Course Details

STOCHASTIC PROCESSES

IE531

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Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS Credits
1IE531STOCHASTIC PROCESSES3+0+037,5

Course Details
Language of Instruction English
Level of Course Unit Master's Degree
Department / Program INDUSTRIAL ENGINEERING
Type of Program Formal Education
Type of Course Unit Elective
Course Delivery Method Face To Face
Objectives of the Course This course intends to teach the students about Stochastic Processes. The course covers the following topics: Wiener process, Poisson process, nonhomogeneous and compound Poisson processes, independent increments, discrete time Markov chains, continuous time Markov chains, Kolmogorov differential equations, birth-death processes and queuing applications, non-Markovian processes, regenerative processes, ergodic theorems, semi-Markov processes, Martingales, applications to reliability and inventory control.
Course Content Wiener process, Poisson process, nonhomogeneous and compound Poisson processes, independent increments, discrete time Markov chains, continuous time Markov chains, Kolmogorov differential equations, birth-death processes and queuing applications, non-Markovian processes, regenerative processes, ergodic theorems, semi-Markov processes, Martingales, applications to reliability and inventory control.
Course Methods and Techniques We will be using various tools for active learning to take place. This is also a student-driven course. It is your responsibility to participate actively in class discussions.
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Asist Prof.Dr. Rahime Şeyma Bekli seyma.bekli@agu.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Ross, Sheldon M. Introduction to Probability Models. Academic Press, 2014.
. S. M. Ross (1983). Stochastic Processes. John Wiley
will be shared on canvas system


Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Yarıl yılSonu Sınavı/Dönem Projesinin Başarı Notuna Katkısı 2 % 25
Quiz/Küçük Sınav 3 % 10
Ödev 3 % 10
Proje/Çizim 1 % 20
Final examination 1 % 35
Total
10
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Grup Sunumu 1 1 1
Grup Projesi 1 46 46
Sınıf İçi Aktivitesi 14 3 42
Kişisel Çalışma 14 1 14
Ders dışı çalışma 14 5 70
Yüz Yüze Ders 3 14 42
Final Sınavı 1 3 3
Total Work Load   Number of ECTS Credits 7,5 218

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Model uncertainty using basic stochastic processes.
2 Set up and analyze Markov chains.
3 Develop Markovian and Semi-Markovian models for IE applications.
4 Derive and apply main formulas for some properties (e.g., stationary probabilities, average waiting and system time, expected number of customers in the queue) of queuing systems.
5 Develop appropriate Markov decision processes to solve problems under uncertainty and risk.
6 Be able to work in a team and share the results of a stochastic process (written and orally) with peers in a meaningful and professional manner.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Wiener process
2 Poisson process, nonhomogeneous and compound Poisson processes
3 Independent increments, discrete time Markov chains
4 Continuous time Markov chains
5 Kolmogorov differential equations, birth-death processes and queuing applications
6 Non-Markovian processes
7 Regenerative processes
8 Spring Break
9 Lecture Free Week
10 Ergodic theorems
11 Semi-Markov processes
12 Martingales
13 Applications to reliability and inventory control.
14 Term Project discussion
15 Term Project Presentations
16 Final Exam, Term Project

Recommended Optional Programme Components
IE521 PROBABILITY THEORY

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
All 5 1
C1 5 1
C2 5 1
C3 5 1
C4 5 1
C5 4 1
C6 5 5 3 3 5

Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant


https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=77286&lang=en
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