Contents

• Introduction
• 1. Theme urgency
• 2. Goal and tasks
• 3. Review of existing methods
• 3.1 Classification of cluster systems
• 3.2 Methods of analysis and evaluation
• References

Introduction

The modern world is not standing still. And in the process of new studies appear more and more tasks.

One example of a computer processing system with distributed clusters is [1]. Cluster computing systems by sharing disk space are classified as follows: shared–disk space, and without access to resources [2].

Discrete Markov models accurately reflect the work computing environment and can effectively parallelize computing structures.

1. Theme urgency

Creation and application of modern supercomputers main task in all countries. Improving the efficiency of processes solving large problems have a major incentive for the development of parallel computing systems. Effectiveness of their use depends on several parameters:

• performance of the processors that are part of the system;
• the capacity of communication channels [4].

Designing modern parallel structures is not possible in the analytical modeling of computational structures. Tasks can not be efficiently implemented on uniprocessor computers. On uniprocessor computers due to insufficient amount of computing resources and a large dimension assigned task.

2. Goal and tasks

Development of methods for increasing the efficiency of cluster systems is the aim of this work.

Main tasks of the research:

• development of Markov models of functioning cluster systems;
• improvement of existing methods for calculating the main characteristics of the functioning of the cluster systems;
• development of parallel algorithms for their implementation large–scale problems;
• development of Markov models of functioning of modern cluster systems taking into account their structure and class solved their tasks;

Objects of study are cluster systems of different topologies.

Subject of research are analytical methods for analysis and synthesis of high-performance computing systems.

3. Review of existing methods

Created a large number of parallel computing systems. Work in this direction require further development. They do not lose their relevance.

Systems theory and queuing networks is an appropriate device for analytical modeling information network, or as they say in English-speaking countries, queuing theory.

Forecast performance is the aim of the analytical and simulation. Performance evaluation of resource use, queue lengths, and delays in them is used for this.

3.1 Classification of cluster systems

To build systems with many processors are used cluster or MPP–approaches. Both of these trends are used as a backbone SMP computing module.

Massively–parallel systems, in contrast to the clusters have more speed, usually specialized, channels of communication between the computing modules, as well as opportunities to scale.

Consider a simplified model of the cluster shared–disk space. Incoming task management server distributes between application servers. Number of application servers — N1. Number of Discs — N2, which can address the server. The number of tasks processed by the computer system — no more than M. Servers and disk drives — multichannel devices.

Cluster has the following properties [2]:

High reliability. If one of the computers, specifying its users are automatically transferred to another computer in the cluster. If the system has multiple controllers and external storage failure of one of them, the other controllers are automatically picked up by his work.

Absolute scalability. The clusters may be composed of dozens of computers, each of which may have a multiprocessor structure.

Reduced price/performance ratio. Using the products of mass production, you can create high–performance complex that power will not yield the largest computers, and cost will be much cheaper.

Expandability. Increasing computing power of the cluster by connecting to it additional computers without additional modification of existing ones.

3.2 Methods of analysis and evaluation

Analytical and simulation models and experimental research methods are used to assess the quality and optimization of parallel computing systems.

Analytical methods are now widely used to evaluate the effectiveness of parallel computing systems, which have a complex heterogeneous structure. Probabilistic models with a high degree of adequacy describe the computational structure [10].

One method of assessing the quality aircraft models is queuing theory, allowing to define quality indicators such as throughput, utilization, average response time, and others. Computing system is considered as a collection of servers, which serve a variety of system resources — workstations, servers, memory, cache memory, and so on. Tasks or processes impose service requests for these devices, so a significant part of quality assessment tasks related to the analysis of queues [11].

In queuing theory the most studied and researched analytical models are the sun that are based on concepts of the theory of Markov chains, using sensitive methods of analysis [12].

With discrete Markov models analyzed a small number of single–processor computing structures as models for the calculation of complex multiprocessor Sun because the Sun is much complicated structure and analytical models have a larger dimension. Analysis of parallel systems with the help of these models with a large number of tasks on uniprocessor computer is impossible, since the number of states of a discrete Markov model combinatorially increases with the number of tasks. In this case, it is advisable to parallelize the algorithm for constructing a discrete model and evaluate the effectiveness of parallelization.

Discrete Markov models, compared with continuous, reflect the work of the computer system more accurately, since the sun is discrete in nature and work in an environment that is an element of probability. However, continuous models are less cumbersome.

Approximate methods of queuing network, for example, decomposition methods, developing lately, allow to extend the class of queuing networks studied, but reasonably accurate model can be obtained only for a certain class of problems [13].

Note

This master's work is not completed yet. Final completion: February 2015.

References

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