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V.</a>; <a href="/authors/?q=ai%3Aivanov.andrey-v%7Civanov.alexey-v%7Civanov.aleksandr-vladimirovich%7Civanov.aleksei-valerevich%7Civanov.aleksei-vladimirovich%7Civanov.aleksandr-valentinovich%7Civanov.aleksandr-vladimirovich.1%7Civanov.alexei-v%7Civanov.anton-valerevich%7Civanov.a-v%7Civanov.aleksei-valerevich.1" title="Author Profile">Ivanov, A. V.</a></div> <h2 class="title"> <strong>Stochastic models for the time complexity of computing tasks. I: Development principles, statistical data mining, and identification problems.</strong> <i>(English)</i> <a class="label nowrap" href="/1553.68055">Zbl 1553.68055</a> </h2> <div class="source"> <a href="/serials/1842" title="Journal Profile">J. Comput. Syst. Sci. Int.</a> <a href="/?q=in%3A521276" title="Articles in this Issue">63, No. 1, 19-30 (2024)</a>. </div> <div class="abstract">Summary: 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.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7954384">Cited in <strong>1</strong> Review</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68M20" title="MSC2020">68M20</a> </td> <td class="space"> Performance evaluation, queueing, and scheduling in the context of computer systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62P30" title="MSC2020">62P30</a> </td> <td class="space"> Applications of statistics in engineering and industry; control charts </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Astochastic+model">stochastic model</a>; <a href="/?q=ut%3Aparameter+estimation">parameter estimation</a>; <a href="/?q=ut%3AM-estimate">M-estimate</a>; <a href="/?q=ut%3Anonconvex+and+nonsmooth+optimization+problems">nonconvex and nonsmooth optimization problems</a>; <a href="/?q=ut%3Astress+testing">stress testing</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1553.68055" data-ciurl="/ci/07954384" data-biburl="/bibtex/07954384.bib" data-amsurl="/amsrefs/07954384.bib" data-xmlurl="/xml/07954384.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07954384.pdf" title="Zbl 1553.68055 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1134/S1064230724700035" aria-label="DOI for “Stochastic models for the time complexity of computing tasks. I: Development principles, statistical data mining, and identification problems”" title="10.1134/S1064230724700035">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">P. Sirohi, A. Agarwal, and P. Maheshwari, “A survey on augmented virtual reality: Applications and future directions,” in Seventh International Conference on Information Technology Trends (ITT) (Abu Dhabi, 2020), pp. 99-106.</td> </tr><tr> <td>[2]</td> <td class="space">P. Gupta, C. Krishna, R. Rajesh, et al., “Industrial Internet of Things in intelligent manufacturing: A review, approaches, opportunities, open challenges, and future directions,” Int. J. Interact. Des. Manuf. (2022). doi:10.1007/s12008-022-01075-w</td> </tr><tr> <td>[3]</td> <td class="space">I. Parveen, C.A., O. Anjali, and R. 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Ljung, System Identification: Theory for the User (Prentice Hall, Englewood Cliffs, N.J., 1987; Nauka, Moscow, 1991). · <a href="/0615.93004" class="nowrap">Zbl 0615.93004</a></td> </tr><tr> <td>[29]</td> <td class="space">Ivchenko, G.; Medvedev, Yu., Mathematical Statistics, 2014, Moscow: URSS, Moscow</td> </tr><tr> <td>[30]</td> <td class="space">A. Panteleev, D. Metlitskaya, and E. Aleshina, Global Optimization Methods. Meta-Heuristic Strategies and Algorithms (Vuzovskaya kniga, Moscow, 2013) [in Russian].</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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