# Purdue Engineering Professional Education

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IE53600 - Stochastic Models In Operations Research I

Spring 2017

Days/Time: TBA / TBA
Credit Hours: 3

Learning Objective:
TBA

Description:
An introduction to techniques for modeling random processes used in operations research. Descrete and continuous random variables. Markov chains, continuous time Markov processes, Markovian queues, reliability and inventory models. Robustness aspects.

Topics Covered:
-Introduction to probability: conditional probability; Bayes' formula; random variables (discrete and continuous); commutative distribution function, probability mass function
-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;
-Conditional probability and expectation: variance; discrete and continuous case; random graphs, non- predetermined probability, Dirichlet distribution, Bose-Einstein statistics
-Markov chains: stochastic processes; transition probabilities; transient and recurrent states; limiting probabilities; mean time spent;
-Continuous time Markov chains: transition rates and approximations; steady-state behavior and convergence theorem; birth-death process
-Queuing theory: Little's Formula; steady-state and limiting probabilities; Queuing system with bulk service; network of queues; generalizations; closed queuing systems
-Reliability theory: structure functions; k-out-of-n systems; minimal paths and cut sets; reliability of systems of independent components

Prerequisites:
Intro probability, basic distributions, expectation

Applied/Theory: 40/60

http://www.itap.purdue.edu/learning/tools/blackboard/

Web Content:
Syllabus, grades, lecture notes, and solutions.

Homework:
There will be a weekly assignment of one problem; due to return before the following class. Accepted via email at nohadani@purdue.edu; please use the subject "IE 536".

Projects:
None.

Exams:
2 midterm exams and 1 final exam.

Textbooks:
*Tentative-check the Office of the Registrar Textbooks for the official list*
None required. Suggested: S. Ross. Introduction to Probability Models. Academic Press, 2007, 9th Edition.

Computer Requirements:
ProEd Minimum Computer Requirements; Pen Tablet Hardware

ProEd Minimum Requirements: view

Tuition & Fees: view

 T. B. D.PhoneNoneEmailproed@purdue.eduOfficeCampusBuildingAddressWest Lafayette, IN 47907