IE53600 - Stochastic Models In Operations Research ISpring 2017
Days/Time: TTh / TBD
Credit Hours: 3
An introduction to techniques for modeling random processes used in operations rese arch. Markov chains, continuous time Markov processes, Markovian queues, reliability and inventory models.
An introduction to techniques for modeling random processes used in operations research. Discrete and continuous random variables. Markov chains, continuous time Markov processes, Markovian queues, reliability and inventory models. Robustness aspects.
1. Introduction to probability: conditional probability; Bayes' formula; random variables (discrete and continuous); commutative distribution function, probability mass function
2. Random variables: bernoulli, binomial, geometric, Poisson, exponential, normal, uniform random numbers and their properties; expectation value and properties; Independent and identically distributed random numbers; moment generating function; strong law of large numbers; central limit theorem;
3. Conditional probability and expectation: variance; discrete and continuous case; random graphs, non- predetermined probability, Dirichlet distribution, Bose-Einstein statistics
4. Markov chains: stochastic processes; transition probabilities; transient and recurrent states; limiting probabilities; mean time spent;
5. Continuous time Markov chains: transition rates and approximations; steady-state behavior and convergence theorem; birth-death process
6. Queuing theory: Little's Formula; steady-state and limiting probabilities; Queuing system with bulk service; network of queues; generalizations; closed queuing systems
7. Reliability theory: structure functions; k-out-of-n systems; minimal paths and cut sets; reliability of systems of independent components.
Course prerequisites are GR-C S 156 and IE 335 or IE 501. A strong working knowledge of basic linear algebra (e.g., MATH 265) and calculus (e.g. MATH 261) is highly recommended.
Syllabus, grades, lecture notes, and solutions.
There will be an assigned homework every two weeks, and is due back in a week. You are highly encouraged to work in groups. Return homework to email@example.com.
Optional Project: Each student has a flexibility to do a research project. The project will be worth 40%, and the maximum of the marks from the project and the final exam would be chosen as the marks for the final exam. If the student however does exceptionally well on both the exam and the project, up to 5% bonus marks can be added at the discretion of the Instructor. If interested, you must notify the instructor of your intent within the following three weeks. There will be a presentation scheduled for the project.
2 midterm exams and 1 final exam.
Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Tentative: S. Ross, Introduction to Probability Models, Academic Press, 2010, 10th Edition. (Required) G.R. Grimmett and D.R. Strizaker, Probability and Random Processes, Oxford University Press, 2010, 3rd Edition (Reference)
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