EM0026 Stochastic Processes and Models

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit
Information About Course

Information
Goal, Content & Resources
Course Learning Outcomes
Relation with Program Learning Outcome
Week Plan
Student Workload - ECTS

Information

Code EM0026
Name Stochastic Processes and Models
Semester . Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Doktora Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator


Course Goal

Explain the techniques and methods of analyzing systems having stochastic processes.

Course Content

Markov Chains, Poisson Processes, Renewal processes and applications

Course Precondition

None

Resources

Richard Durrett,Essentials of Stochastic Processes,3rd Edition 2016, Springer Books

Notes

Richard Durrett,Essentials of Stochastic Processes,3rd Edition 2016, Springer Books


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Can analyze the stochastic process
LO02 Can simulate stochastic processes and interpret the results
LO03 Can analyze production systems having stochastic processes
LO04 Can compare the deterministic process and stochastic processes


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Conducts scientific research in industrial engineering, understands, interprets and applies knowledge in his/her field domain both in-depth and in-breadth.
PLO02 Bilgi - Kuramsal, Olgusal Keeps up with the recent changes and applications in the field of Industrial Engineering and examines and learns these innovations when necessary. 2
PLO03 Bilgi - Kuramsal, Olgusal Acquires detailed knowledge for methods and tools of industrial engineering and their limitations.
PLO04 Bilgi - Kuramsal, Olgusal Identifies, gathers and uses necessary information and data.
PLO05 Beceriler - Bilişsel, Uygulamalı Develops original definitions that will provide innovation to the field at the level of expertise for current and advanced information in the field based on graduate qualifications.
PLO06 Beceriler - Bilişsel, Uygulamalı Designs and performs analytical modeling and experimental research and analyze/solves complex matters emerged in this process.
PLO07 Beceriler - Bilişsel, Uygulamalı Has the ability to develop/propose new and/or original ideas and methods, propose new solutions for designing systems, components or processes. 2
PLO08 Beceriler - Bilişsel, Uygulamalı Designs Industrial Engineering problems, develops new methods to solve the problems and applies them. 4
PLO09 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Works in multi-disciplinary teams, take a leading role and responsibility and develop solutions for complex problems. 4
PLO10 Yetkinlikler - Öğrenme Yetkinliği Completes and applies the knowledge by using limited resources in scientific methods and integrates the knowledge in the field with the knowledge form various disciplines.
PLO11 Yetkinlikler - İletişim ve Sosyal Yetkinlik Uses a foreign language in verbal and written communication at least B2 level of European Language Portfolio.
PLO12 Yetkinlikler - İletişim ve Sosyal Yetkinlik Presents his/her research findings systematically and clearly in oral or written forms in national and international platforms.
PLO13 Yetkinlikler - İletişim ve Sosyal Yetkinlik Understands social and environmental implications of engineering practice.
PLO14 Yetkinlikler - Öğrenme Yetkinliği Considers social, scientific and ethical values in data collection, interpretation and announcement processes and professional activities.


Week Plan

Week Topic Preparation Methods
1 Markov Chains Definitions and Examples Studying from text book Öğretim Yöntemleri:
Soru-Cevap, Alıştırma ve Uygulama
2 Multistep transition probabilities Classification of States Studying from text book Öğretim Yöntemleri:
Soru-Cevap, Alıştırma ve Uygulama, Anlatım
3 Poisson Processes Exponential distribution Compound Poisson Processes Studying from text book Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
4 Renewal Processes Studying from text book Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
5 Laws of Large Numbers Studying from text book Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
6 Applications to Queueing Theory Studying from text book Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
7 G/G/1 queues Studying from text book Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
8 Simulation of G/G/1 Queues Studying from text book Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
9 Midterm exam Ölçme Yöntemleri:
Yazılı Sınav, Sözlü Sınav, Performans Değerlendirmesi
10 Analyzing the G/G/s queues Studying from text books Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Tartışma
11 Simulating the G/G/s queues Studying from text books Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
12 Martingales Studying from text book Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
13 Continuous Time Markov Chains . . Studying from text books Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
14 Computing the Transition Probability Studying from text books Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
15 Detailed Balance Condition at continous time Markov Chains Studying from text books Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
16 Analyzing the queing networks Studying from text books Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
17 Final exam Studying from text books Ölçme Yöntemleri:
Yazılı Sınav, Performans Değerlendirmesi


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 3 42
Out of Class Study (Preliminary Work, Practice) 14 5 70
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 14 14
Final Exam 1 24 24
Total Workload (Hour) 150
Total Workload / 25 (h) 6,00
ECTS 6 ECTS