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Information
| Code | EM0026 |
| Name | Stochastic Processes and Models |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| 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 Instructor |
1 |
Course Goal / Objective
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 | ||