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 with a capacity, that can be chosen using the Dynamic Voltage and Frequency Scaling (DVFS) method, and with a probability of failure. On the other hand, we assume that the services run as a set of independent instances of identical Virtual Machines (VMs). 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 that must be alive at anytime, and the Cloud provider offers a list of pairs (price, compensation), the compensation having to be paid by the Cloud provider if it fails to keep alive the required number of services. On the Cloud provider side, each pair actually corresponds to a guaranteed reliability 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 (both capacity and reliability constraints). Moreover, it should remain valid during a time period (with a given reliability in presence of failures) while minimizing the energy consumption of used resources. We assume in this paper that this time period, that typically takes place between two redistributions, is fixed and known in advance. We prove deterministic approximation ratios on the consumed energy for algorithms that provide guaranteed reliability and we provide an extensive set of simulations that prove that homogeneous solutions are close to optimal.