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Бакалавриат 2019/2020

## Теория массового обслуживания

Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Статус: Курс по выбору (Программная инженерия)
Направление: 09.03.04. Программная инженерия
Когда читается: 3-й курс, 1, 2 модуль
Формат изучения: Full time
Язык: английский
Кредиты: 5

### Course Syllabus

#### Abstract

This course gives a detailed introduction into queueing theory along with insights into stochastic processes and simulation techniques useful for modeling queueing systems. A queue is a waiting line, and a queueing system is a system which provides service to some jobs (customers, clients) that arrive with time and wait to get served. Examples are: - a telecommunication system that processes requests for communication; - a hospital facing randomly occurring demand for hospital beds; - central processing unit that handles arriving jobs. Queueing theory is a branch of probability theory dealing with abstract representation of such systems. It helps obtain useful and unobvious answers to questions concerning waiting times for both jobs and servers, like “how much servers should a system have, so that a customer would not have to wait more than … on average?” or “what is the mean queue length corresponding to a certain capacity utilisation level?” Such questions arise, for example, in computer systems performance evaluation. These problems require knowledge of stochastic processes, therefore the course provides a review of point processes (Poisson, Erlang etc.) and Markov chains in discrete and continuous time, paying special attention to a birth-death process, often used in queueing models. It also includes a detailed insight into simulation, because queueing problems often do not have analytic solution. The course is aimed at students interested in applied probability, Monte Carlo simulation and computer systems performance evaluation. #### Learning Objectives

• to make students familiar with stochastic process theory and its applications
• to develop mathematical and modeling skills required for evaluating queueing systems performance
• to give a theoretical background needed to understand academic literature on the subject #### Expected Learning Outcomes

• be able to describe the structure of a certain queueing system
• to know characteristics of queueing processes
• to know common areas of queueing theory application
• be able to find steady-state solutions for basic stochastic processes and queueing models
• to know the basics of stochastic processes theory
• to know measures of effectiveness of queueing systems
• be able to evaluate measures of effectiveness
• to know the basics of random number generation and Monte Carlo simulation
• be able to simulate stochastic processes and queueing systems
• to know common queueing models
• be able to choose appropriate model for a system
• know common queueing models
• be able to read and understand academic literature on stochastic processes, queueing and computer systems performance evaluation
• know the basics of stochastic processes theory
• be able to estimate parameters of a queueing process from data
• be able to solve simple differential and difference equations
• know probabilistic models for timing of events #### Course Contents

• Introduction to queueing theory
• Differential and difference equations
• Modeling arrivals: Poisson stream and other point processes.
• Markov chains
• Single-channel exponential queueing models
• Simulating queues
• Simple Markovian birth-death queueing models
• Advanced models (general service pattern, queues with impatience etc.)
• Elements of computer systems performance evaluation
• Generating functions
• Statistical inference in queueing #### Assessment Elements

• test
• homework
• exam #### Interim Assessment

• Interim assessment (2 module)
0.5 * exam + 0.25 * homework + 0.25 * test #### Recommended Core Bibliography

• Gorain, G. C. (2014). Introductory Course on Differential Equations. New Delhi: Alpha Science Internation Limited. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1878058