M.SC. in Computer Engineering (Without Thesis)

IE 502 | Course Introduction and Application Information

Course Name

Probabilistic Systems Analysis

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
IE 502	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Second Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Problem Solving Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Dr. Öğr. Üyesi Oktay KARABAĞ
Course Lecturer(s)	Dr. Öğr. Üyesi Oktay KARABAĞ
Assistant(s)	-

Course Objectives

Most problems encountered in scientific research requires acquaintance with stochastic models and the solution techniques used for these models. The stochastic versions of deterministic problems may also be defined and modelled. Using the models and techniques taught in this course, solution approaches will be sought to problems that are stochastic in nature or to the stochastic versions of deterministic problems. The student will gain the ability to build and analyze models.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	Discuss a scientific paper that involves stochastic models
2	Model any process that evolves over time.
3	Make scientific predictions about the future of a process using the models and techniques of stochastic processes.
4	Compare and contrast the models and techniques used in stochastic processes with those of other industrial engineering/operations research tools.
5	Classify the stochastic processes models.
6	Derive the equations of stochastic models, follow the proofs of theorems, and prove the validity of a solution.

Course Description

The course involves defining and modelling a stochastic process and solving the problems related to the stochastic process being investigated. The underlying theory will be taught, followed by applications that illustrate the use of a stochastic process.

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Related Preparation	Learning Outcome
1	Probability concept, Conditional Probability, and Bayes Theorem
2	Random variable, Expectation, and Variance
3	Basic univariate discrete probability distributions
4	Basic univariate continous probability distributions
5	Two-dimensional joint discrete and continuous distributions, Covariance, Correlation and Introduction to Random processes
6	Two-dimensional joint discrete and continuous distributions, Covariance, Correlation and Introduction to Random processes (Cont’d)
7	Midterm Exam
8	Discrete-time Markov chains: Definitions, Modeling and the Chapman-Kolmogorov equation
9	Discrete-time Markov chains: State classification and First step analysis
10	Discrete-time Markov chains: Absorbing chains and Long-run analysis
11	Poisson Processes: Definition and Properties
12	Poisson Processes: Non-homogeneous and Compound Poisson processes
13	Continuous time Markov chains: Concepts and Birth-death processes
14	Continuous time Markov chains: Transition probability function and calculation of transition probabilities
15	Review of the Semester
16	Final Exam

Course Notes/Textbooks

[1] Ross, Sheldon. Introduction to Probability Models, 11^th edition, Academic Press, 2014. ISBN: 978-0124079489

[2] Taylor, Howard M. and Karlin, Samuel. An Introduction to Stochastic Modeling, 3rd Edition, Academic Press, 1998, ISBN: 978-0-12-684887-8.

[3] Frederick S. Hillier, Gerald J. Lieberman, Introduction to Operations Research, 10^th Edition, 2010 Mc GrawHill, ISBN: 9780071267670

Suggested Readings/Materials

[4] Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena, Scientific, 2008. ISBN: 9781886529236.

[5] Sheldon Ross, Stochastic Processes, 2^nd edition, Wiley, 1995. ISBN: 978-0471120629

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6
Participation	1	10
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	20
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	35
Final Exam	1	35
Total

Weighting of Semester Activities on the Final Grade	3	65
Weighting of End-of-Semester Activities on the Final Grade	1	35
Total

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	16	5	80
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	3	15	45
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	24	24
Final Exam	1	28	28
		Total	225

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information.		-	-	-	-	X
2	Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.		-	-	-	X	-
3	Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines.		-	-	-	-	X
4	Is informed about new and upcoming applications in the field and learns them whenever necessary.		-	-	-	X	-
5	Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.		-	-	-	-	X
6	Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.		-	-	-	-	X
7	Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process.		-	X	-	-	-
8	Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility.		-	-	X	-	-
9	Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.		-	-	X	-	-
10	Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.		-	-	X	-	-
11	Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications.		-	X	-	-	-
12	Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.		-	X	-	-	-