Approximation Algorithms for Energy Minimization in Cloud Service Allocation under Reliability Constraints

We consider allocation problems that arise in the context of service allocation in Clouds. More specifically, we assume on the one part that each computing resource is associated to a capacity constraint, that can be chosen using Dynamic Voltage and Frequency Scaling (DVFS) method, and to a probability of failure. On the other hand, we assume that the service runs as a set of independent instances of identical Virtual Machines. Moreover, there exists a Service Level Agreement (SLA) between the Cloud provider and the client that can be expressed as follows: the client comes with a minimal number of service instances which must be alive at the end of the day, and the Cloud provider offers a list of pairs (price,compensation), this compensation being paid by the Cloud provider if it fails to keep alive the required number of services. On the Cloud provider side, each pair corresponds actually to a guaranteed success probability of fulfilling the constraint on the minimal number of instances. In this context, given a minimal number of instances and a probability of success, the question for the Cloud provider is to find the number of necessary resources, their clock frequency and an allocation of the instances (possibly using replication) onto machines. This solution should satisfy all types of constraints during a given time period while minimizing the energy consumption of used resources. We consider two energy consumption models based on DVFS techniques, where the clock frequency of physical resources can be changed. For each allocation problem and each energy model, we prove deterministic approximation ratios on the consumed energy for algorithms that provide guaranteed probability failures, as well as an efficient heuristic, whose energy ratio is not guaranteed

Adaptive Electricity Scheduling in Microgrids

Microgrid (MG) is a promising component for future smart grid (SG) deployment. The balance of supply and demand of electric energy is one of the most important requirements of MG management. In this paper, we present a novel framework for smart energy management based on the concept of quality-of-service in electricity (QoSE). Specifically, the resident electricity demand is classified into basic usage and quality usage. The basic usage is always guaranteed by the MG, while the quality usage is controlled based on the MG state. The microgrid control center (MGCC) aims to minimize the MG operation cost and maintain the outage probability of quality usage, i.e., QoSE, below a target value, by scheduling electricity among renewable energy resources, energy storage systems, and macrogrid. The problem is formulated as a constrained stochastic programming problem. The Lyapunov optimization technique is then applied to derive an adaptive electricity scheduling algorithm by introducing the QoSE virtual queues and energy storage virtual queues. The proposed algorithm is an online algorithm since it does not require any statistics and future knowledge of the electricity supply, demand and price processes. We derive several "hard" performance bounds for the proposed algorithm, and evaluate its performance with trace-driven simulations. The simulation results demonstrate the efficacy of the proposed electricity scheduling algorithm.Comment: 12 pages, extended technical repor

On Power and Load Coupling in Cellular Networks for Energy Optimization

We consider the problem of minimization of sum transmission energy in cellular networks where coupling occurs between cells due to mutual interference. The coupling relation is characterized by the signal-to-interference-and-noise-ratio (SINR) coupling model. Both cell load and transmission power, where cell load measures the average level of resource usage in the cell, interact via the coupling model. The coupling is implicitly characterized with load and power as the variables of interest using two equivalent equations, namely, non-linear load coupling equation (NLCE) and non-linear power coupling equation (NPCE), respectively. By analyzing the NLCE and NPCE, we prove that operating at full load is optimal in minimizing sum energy, and provide an iterative power adjustment algorithm to obtain the corresponding optimal power solution with guaranteed convergence, where in each iteration a standard bisection search is employed. To obtain the algorithmic result, we use the properties of the so-called standard interference function; the proof is non-standard because the NPCE cannot even be expressed as a closed-form expression with power as the implicit variable of interest. We present numerical results illustrating the theoretical findings for a real-life and large-scale cellular network, showing the advantage of our solution compared to the conventional solution of deploying uniform power for base stations.Comment: Accepted for publication in IEEE Transactions on Wireless Communication