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A quantum optimization scheme in network cluster server task scheduling is proposed. We explore and research the distribution theory of energy field in quantum mechanics; specially, we apply it to data clustering. We compare the quantum optimization method with genetic algorithm (GA), ant colony optimization (ACO), simulated annealing algorithm (SAA). At the same time, we prove its validity and rationality by analog simulation and experiment.

Cluster technology is connecting multiple independent servers and providing services as a whole by a cluster. To achieve parallel program in a high efficiency, service request must be allocated to each server, reduce the access time, and optimize the overall performance. Load balancing mechanism is the core cluster technology.

In the literature [

The state of web applications communicates and coordinates with lot of geographically distributed information resources offering information to great number of clients. Homogeneous server clusters are unable to meet the growing demand of the applications including real-time video and audio, ASP, JSP, and PHP. Moreover, it also provides better reliability by gracefully transferring the load from server which is unavailable due to failure or for preventive maintenance. Heterogeneity with scalability makes the system more complex. The literature [

In the literature [

A load balancing arithmetic named dynamic weighed random (DWR) algorithm for the session initiation protocol (SIP) application server cluster is put forward in the literature [

The literature [

The consolidation of server is due to virtualization technology, which enables multiple servers to run on one platform. Moreover, virtualization may bring the overheads on performance. The prediction of virtualization performance is very important. The literature [

The response time of a website needs to be improved, which one replicates the site on multiple servers. It will depend on how the incoming requests are distributed among replicas, where the effectiveness of a replicated server system. In the literature [

A key issue for cluster system is the utilizing efficiency of system resources, in which the method of load balance is very important to realize the efficient resources. Based on server cluster system, the literature [

Effective load balancing mechanism can extend the “capacity” of the server and improve system throughput. In early studies of load balancing algorithm, genetic algorithm (GA), dynamic feedback algorithm (DFA), ant colony algorithm (ACO), simulated annealing algorithm (SAA), round robin (RR), Min-Min algorithm, Max-Min algorithm, and so on have some improvements in different degree at different perspective on the load balancing system.

They provide solutions to the problem of load balancing for server cluster by these arithmetics mentioned above. But these arithmetics have this or that problem such as local premature problem and divergence problem.

In order to overcome the instability of the above algorithms, the server load balancing method based on quantum algorithm is proposed. And we prove it better than GA, ACO, and SAA by simulation experiments.

The quantum optimization method of clustering algorithm is mainly used in this particle. The method is put forward by clustering idea based on quantum theory, which is a kind of unsupervised clustering method. It is also applied to the traditional clustering algorithm, by the study of the theory of energy distribution in quantum mechanics, theory study, we found that the microscopic particles distribution in the energy field relies on the potential energy which associates with particles themselves, the smaller the potential energy around the particles, the more they are absorbed. In the energy field with particle distribution described by a wave function, the particle distribution will ultimately depend on the potential energy in the energy field. For the design of clustering algorithm, the potential energy function is used and the cluster center is determined by the particle distribution. Similarly, how to determine the cluster center and the corresponding number of samples of clusters is also the main task of cluster analysis. Therefore, distribution of particles in space studied by quantum mechanics theory is similar to the distribution of samples studied by clustering algorithm. The known clustering process of sample distribution can be regarded as the known wave function which describes the particle distribution.

The clustering process can be expressed as follows: with the known wave function, solve the potential energy function by the Schrödinger equation. Particle distribution ultimately depends on the value of the potential energy function.

Quantum state of a particle wave function is as follows:

From formula (

In cluster services, the loading balance can be described as follows:

Suppose there are m servers (or nodes) and n tasks. Each task has to be assigned to only one server. In this paper,

We use

Obviously,

We consider that the optimal state occurs with these conditions: (1) the whole system has a relative short time of processing, and meanwhile (2) the throughput of system in unite time is relatively large. We can use the following equations to describe this state:

The model of loading balance by quantum optimization can be described as a tetrad (task, weight, function, and scheduling); among them, task is the task to be assigned and scheduling is to assign the task according to the rules [

The relation of task and schedule is described as

Suppose

For cluster samples

Constraint rule in competition is as follows.

Suppose

According to Definition

Adjust

Set initial value for

Set the maximum step size as Max_length. Initialize the learning rate

Calculate learning rate and neighborhood radius by the following equations:

Take out a sample vector

In node array, neighborhood

Consider

For a set of samples in one type

Calculate the learning rate:

Take out a type set

Consider

In order to compare quantum clustering optimization algorithm (QOA), genetic algorithm (GA), ant colony optimization (ACO), and simulated annealing algorithm (SAA), select five servers as nodes with the number of tasks from 0 (or 100) to 1000 (or 800) to compare the results of the three methods by MatLab. The correlation parameters of selected servers for experiments are in Table

Parameters of selected servers.

Brands and models | Sun 880 | SUN T2000 | IBM p615 |
---|---|---|---|

CPU | AMD Opteron 1.2 GHz * 2 | UltraSPARC T1 1 GHz * 4 | POWER4, 1.45 GHz * 2 |

Main storage size | 8.0 G | 16.0 G | 16.0 G |

Network adapter | 2 * 1000 M | 4 * 1000 M | 2 * 1000 M |

Operation system | Linux | Solaris | Unix |

The topological structure of the network servers is as in Figure

The topological structure of the network servers.

Figure

The load balancing degrees of SUN T2000 in GA, SAA, ACO, and QOA.

Figure

The throughput rate of SUN 880 in GA, SAA, ACO, and QOA.

Figures

From the results, it is clear that quantum optimization algorithm (QOA) is better in cluster server task scheduling than genetic algorithm (GA), simulated annealing algorithm (SAA), and ant colony optimization (ACO). QOA is more effective in task scheduling (Figure

The throughput capacity, the task quantity, and the time of SUN 880. And the QOA is better than GA, SAA, and ACO.

The throughput of IBM p615 in GA during one day.

The throughput of IBM p615 in QOA during one day.

The throughput of IBM p615 in SAA during one day.

The throughput of IBM p615 in ACO during one day.

The paper gives a quantum optimization model and arithmetic on cluster server and proves their validity by analog simulation and experiments. The model and the arithmetic increase the throughput and efficiency of the system, and they had some merits than traditional model and arithmetic.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This study is supported by the National Natural Science Foundation of China (61173056).