{"title":"Stochastic Models for the Time Complexity of Computing Tasks: I. Development Principles, Statistical Data Mining, and Identification Problems","authors":"A. V. Borisov, A. V. Ivanov","doi":"10.1134/s1064230724700035","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper contains the first part of a study on the design of mathematical models for the execution time of user tasks on virtual calculating nodes. It is assumed that the execution time is a random value with the mean and variance depending on the node resources, task parameters, and the current characteristics of the node state. We discover the key features of the mean and variance functions and specify some of their particular cases. Both the mean and variance functions depend on the unknown parameters, and the design of the stochastic model for time complexity leads to parameter identification in the form of the generalized maximum likelihood estimates under heterogeneous statistical information. This paper also contains recommendations concerning the gathering and subsequent use of this information: the node testbed preparation, stress test planning, and processing of the data obtained. Specific illustrating examples of the proposed mathematical model will be presented in the subsequent parts of the study.</p>","PeriodicalId":50223,"journal":{"name":"Journal of Computer and Systems Sciences International","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computer and Systems Sciences International","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s1064230724700035","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
This paper contains the first part of a study on the design of mathematical models for the execution time of user tasks on virtual calculating nodes. It is assumed that the execution time is a random value with the mean and variance depending on the node resources, task parameters, and the current characteristics of the node state. We discover the key features of the mean and variance functions and specify some of their particular cases. Both the mean and variance functions depend on the unknown parameters, and the design of the stochastic model for time complexity leads to parameter identification in the form of the generalized maximum likelihood estimates under heterogeneous statistical information. This paper also contains recommendations concerning the gathering and subsequent use of this information: the node testbed preparation, stress test planning, and processing of the data obtained. Specific illustrating examples of the proposed mathematical model will be presented in the subsequent parts of the study.
期刊介绍：
Journal of Computer and System Sciences International is a journal published in collaboration with the Russian Academy of Sciences. It covers all areas of control theory and systems. The journal features papers on the theory and methods of control, as well as papers devoted to the study, design, modeling, development, and application of new control systems. The journal publishes papers that reflect contemporary research and development in the field of control. Particular attention is given to applications of computer methods and technologies to control theory and control engineering. The journal publishes proceedings of international scientific conferences in the form of collections of regular journal articles and reviews by top experts on topical problems of modern studies in control theory.
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