in large scales due to sophisticated control and network inhomogeneity. This paper presents a new fully distributed online optimization to asymptotically minimize the time-average cost of fog computing, where tasks are selected to be offloaded and processed independently between different links and devices by measuring their cost effectiveness at each time slot. A key contribution is that we optimize the cost-effectiveness measures which achieve the asymptotic optimality over infinite time. Another contribution is that we optimize placeholders at the devices; which create collaborative computing regions of tasks in the vicinity of the point of capture, prevent tasks being offloaded beyond, preserve the asymptotic optimality and reduce delay. This is achieved in a distributed fashion by discovering the optimal substructure of the placeholders. Simulations show that the average size of collaborative regions is only 3.2 out of total 500 servers, and the system income increases by 43% as compared with existing techniques.

Managing rail transit peak-hour congestion with a fare-reward scheme

This paper describes a new fare-reward scheme for managing a commuter's departure time choice in a rail transit bottleneck, which aims to incentivize a shift in departure time to the shoulder periods of the peak hours to relieve queuing congestion at transit stations. A framework of the rail transit bottleneck is provided and the user equilibrium with a uniform-fare and the social optimum with service run-dependent fares are determined. A fare-reward scheme (FRS) is then introduced that rewards a commuter with one free trip during shoulder periods after a certain number of paid trips during the peak hours. For a given number of peak-hour commuters and ex-ante uniform fare, the FRS determines the free fare intervals and the reward ratio (the ratio of the free trips to the total number of trips, which is equivalent to the ratio of the number of rewarded commuters to the total number of commuters on each day during the peak hours). The new fare under the FRS is determined so that the transit operator's revenue remains unchanged before and after introducing the FRS. Our study indicates that, depending on the original fare, FRS results in an optimal reward ratio up to 50% and yields a reduction of system total time costs and average equilibrium trip costs by at least 25% and 20%, respectively.

A linear time-dependent deteriorating inventory model with linearly time-dependent demand rate and inflation

This paper considers inventory model for linearly time-dependent deteriorating items with linearly time dependent demand. Inflation is also taken into account. The model discusses allowable shortages. Mathematical model has been derived to obtain the optimal cycle time and optimal total average cost for items. The objective of this is to minimise the total average cost. Numerical examples are provided to validate the proposed model. Results are also illustrated with the help of sensitivity analysis.

Data Center Server Provision: Distributed Asynchronous Control for Coupled Renewal Systems

This paper considers a cost minimization problem for data centers with $N$ servers and randomly arriving service requests. A central router decides which server to use for each new request. Each server has three types of states (active, idle, and setup) with different costs and time durations. The servers operate asynchronously over their own states and can choose one of multiple sleep modes when idle. We develop an online distributed control algorithm so that each server makes its own decisions. The request queues are bounded and the overall time average cost is near optimal with probability 1. First the algorithm does not need probability information for the arrival rate or job sizes. Finally, an improved algorithm that uses a single queue is developed via a “virtualization” technique, which is shown to provide the same (near optimal) costs. Simulation experiments on a real data center traffic trace demonstrate the efficiency of our algorithm compared with other existing algorithms.

HELOS: Heterogeneous Load Scheduling for Electric Vehicle-Integrated Microgrids

With increasing concerns about worldwide environmental conditions and rapid development of renewable energy technologies, microgrids have been regarded as a promising solution to reduce the burden of infrastructure-based power systems. However, due to the intrinsically intermittent features of existing renewable energy, along with random residential behavior patterns, unpredictable plugged-in or unplugged actions of electric vehicles (EVs) and the time-varying price of electricity, it is challenging for microgrid operators to efficiently perform load scheduling and energy management. In this paper, we propose an online algorithm to conduct cost-aware scheduling of EV loads and energy supplies for microgrids. We formulate this problem into a stochastic optimization problem with the objective of minimizing the time-average cost of a microgrid, including the purchase cost of electricity from the main grid, the cost of charging and discharging batteries, renewable harvesting costs, and life-cycle greenhouse-gas emission costs. To solve this problem, the key idea is to exploit the dynamics of the price of electricity to conduct battery charging and discharging operations, renewable energy harvesting, and schedule EV loads properly. Our method is based on the Lyapunov optimization technique, which has low computational complexity and only requires limited prediction of price information. The theoretical analysis of our algorithm confirms that the proposed strategy can achieve optimality with explicit bound. By conducting extensive real-data driven simulations, we demonstrate that our proposed algorithm can achieve much lower cost and be more eco-friendly than other alternative solutions.

Towards Cost Minimization With Renewable Energy Sharing in Cooperative Residential Communities

The recent increasing evolution of renewable energy technologies makes it possible for common residents to afford the cost of installing renewable energy devices (REDs) and energy storage systems (ESSs) in their own houses. With the prevalence of REDs and ESSs, it is a beneficial and also promising idea for residents in a community to share extra energy with others, especially, when they have different electricity usage patterns. However, considering the unpredictable energy usage patterns, radically intermittent characteristics of renewable energy generation, and dynamic electricity price, it would be difficult for residents in a community to intelligently share their energy with others and thus minimize the overall cost of the whole community. In this paper, we design an online algorithm, which can tackle cost-aware energy sharing among residents in a cooperative community. We formulate the problem as a stochastic constrained problem and the objective is to minimize the time-average cost in the whole community, which includes the cost of purchasing electricity from the main grid, and the cost of charging and discharging ESSs. By exploiting the dynamics of electricity price, we can determine the charging and discharging behaviors of ESSs. We explore our method based on the Lyapunov optimization theory, which does not need any future statistics and possesses low computational complexity. Through theoretical analysis of our algorithm, we can conclude that our strategy can approximate the optimality with provable bounds. Meanwhile, we design a revenue division algorithm based on the Nash bargaining theory to fairly share the revenue among residents. We also conduct extensive trace-driven simulations and results show that our algorithm can obtain nearly 12% of cost reduction for the community when compared with noncooperative algorithms, and ensure the fairness among residents in the meanwhile.

Distributed Control for Charging Multiple Electric Vehicles with Overload Limitation

Severe pollution induced by traditional fossil fuels arouses great attention on the usage of plug-in electric vehicles (PEVs) and renewable energy. However, large-scale penetration of PEVs combined with other kinds of appliances tends to cause excessive or even disastrous burden on the power grid, especially during peak hours. This paper focuses on the scheduling of PEVs charging process among different charging stations and each station can be supplied by both renewable energy generators and a distribution network. The distribution network also powers some uncontrollable loads. In order to minimize the on-grid energy cost with local renewable energy and non-ideal storage while avoiding the overload risk of the distribution network, an online algorithm consisting of scheduling the charging of PEVs and energy management of charging stations is developed based on Lyapunov optimization and Lagrange dual decomposition techniques. The algorithm can satisfy the random charging requests from PEVs with provable performance. Simulation results with real data demonstrate that the proposed algorithm can decrease the time-average cost of stations while avoiding overload in the distribution network in the presence of random uncontrollable loads.

Dynamic Request Redirection and Resource Provisioning for Cloud-Based Video Services under Heterogeneous Environment

Cloud computing provides a new opportunity for Video Service Providers (VSP) to running compute-intensive video applications in a cost effective manner. Under this paradigm, a VSP may rent virtual machines (VMs) from multiple geo-distributed datacenters that are close to video requestors to run their services. As user demands are difficult to predict and the prices of the VMs vary in different time and region, optimizing the number of VMs of each type rented from datacenters located in different regions in a given time frame becomes essential to achieve cost effectiveness for VSPs. Meanwhile, it is equally important to guarantee users’ Quality of Experience (QoE) with rented VMs. In this paper, we give a systematic method called Dy namical Re quest Redire c t i on and R e source Pro v isioning ( DYRECEIVE ) to address this problem. We formulate the problem as a stochastic optimization problem and design a Lyapunov optimization framework based online algorithm to solve it. Our method is able to minimize the long-term time average cost of renting cloud resources while maintaining the user QoE. Theoretical analysis shows that our online algorithm can produce a solution within an upper bound to the optimal solution achieved through offline computing. Extensive experiments shows that our method is adaptive to request pattern changes along time and outperforms existing algorithms.

Resource Allocation With Video Traffic Prediction in Cloud-Based Space Systems

This paper considers the resource allocation problems for video transmission in space-based information networks. The queueing system analyzed in this study is constituted by multiple users and a single server. The server is operated as a cloud that can sense the traffic arrivals to each user's queue and then allocates the transmission resource and service rate for users. The objectives are to make configurations over time to minimize the time average cost of the system, and to minimize the waiting time of packets after they enter the queue. Meanwhile, the constraints on the queue stability of the system must be satisfied. In this paper, we introduce a predictive backpressure algorithm, which considers the future arrivals with a certain prediction window size into the consideration of resource allocation to make decisions on which packets to be served first. In addition, this paper designs a multiresolution wavelet decomposition-based backpropagation network for the prediction of video traffic, which exhibits the long-range dependence property. Simulation results indicate that the delay of the queueing system can be reduced through this prediction-based resource allocation, and the prediction accuracy for the video traffic is improved according to the proposed prediction system.

Optimal steady-state and transient trajectories of multi-queue switching servers with a fixed service order of queues

The optimal scheduling problem of a system with two fluid queues attended by a switching server is addressed from two angles, the optimal steady-state and the optimal transient problem. The considered system includes features, such as setup times, setup costs, backlog and constraints on queue contents, cycle times and service times. First, the steady-state problem is formulated as a quadratic problem (QP), given a fixed cycle time. Evaluation of the QP problem over a range of cycle times results in the optimal steady-state trajectory, minimizing the total cycle costs or time average costs. Second, given initial conditions, we derive the optimal transient trajectory that leads to the optimal steady-state trajectory in a finite amount of time at minimal costs. For systems with backlog, we introduce additional costs on the number of cycles required to reach the steady-state trajectory in order to simplify the transient trajectory. The transient switching behavior and optimal initial modes are also addressed. Furthermore, we show by means of an example that the method can be extended to multi-queue switching servers.

Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: a direct treatment of time-average cost

Supply contracts are designed to minimize inventory costs or to hedge against undesirable events (e.g., shortages) in the face of demand or supply uncertainty. In particular, replenishment terms stipulated by supply contracts need to be optimized with respect to overall costs, profits, service levels, etc. In this paper, we shall be primarily interested in minimizing an inventory cost function with respect to a constant replenishment rate. Consider a single-product inventory system under continuous review with constant replenishment and compound Poisson demands subject to lost-sales. The system incurs inventory carrying costs and lost-sales penalties, where the carrying cost is a linear function of on-hand inventory and a lost-sales penalty is incurred per lost sale occurrence as a function of lost-sale size. We first derive an integro-differential equation for the expected cumulative cost until and including the first lost-sale occurrence. From this equation, we obtain a closed form expression for the time-average inventory cost, and provide an algorithm for a numerical computation of the optimal replenishment rate that minimizes the aforementioned time-average cost function. In particular, we consider two special cases of lost-sales penalty functions: constant penalty and loss-proportional penalty. We further consider special demand size distributions, such as constant, uniform and Gamma, and take advantage of their functional form to further simplify the optimization algorithm. In particular, for the special case of exponential demand sizes, we exhibit a closed form expression for the optimal replenishment rate and its corresponding cost. Finally, a numerical study is carried out to illustrate the results.

Towards big data processing in clouds: An online cost-minimization approach

Due to its elastic and on-demand nature of resource provisioning, cloud computing provides a cost effective and powerful technology for the processing of big data. Under this paradigm, Data Service Provider (DSP) may rent geographically distributed datacenters to process their large amount of data. As the data are dynamically generated and the resource pricing varies over time, moving the data from differently geographic locations to different datacenters while provisioning adequate computation resource to process them is an essential task to achieve cost effectiveness for DSP. In this paper, a joint online approach is proposed to address this task. We formulate the problem into a joint stochastic optimization problem, which is then decoupled into two independent subproblems via the Lyapunov framework. Our method is able to minimize the long-term time average cost including computing cost, storage cost, bandwidth cost and latency cost. Theoretical analysis shows that our online algorithm can produce a solution within an upper bound to the optimal solution achieved through offline computing and guarantee that the data processing can be completed with preset delays.

Low‐complexity variable forgetting factor mechanisms for adaptive linearly constrained minimum variance beamforming algorithms

In this work, the authors propose two low-complexity variable forgetting factor (VFF) mechanisms for recursive least squares-based adaptive beamforming algorithms. The proposed algorithms are designed according to the linearly constrained minimum variance (LCMV) criterion and operate in the generalised sidelobe canceller structure. To obtain a better performance of convergence and tracking, the proposed VFF mechanisms adjust the forgetting factor by employing updated components related to the time-averaged LCMV cost function. They carry out the analyses of the proposed algorithms in terms of the computational complexity and the convergence properties and derive an analytical expression of the steady-state mean-square-error. Simulation results in non-stationary environments are presented, showing that the adaptive beamforming algorithms with the proposed VFF mechanisms outperform the existing methods at a significantly reduced complexity.

Decentralised dynamic games for large population stochastic multi‐agent systems

In this study, the authors consider the large population dynamic games where each agent evolves according to a dynamic equation containing the input average of all agents. The long time average (LTA) cost that each agent aims to minimise is coupled with other agents’ states via a population state average (PSA), which is also known as the mean field term. In order to design decentralised controls, the Nash certainty equivalence is introduced. It is shown that the resulting decentralised mean field control laws lead the system to mean-consensus asymptotically as time goes to infinity. The stability property of the mass behaviour and the almost sure asymptotic Nash equilibrium property of the optimal controls are also guaranteed, and the case with non-linear system dynamics is also discussed. In addition, the influence of inaccurate mean field information on individual agent is analysed. Finally, they investigate the socially cooperative formulation where the objective is to minimise the social cost as the sum of all individual LTA costs containing the PSA. In this case, they show that the decentralised mean field social controls are the same as the mean field Nash controls for infinite population systems.

Optimized Electric Vehicle Charging With Intermittent Renewable Energy Sources

Renewable energy and Electric Vehicles (EVs) are promising solutions for energy cost savings and emission reduction. However, integration of renewable energy sources into the electric grid could be a difficult task, because of the generation source intermittency and inconsistency with energy usage. In this paper, we present results of our study on the problem of allocating energy from renewable sources to EVs in a cost efficient manner. We have assumed that the renewable energy supply is time variant and in many ways unpredictable. EVs' charging requests should be satisfied within a specified time frame, which may incur a cost of drawing additional energy (possibly non-renewable energy) from the power grid if the renewable energy supply is not sufficient to meet the deadlines and may also reduce energy efficiency. We have formulated a stochastic optimization problem based on queuing model to minimize the time average cost of using non-renewable energy sources. The proposed approach fully considers the individual charging rate limit and deadline of each EV. The Lyapunov optimization technique is used to solve the problem. The developed dynamic control algorithm does not require knowledge of the statistical distribution of the time-varying renewable energy generation, EV charging demand, or extra energy pricing. Simulation results using different wind power generation profiles were performed and analyzed in the study. The results show that our EV charging scheduling method based on Lyapunov optimization can reduce both charging cost and mean delay time of fulfilling EV charging requests.

Uniform Assymptotics in the Average Continuous Control of Piecewise Deterministic Markov Processes : Vanishing Approach

We prove a uniform Abelian result for controlled systems with piecewise deterministic Markov dynamics : the existence of a uniform limit for value functions with discounted costs as the discount factor decreases to zero implies the existence of a (uniform) value function with long time average cost. The result is independent of dissipativity properties of the control system.