Given an application which is 80% parallelizable and a single-core system is suf

Question

Given an application which is 80% parallelizable and a single-core system is sufficient for the application, how much dynamic power savings will be from a quad-core system whose operating voltage can not drop below 40% of the initial voltage (called the voltage floor),when compared with its single-core counterpart? (Note that the voltage(V) decreases linearly with the frequency(f) until it reaches the voltage floor,and any further reduction in frequency does not bring down the voltage below its florr. Dynamic power is proportional to V^2 *f. All cores are under one single voltage domain but they can be turned off individually at will by power gating. Show your work.

Explanation / Answer

discusses a simplified problem of determining the time to migrate a VM from an oversubscribed host to minimize the cost consisting of the cost of energy consumption and the cost incurred by the Cloud provider due to a violation of the QoS requirements defined in the SLAs. Next, the cost of an optimal offline algorithm for this problem, as well as the competitive ratio of an optimal online deterministic algorithm are determined and proved. Then, a more complex problem of dynamic consolidation of VMs considering multiple hosts and multiple VMs is investigated. The competitive ratio of an optimal online deterministic algorithm for this problem is proved and presented., most of the related approaches to energy-efficient resource management in virtualized data centers constitute “systems” work focusing more on the implementation aspect rather than theoretical analysis. However, theoretical analysis of algorithms is important since it provides provable guarantees on the algorithm performance, as well as insights into the future algorithm design. Recent analytic work on reducing the cost of energy consumption in data centers includes online algorithms for load balancing across geographically distributed data centers [76, 78]. In contrast, the focus of this work is on energy and performance efficient VM management within a data center. Plaxton et al. [98] analyzed online algorithms for resource allocation for a sequence of requests arriving to a data center. Irani et al. [62] proposed and proved the competitiveness of an online algorithm for dynamic power management of a server with multiple power states. Lin et al. [77] proposed a 3-competitive algorithm for request distribution over the servers of a data center to provide powerproportionality, i.e., power consumption by the resources in proportion to the load. This work differs from the prior analytic literature in the way the system and workload are modeled. Rather than modeling the workload as a sequence of arriving requests, this work is based on an IaaS-like model, where a set of independent long-running applications of different types share the computing resources. Each application generates time-varying CPU utilization and is deployed on a VM, which can be migrated across physical servers transparently for the application. This model is a representation of an IaaS Cloud, where multiple independent users instantiate VMs, and the provider is not aware of the types of applications deployed on the VMs. No results have been found to be published on competitive analysis of online algorithms for the problem of energy and performance efficient dynamic consolidation of VMs in such environments. In the definition and analysis of the problems in this chapter, it is assumed that future events cannot be predicted based on the knowledge of past events. Although this assumption may not be satisfied for all types of real-world workloads, it enables the theoretical analysis of algorithms that do not rely on predictions of the future workload. Moreover, the higher the variability of the workloads, the closer they are to satisfying the unpredictability assumption. Since Cloud applications usually experience highly dynamic workloads, the unpredictability assumption is justifiableIn a real world setting, a control algorithm does not have the complete knowledge of future events, and therefore, has to deal with an online problem. According to Borodin and El-Yaniv [25], optimization problems in which the input is received in an online manner and in which the output must be produced online are called online problems. Algorithms that are designed for online problems are called online algorithms. One of the ways to characterize the performance and efficiency of online algorithms is to apply competitive analysis. In the framework of competitive analysis, the quality of online algorithms is measured relatively to the best possible performance of algorithms that have complete knowledge of the future. An online algorithm ALG is c-competitive if there is a constant a, such that for all finite sequences I: ALG(I) c · OPT(I) + a, where ALG(I) is the cost incurred by ALG for the input I; OPT(I) is the cost of an optimal offline algorithm for the input sequence I; and a is a constant. This means that for all possible inputs, ALG incurs a cost within the constant factor c of the optimal offline cost plus a constant a. c can be a function of the problem parameters, but it must be independent of the input I. If ALG is c-competitive, it is said that ALG attains a competitive ratio c.

This section applies competitive analysis [25] to analyze a sub-problem of the problem of energy and performance efficient dynamic consolidation of VMs. There is a single physical server, or host, and M VMs allocated to that host. In this problem the time is discrete and can be split into N time frames, where each time frame is 1 second. The resource provider pays the cost of energy consumed by the physical server. It is calculated as Cptp, where Cp is the cost of power (i.e. energy per unit of time), and tp is a time period. The resource capacity of the host and resource usage by VMs are characterized by a single parameter, the CPU performance. The VMs experience dynamic workloads, which means that the CPU usage by a VM arbitrarily varies over time. The host is oversubscribed, i.e. if all the VMs request their maximum allowed CPU performance, the total CPU demand will exceed the capacity of the CPU. It is defined that when the demand of the CPU performance exceeds the available capacity, a violation of the SLAs established between the resource provider and customers occurs. An SLA violation results in a penalty incurred by the provider, which is calculated as Cvtv, where Cv is the cost of SLA violation per unit of time, and tv is the time duration of the SLA violation. Since it is necessary to represent the relative difference between Cp and Cv, without loss of generality, the following relations can be defined: Cp = 1 and Cv = s, where s R+. This is equivalent to defining Cp = 1/s and Cv = 1. At some point in time v, an SLA violation occurs and continues until N. In other words, due to the over-subscription and variability of the workload experienced by VMs, at the time v the overall demand for the CPU performance exceeds the available CPU

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