A High Performance Model for Task Allocation in Distributed Computing System Using K-Means Clustering Technique

2018 ◽  
Vol 9 (3) ◽  
pp. 1-23 ◽  
Author(s):  
Harendra Kumar ◽  
Nutan Kumari Chauhan ◽  
Pradeep Kumar Yadav
Keyword(s):  
Mathematical Model ◽  
Distributed Computing ◽  
High Performance ◽  
Computing System ◽  
Performance Model ◽  
Communication Costs ◽  
Clustering Technique ◽  
Proposed Model ◽  
Two Stages ◽  
The Mathematical Model

Tasks allocation is an important step for obtaining high performance in distributed computing system (DCS). This article attempts to develop a mathematical model for allocating the tasks to the processors in order to achieve optimal cost and optimal reliability of the system. The proposed model has been divided into two stages. Stage-I, makes the ‘n' clusters of set of ‘m' tasks by using k-means clustering technique. To use the k-means clustering techniques, the inter-task communication costs have been modified in such a way that highly communicated tasks are clustered together to minimize the communication costs between tasks. Stage-II, allocates the ‘n' clusters of tasks onto ‘n' processors to minimize the system cost. To design the mathematical model, executions costs and inter tasks communication costs have been taken in the form of matrices. To test the performance of the proposed model, many examples are considered from different research papers and results of examples have compared with some existing models.

A High Performance Model for Task Allocation in Distributed Computing System Using K-Means Clustering Technique

2021 ◽  
pp. 1244-1268
Author(s):  
Harendra Kumar ◽  
Nutan Kumari Chauhan ◽  
Pradeep Kumar Yadav
Keyword(s):  
Mathematical Model ◽  
Distributed Computing ◽  
High Performance ◽  
Computing System ◽  
Performance Model ◽  
Communication Costs ◽  
Clustering Technique ◽  
Proposed Model ◽  
Two Stages ◽  
The Mathematical Model

Tasks allocation is an important step for obtaining high performance in distributed computing system (DCS). This article attempts to develop a mathematical model for allocating the tasks to the processors in order to achieve optimal cost and optimal reliability of the system. The proposed model has been divided into two stages. Stage-I, makes the ‘n' clusters of set of ‘m' tasks by using k-means clustering technique. To use the k-means clustering techniques, the inter-task communication costs have been modified in such a way that highly communicated tasks are clustered together to minimize the communication costs between tasks. Stage-II, allocates the ‘n' clusters of tasks onto ‘n' processors to minimize the system cost. To design the mathematical model, executions costs and inter tasks communication costs have been taken in the form of matrices. To test the performance of the proposed model, many examples are considered from different research papers and results of examples have compared with some existing models.

Mathematical Model for Approximation the Efficiency of Parallel Computing on Single Board Cluster with Least-squares Approximation

2020 ◽  
Vol 12 (7) ◽  
Author(s):  
Chotitham Thanrak ◽  
◽  
Sasalak Tongkaw ◽  
Keyword(s):  
Mathematical Model ◽  
Parallel Processing ◽  
Least Squares ◽  
High Performance ◽  
Computing System ◽  
Raspberry Pi ◽  
Processing Efficiency ◽  
High Performance Computing System ◽  
The Mathematical Model ◽  
The Relationship

This research aims to study the relationship between parallel processing efficiency and several nodes on a single board cluster using a mathematical model, approximating least squares. This research tested on the Raspberry Pi single-board in the form of a high-performance computing system. It divided the tasks that need to be processed in each particular part and sent it to each unit to process simultaneously via the MPI (Messaging Passing Interface). This process is the standard division of work with communication between processors in the form of messages on the cluster system. It consists of eight nodes of Raspberry Pi. It measures the instruction set's ability to perform decimal operations per second or Floating-point Operation Per Second (FLOPS) with High-Performance Linpack Benchmarks (HPL). As a result, the efficiency of the ability to process instruction set in decimal per second increases the performance continuously when increasing the number of the node on the cluster. Which corresponds to the mathematical model obtained f(x) = 1.0684x^(0.8256).It shows a relationship between parallel processing performance values and the number of nodes on the cluster and can be estimated with the mathematical model above.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

scholarly journals Content Dependent Representation Selection Model for Systems Based on MPEG DASH

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1843
Author(s):  
Jelena Vlaović ◽  
Snježana Rimac-Drlje ◽  
Drago Žagar
Keyword(s):  
Mathematical Model ◽  
Spatial Information ◽  
Relevant Literature ◽  
Video Quality ◽  
Similarity Index ◽  
Video Encoding ◽  
Adaptation Algorithm ◽  
Subjective Testing ◽  
Proposed Model ◽  
The Mathematical Model

A standard called MPEG Dynamic Adaptive Streaming over HTTP (MPEG DASH) ensures the interoperability between different streaming services and the highest possible video quality in changing network conditions. The solutions described in the available literature that focus on video segmentation are mostly proprietary, use a high amount of computational power, lack the methodology, model notation, information needed for reproduction, or do not consider the spatial and temporal activity of video sequences. This paper presents a new model for selecting optimal parameters and number of representations for video encoding and segmentation, based on a measure of the spatial and temporal activity of the video content. The model was developed for the H.264 encoder, using Structural Similarity Index Measure (SSIM) objective metrics as well as Spatial Information (SI) and Temporal Information (TI) as measures of video spatial and temporal activity. The methodology that we used to develop the mathematical model is also presented in detail so that it can be applied to adapt the mathematical model to another type of an encoder or a set of encoding parameters. The efficiency of the segmentation made by the proposed model was tested using the Basic Adaptation algorithm (BAA) and Segment Aware Rate Adaptation (SARA) algorithm as well as two different network scenarios. In comparison to the segmentation available in the relevant literature, the segmentation based on the proposed model obtains better SSIM values in 92% of cases and subjective testing showed that it achieves better results in 83.3% of cases.

scholarly journals An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

2016 ◽  
Vol 10 (10) ◽  
pp. 133
Author(s):  
Mohammad Ali Nasiri Khalili ◽  
Mostafa Kafaei Razavi ◽  
Morteza Kafaee Razavi
Keyword(s):  
Mathematical Model ◽  
Mixed Integer ◽  
Logistics System ◽  
Proposed Model ◽  
Multiple Objective Decision Making ◽  
System Requirements ◽  
Purchasing Logistics ◽  
The Cost ◽  
The Mathematical Model ◽  
First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

Influence of Tooth Errors and Truing Principles of Grinding Wheel Abrasion for Machining Arc Enveloping Worm

2013 ◽  
Vol 652-654 ◽  
pp. 2153-2158
Author(s):  
Wu Ji Jiang ◽  
Jing Wei
Keyword(s):  
Mathematical Model ◽  
Case Studies ◽  
High Precision ◽  
High Performance ◽  
New Method ◽  
Grinding Wheel ◽  
Grinding Process ◽  
The Mathematical Model

Controlling the tooth errors induced by the variation of diameter of grinding wheel is the key problem in the process of ZC1 worm grinding. In this paper, the influence of tooth errors by d1, m and z1 as the grinding wheel diameter changes are analyzed based on the mathematical model of the grinding process. A new mathematical model and truing principle for the grinding wheel of ZC1 worm is presented. The shape grinding wheel truing of ZC1 worm is carried out according to the model. The validity and feasibility of the mathematical model is proved by case studies. The mathematical model presented in this paper provides a new method for reducing the tooth errors of ZC1 worm and it can meet the high-performance and high-precision requirements of ZC1 worm grinding.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

First Principle-Based Control Oriented Model of a Gasoline Engine

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Ahmed Yar ◽  
A. I. Bhatti ◽  
Qadeer Ahmed
Keyword(s):  
Mathematical Model ◽  
Gasoline Engine ◽  
Mean Value ◽  
First Principle ◽  
Unified Framework ◽  
Engine Model ◽  
Proposed Model ◽  
Suitable Form ◽  
Speed Fluctuations ◽  
The Mathematical Model

A first principle based-control oriented gasoline engine model is proposed that is based on the mathematical model of the actual piston and crankshaft mechanism. Unlike conventional mean value engine models (MVEMs), which involve approximating the torque production mechanism with a volumetric pump, the proposed model obviates this rather over-simplistic assumption. The alleviation of this assumption leads to the additional features in the model such as crankshaft speed fluctuations and tension in bodies forming the mechanism. The torque production dynamics are derived through Lagrangian mechanics. The derived equations are reduced to a suitable form that can be easily used in the control-oriented model. As a result, the abstraction level is greatly reduced between the engine system and the mathematical model. The proposed model is validated successfully against a commercially available 1.3 L gasoline engine. Being a transparent and more capable model, the proposed model can offer better insight into the engine dynamics, improved control design and diagnosis solutions, and that too, in a unified framework.

scholarly journals A Hysteresis-Based Steering Feel Model for Steer-by-Wire Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
M. Selçuk Arslan
Keyword(s):  
Mathematical Model ◽  
Steering System ◽  
Steering Wheel ◽  
Hysteresis Model ◽  
Steering Feel ◽  
Proposed Model ◽  
Steer By Wire ◽  
Wheel Torque ◽  
Tire Dynamics ◽  
The Mathematical Model

A mathematical model of steering feel based on a hysteresis model is proposed for Steer-by-Wire systems. The normalized Bouc-Wen hysteresis model is used to describe the steering wheel torque feedback to the driver. By modifying the mathematical model of the hysteresis model for a steering system and adding custom parameters, the availability of adjusting the shape of steering feel model for various physical and dynamic conditions increases. Addition of a term about the tire dynamics to the steering feel model renders the steering wheel torque feedback more informative about the tire road interaction. Some simulation results are presented to establish the feasibility of the proposed model. The results of hardware-in-the-loop simulations show that the model provides a realistic and informative steering feel.

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