sustainНадежностьDependability1729-26462500-3909RAMS Journal Limited liability company10.21683/1729-2646-2025-25-4-3-16sustain-688Research ArticleСИСТЕМНЫЙ АНАЛИЗ В ЗАДАЧАХ НАДЕЖНОСТИ И БЕЗОПАСНОСТИSYSTEM ANALYSIS IN DEPENDABILITY AND SAFETYТребования к точности и достоверности в вероятностных моделяхAccuracy and precision requirements in probability modelsКруглыйЗ.KrouglyZ.

Зиновий Круглый, Факультет Прикладной Математики

Лондон, Онтарио

Zinovi Krougly, Department of Applied Mathematics

London, Ontario

zkrougly@uwo.caЗападный УниверситетКанадаWestern UniversityCanada202507122025254316Copyright © Круглый З., 20252025Круглый З.Krougly Z.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.dependability.ru/jour/article/view/688

Численное преобразование Лапласа и его обратное преобразование – сложная задача в теории массового обслуживания и других вероятностных моделях. Для нахождения стабильных и вычислительно эффективных методов используется подход двойного преобразования. Для проверки и улучшения полученного инверсионного решения выполняются прямые преобразования Лапласа от численно инвертированных преобразований с последующим сравнением с исходной функцией. Наиболее перспективные методы были применены к вычислительным вероятностным моделям, когда не существует аналитических решений для обратного преобразования Лапласа. Вычислительная эффективность, обеспечиваемая в зависимости от заданного уровня точности, продемонстрирована для различных моделей M/G/1 систем массового обслуживания.

Numerical Laplace transform and inverse Laplace transform is a challenging task in queueing theory and others probability models. A double transformation approach is used to find stable, accurate, and computationally efficient methods for performing the numerical Laplace and inverse Laplace transform. To validate and improve the inversion solution obtained, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. Algorithms provide increasing accuracy as precision level increases. The most promising methods were applied to computational probability models, when there are no closed-form solutions of the Laplace transform inversion. The computational efficiency compared to precision levels is demonstrated for different service models in M/G/1 queuing systems.

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The authors declare that there are no conflicts of interest present.