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Queueing Theory (MAE634): Διαφορά μεταξύ των αναθεωρήσεων

Queueing Theory (MAE634): Διαφορά μεταξύ των αναθεωρήσεων

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! Prerequisite Courses
! Prerequisite Courses
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| It is desirable to have an elementary knowledge of probability theory and Markov chains.
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! Language of Instruction and Examinations
! Language of Instruction and Examinations
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! Learning outcomes
! Learning outcomes
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The course learning outcomes are: the study and development models that describe and analyse the behaviour and performance of queueing systems and their applications for optimal decision making. Upon successful completion of the course the student will be able to:
Queuing phenomena are encountered in several real-life situations. Prominent examples are service counters, elevators and traffic networks, but queuing effects also arise in supply chains, production systems and communication networks. In this course you will learn basic mathematical models for analyzing congestion effects in terms of queue lengths and waiting times. You will also develop insight into the applications of such approaches for improving the design and performance of service operations.
* recognize and implement M/M/1 queue model and its variants
 
* apply the Little's result
The course aims to enable students to:
* recognize and implements M/G/1 queue model
* explain the queuing models used in production and service systems,
* apply Markov processes to model queueing systems
* introduce the theory and mathematical models used to solve these models.
* apply queueing models for decision making.
 
At the end of the course, the student will be able to:
* Learn foundations of queueing theory: basic models, key ideas and methods.
* Understand how to apply queueing theory to model and analyze engineering systems.
* Develop background and skills, which will allow students to subsequently study other and/or more advanced topics in queuing theory.
 
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! General Competences
! General Competences
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* Synthesis of data and information, with the use of the necessary technology.
* Synthesis of data and information, with the use of the necessary technology.
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=== Syllabus ===
=== Syllabus ===
Introduction. Birth death process. Transforms. Markovian Queueing Systems (Μ/Μ/1/∞, Μ/Μ/m/k, Μ/Μ/m/m, Μ/Μ/∞/∞). Queue with group arrival, Queue with group services, M/G/1/∞. Applications for optimal decision making.
 
Introduction, modelling examples, basic concepts, Kendall’s notation, Review of the basic stochastic processes (Poisson process, birth-death processes), Queueing notation and basics, Littles law, mean value analysis. Simple Markovian systems: M/M/1, M/M/c and extensions. General Markovian systems: Queues with batch arrivals and services, Non-Markovian systems: Erlang queues, M/G/1, G/M/1. Markovian networks: Jackson networks. Priority systems.
 
=== Teaching and Learning Methods - Evaluation ===
=== Teaching and Learning Methods - Evaluation ===
{| class="wikitable"
{| class="wikitable"
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LANGUAGE OF EVALUATION: Greek
LANGUAGE OF EVALUATION: Greek
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METHODS OF EVALUATION: Final exam (100%)
METHODS OF EVALUATION: Final exams (100%) including Theory and Exercises.
|}
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=== Attached Bibliography ===
=== Attached Bibliography ===


Τελευταία αναθεώρηση της 23:48, 16 Ιανουαρίου 2025

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE634

Semester

6

Course Title

Queueing Theory 

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses It is desirable to have an elementary knowledge of probability theory and Markov chains.
Language of Instruction and Examinations

Greek

Is the Course Offered to Erasmus Students

Yes

Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

Queuing phenomena are encountered in several real-life situations. Prominent examples are service counters, elevators and traffic networks, but queuing effects also arise in supply chains, production systems and communication networks. In this course you will learn basic mathematical models for analyzing congestion effects in terms of queue lengths and waiting times. You will also develop insight into the applications of such approaches for improving the design and performance of service operations.

The course aims to enable students to:

  • explain the queuing models used in production and service systems,
  • introduce the theory and mathematical models used to solve these models.

At the end of the course, the student will be able to:

  • Learn foundations of queueing theory: basic models, key ideas and methods.
  • Understand how to apply queueing theory to model and analyze engineering systems.
  • Develop background and skills, which will allow students to subsequently study other and/or more advanced topics in queuing theory.
General Competences
  • Working independently
  • Decision-making
  • Adapting to new situations
  • Production of free, creative and inductive thinking
  • Synthesis of data and information, with the use of the necessary technology.

Syllabus

Introduction, modelling examples, basic concepts, Kendall’s notation, Review of the basic stochastic processes (Poisson process, birth-death processes), Queueing notation and basics, Littles law, mean value analysis. Simple Markovian systems: M/M/1, M/M/c and extensions. General Markovian systems: Queues with batch arrivals and services, Non-Markovian systems: Erlang queues, M/G/1, G/M/1. Markovian networks: Jackson networks. Priority systems.

Teaching and Learning Methods - Evaluation

Delivery

Face-to-face

Use of Information and Communications Technology -

Software for the calculation of queueing systems performance measures, Email, class web

Teaching Methods
Activity Semester Workload
Lectures 39
Independent study 78
Fieldwork (3-4 set of homework) 33
Course total 150
Student Performance Evaluation

LANGUAGE OF EVALUATION: Greek
METHODS OF EVALUATION: Final exams (100%) including Theory and Exercises.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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