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Models of Queuing Systems
Major: Applied Mathematics
Code of subject: 7.113.01.O.003
Credits: 6.00
Department: Applied Mathematics
Lecturer: PhD, associate professor Pizyur Ya. V.
Semester: 1 семестр
Mode of study: денна
Завдання: . The study of a discipline involves the formation and development of the following students competencies:
• general:
ЗК2, ЗК3, ЗК4, ЗК5, ЗК8, ЗК9, ЗК12, ЗК15 according to EPP;
• professional:
ФК1, ФК2, ФК3, ФК5, ФК6, ФК8 according to EPP.
Learning outcomes: • know the main types flow of random events, basics of the theory of Markov random processes, main types of queueing systems;
• be able to build a graph of states of the system, to build the Kolmogorov equation system, determine the type of queueing systems and identify characteristics of effective queueing systems.
Required prior and related subjects: • probability theory;
• mathematical statistics;
• random processes.
Summary of the subject: Flows of random events: ordinary, nonstationary Poisson, with limited aftereffect (Palm), Erlang flows. Markov processes with discrete and continuous time, the system of differential equations for finding probabilities of the states, the system of algebraic equations for finding the limiting probabilities of the states, processes of death and reproduction. Models of queueing systems: with rejections, with queue, with limited waiting time, closed.
Опис: Introductory lecture.
1. Flows.
2. The connection between the queueing theory and the theory of Markov processes.
3. Models of queueing systems.
Assessment methods and criteria: Completion of homework and surveys in practical classes;
taking tests in a virtual learning environment;
performance of individual research tasks;
taking the exam.
Критерії оцінювання результатів навчання: Current control – 30 p.
Final control (exam) – 70 p.
Total for discipline – 100 p.
Порядок та критерії виставляння балів та оцінок: 100-88 points - certified with an “excellent” grade - High level: the student demonstrates an in-depth mastery of the conceptual and categorical apparatus of the discipline, systematic knowledge, skills and abilities of their practical application. The mastered knowledge, skills and abilities provide the ability to independently formulate goals and organize learning activities, search and find solutions in non-standard, atypical educational and professional situations. The applicant demonstrates the ability to make generalizations based on critical analysis of factual material, ideas, theories and concepts, to formulate conclusions based on them. His/her activity is based on interest and motivation for self-development, continuous professional development, independent research activities, implemented with the support and guidance of the teacher. 87-71 points - certified with a grade of “good” - Sufficient level: involves mastery of the conceptual and categorical apparatus of the discipline at an advanced level, conscious use of knowledge, skills and abilities to reveal the essence of the issue. Possession of a partially structured set of knowledge provides the ability to apply it in familiar educational and professional situations. Aware of the specifics of tasks and learning situations, the student demonstrates the ability to search for and choose their solution according to the given sample, to argue for the use of a particular method of solving the problem. Their activities are based on interest and motivation for self-development and continuous professional development. 70-50 points - certified with a grade of “satisfactory” - Satisfactory level: outlines the mastery of the conceptual and categorical apparatus of the discipline at the average level, partial awareness of educational and professional tasks, problems and situations, knowledge of ways to solve typical problems and tasks. The applicant demonstrates an average level of skills and abilities to apply knowledge in practice, and solving problems requires assistance, support from a model. The basis of learning activities is situational and heuristic, dominated by motives of duty, unconscious use of opportunities for self-development. 49-00 points - certified with a grade of “unsatisfactory” - Unsatisfactory level: indicates an elementary mastery of the conceptual and categorical apparatus of the discipline, a general understanding of the content of the educational material, partial use of knowledge, skills and abilities. The basis of learning activities is situational and pragmatic interest.
Recommended books: 1. Литвинов А. Л. Теорія систем масового обслуговування : навч. посібник. – Харків: ХНУМГ ім. О. М. Бекетова, 2018. – 141 с.
2. Ложковський А.Г. Теорія масового обслуговування в телекомунікаціях. – Одеса: ОНАЗ ім. О.С. Попова, 2010. – 112 с.
3. Савчук О.В., Моргаль О.М. Моделювання процесів і систем / Лабораторний практикум [Електронний ресурс]: навч. посібник. –– Київ: КПІ ім. Ігоря Сікорського, 2021. – 220 с
4. Рудавський Ю.К., Костробій П.П., Лозинський О.Ю., Уханська Д.В. Елементи теорії випадкових процесів. Навч. посібник.– Львів: Видавництво НУ «Львівська політехніка», 2004.– 240 с.
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