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0408U003126,
к.ф.-м.н.
19-06-2008
o
Investigation of the queueing systems with finite waiting space
Bratiychuk Andriy Mykolayovich,
popup.head Lebedev Evgeniy Alexandrovich
popup.opponent Коба Олена Вікторівна
popup.opponent Самойленко Ігор Валерійович
У дисертації розглядаються системи масового обслуговування з пуассонівським вхідним потоком замовлень, загальним розподілом часу обслуговування та обмеженою чергою. Допускається групове надходження замовлень. Також розглядається узагальнення таких систем шляхом введення відновлюючого рівня вхідного потоку замовлень. Запропоновано модифікацію методу потенціалу Королюка для дослідження характеристик таких систем. Розроблений метод дозволив не лише отримати зображення для перетворень Лапласа функціоналів, які вивчаються в дисертації за допомогою стандартного підходу, а також дав можливість написати обчислювальні алгоритми та програми для стаціонарних характеристик, що мають суттєві переваги перед відомими. Ці алгоритми використовуються для розв'язування оптимізаційних задач, а також для синтезу систем із заданими характеристиками. Отримані нові зображення для характеристик головних функціоналів, а також проведено асимптотичний аналіз їх розподілів при зростанні довжини черги. Для систем з відновлюючим рівнем вхідного потоку замовлень отримані граничні теореми для періоду зайнятості та числа замовлень, обслужених за цей період.
2008-06-19
2020-04-04
Updated: 2025-12-08
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