Introduction To Stochastic Processes
ebru.angun@gmail.com
Content
Objective
The stochastic processes, which is one of the major areas of interest for an industrial engineer, enable the modeling of systems with random components. The stochastic models have several application areas including supply chain management, inventory systems management, and call-center management. The aim is to introduce the logic of modeling of stochastic systems, which can further be useful for academic studies and in industry. Hence, the objectives of the course are determined as follows:
• Introduce discrete-time and discrete-state processes.
• Introduce continuous-time and discrete-state processes.
• Introduce the concepts of conditional expectation and conditional probability.
• Make the students comprehend how they can analyze the performance of systems modeled through stochastic processes.
• Make the students apply their theoretical knowledge to model queuing, reliability, and inventory systems.
Course Learning Outcomes
Upon successful completion of this course, the student will be able to LO 1: Define different types of stochastic models.
LO 2: Classify the states of Markov processes.
LO 3: Calculate the transition probabilities and mean time spent in transient states for Markov chains.
LO 4: Define the concepts of conditional probability and conditional expectation.
LO 5: Define the branching process.
LO 6: Define the Bernoulli and Poisson processes.
LO 7: Define the birth and death process.
LO 8: Model a problem through the appropriate stochastic process.
LO 9: Analyze various permance measures such as mean queue length, mean time in system, etc. for steady-state stochastic processes.
ÖÇ 10: Define queuing, reliability, and inventory models.
References
Ross, S., “Introduction to Probability Models”, 9th Edition, Academic Press, New York, 2007.
Çınlar, E., “Introduction to Stochastic Processes”, 2nd Edition, Dover, New Jersey, 2013.
Weekly Contents
| Week | Weekly Contents |
|---|---|
| 1 | Review of probability (Ross, Chapter 1) |
| 2 | Review of probability (Ross, Chapter 2) |
| 3 | Conditional probability and conditional expectation (Ross, Chapter 3) |
| 4 | Conditional probability and conditional expectation (Ross, Chapter 3) |
| 5 | Markov chains, Chapman-Kolmogorov equations, and classification of states (Ross, Chapter 4) |
| 6 | Gambler’s ruin problem, branching process (Ross, Chapter 4) |
| 7 | Bernoulli process (Çınlar, Chapter 3) |
| 8 | Midterm |
| 9 | Poisson process and exponential distribution (Ross, Chapter 5) |
| 10 | Poisson process and exponential distribution (Ross, Chapter 5) |
| 11 | Markov process, birth and death processes (Ross, Chapter 6) |
| 12 | Birth and death processes, transition and limiting probabilities (Ross, Chapter 6) |
| 13 | Queuing models M/M/1, M/M/k, M/G/1 and M/G/k, and embedded Markov chain (Ross, Chapter 8, Çınlar, Chapter 6) |
| 14 | Reliability and inventory models (Ross, Chapter 9) |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 6 | 50 |
| Contribution of final exam to overall grade | 1 | 50 |
| Total | 7 | 100 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 5 | 20 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 30 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Total | 6 | 50 |
Relation of Proficiency
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Knowledge and understanding of a wide range of basic sciences (math, physics, ...) and the main concepts of engineering | X | ||||
| 2 | Ability to combine the knowledge and skills to solve engineering problems and provide reliable solutions | X | ||||
| 3 | Ability to select and apply methods of analysis and modeling to ask, reformulate and solve the complex problems of industrial engineering | X | ||||
| 4 | Ability to conceptualize complex systems, processes or products under practical constraints to improve their performance, ability to use innovative methods of design | |||||
| 5 | Ability to design, select and apply methods and tools needed to solve problems related to the practice of industrial engineering, ability to use computer technology | |||||
| 6 | Ability to design experiments, collect and interpret data and analyze results | X | ||||
| 7 | Ability to work independently, ability to participate in working groups and have a multidisciplinary team spirit | |||||
| 8 | Ability to communicate effectively, ability to speak at least two foreign languages | X | ||||
| 9 | Awareness of the need for continuous improvement of lifelong learning, ability to keep abreast of scientific and technological developments to use the tools of information management | |||||
| 10 | Awareness of professional and ethical responsibility | |||||
| 11 | Knowledge of the concepts of professional life as "project management", "risk management" and "management of change" | |||||
| 12 | Knowledge on entrepreneurship, innovation and sustainability | |||||
| 13 | Understanding of the effects of Industrial Engineering applications on global and social health, environment and safety. | |||||
| 14 | Knowledge of the problems of contemporary society | |||||
| 15 | Knowledge of the legal implications of the practice of industrial engineering | |||||
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Working Hours out of Class | 13 | 2 | 26 |
| Assignments | 5 | 3 | 15 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Final Examinations (including preparation) | 1 | 17 | 17 |
| Total Workload | 110 | ||
| Total Workload / 25 | 4.40 | ||
| Credits ECTS | 4 | ||