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DOI 10.34229/KCA2522-9664.26.5.9
УДК 519.872

А. МЕЛІКОВ
Бакинський інженерний університет, Баку, Азербайджан; Інститут математики
Міністерства науки та освіти Азербайджанської республіки, Баку, Азербайджан,
a.melikov@beu.edu.az

Л. ПОЛАДОВА
Бакинський інженерний університет, Баку, Азербайджан,
lamanpoladova@gmail.com


НАБЛИЖЕНИЙ РОЗВ’ЯЗОК У ВИГЛЯДІ ДОБУТКУ
ДЛЯ СИСТЕМ ОБСЛУГОВУВАННЯ–ЗАПАСАННЯ
З ОБМЕЖЕНОЮ ЧЕРГОЮ ТА КАТАСТРОФАМИ

Анотація. У роботі розглянуто марковську модель системи обслуговування–запасання з обмеженою чергою та катастрофами. Внаслідок катастроф усі запаси на складі миттєво знищуються. Окрім споживчих заявок, у системі також враховуються заявки, що не потребують ні обслуговування, ні запасів, проте витісняють одну заявку із системи. Поповнення запасів фіксованого обсягу здійснюється з випадковими затримками. Для математичного аналізу цієї системи побудовано двовимірний марковський ланцюг і знайдено наближений розв’язок у вигляді добутку для обчислення його стаціонарних імовірностей. Високу точність отриманих наближених формул підтверджено числовими експериментами. Продемонстровано поведінку характеристик системи залежно від вихідних параметрів і виконано оптимізацію досліджуваної системи.

Ключові слова: система обслуговування–запасання, обмежена черга, катастрофи, двовимірний марковський ланцюг, наближений розв’язок у вигляді добутку.


повний текст

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