Undergrad and Grad Courses
Jeffrey P. Kharoufeh

Courses at University of Pittsburgh

IE 2072: Probability
This course develops important probability concepts for advanced undergraduate and first-year graduate students. Topics include measure-theoretic preliminaries, counting methods, conditional probability and expectation, Bayes' theorem, random variables and distributions, discrete and continuous transforms, functions of random variables, limit theorems, including strong and weak laws of large numbers, central limit theorem(s), and stochastic ordering concepts. Prerequisite(s): Multivariable calculus and one course in probability.

IE 2084: Stochastic Processes
The primary objective of this course is to provide graduate students with a strong foundation in the theory and applications of stochastic processes. The course emphasizes processes most relevant to industrial engineering and operations research. Specific topics include discrete- and continuous-time Markov chains, the Poisson process and its variants, renewal and Markov-renewal theory, regenerative and Markov-regenerative processes, Brownian motion and martingales. Applications in queueing, reliability, inventory and finance will be discussed. Prerequisite(s): IE 2072.

IE 3085: Queueing Theory
The primary aim of this course is to provide graduate students with a foundation in the theory and applications of queueing systems. The course will emphasize analytical techniques while introducing applications in manufacturing, service, transportation, and communications systems. Specific topics include Little's Law and related results, PASTA, Markovian queueing systems, semi-Markovian queueing systems, loss systems, heavy traffic approximations, fluid queueing models, priority queues and scheduling, as well as an introduction to queueing networks. Prerequisite(s): IE 2084.

Courses at Northeastern University

MIM U515: Operations Research
This course introduces deterministic models in Operations Research including linear programming, duality and post-optimality analysis, transportation and assignment problems, network flows such as shortest path, minimum spanning tree, maximum flow, and dynamic programming models and applications.  Text: Hillier, F.S. and Lieberman, G.J., Introduction to Operations Research, 8th Edition, McGraw-Hill, 2005.  Prerequisite(s):  MTH U343.

IEM G230: Probabilistic Operations Research
This course applies fundamental probability theory to develop stochastic models in Operations Research, emphasizing stochastic processes on a countable state space. Specific topics include conditional probability and expectation, the Poisson process and exponential distribution, transient and stationary analysis of discrete-time Markov chains, transient and stationary analysis of continuous-time Markov chains, birth-and-death processes, elementary (exponential) queueing models and intermediate (non-exponential) queueing models. Applications in manufacturing systems, computer and communication networks, transportation systems, reliability and risk analysis will be discussed. Text: Kulkarni, V.G., Modeling & Analysis of Stochastic Systems, Chapman-Hall, 1995.Prerequisite(s):  IEM G200 or its equivalent. 

Courses at Air Force Institute of Technology

OPER 540: Stochastic Modeling and Analysis I
This course applies fundamental probability theory to develop standard approaches to stochastic modeling in operations research. Specific topics include conditional probability and expectation, the Poisson process and exponential distribution, discrete-time Markov chains, and continuous-time Markov chains. We shall also discuss applications in queueing, reliability, and inventory theory. Upon completion of the course, the student should be able to stochastically model and analyze a variety of real-world systems. In order to carry out numerical analyses, the student will also be introduced to computer programming in the MATLAB computing environment. Text: Kulkarni, V.G., Modeling & Analysis of Stochastic Systems, Chapman-Hall, 1995.

OPER 641: Stochastic Modeling and Analysis II
This course further develops concepts in the modeling and analysis of complex stochastic systems. Specific topics include generalizations of the Poisson process, renewal theory, regenerative processes, Markov-renewal theory, and Markov-regenerative processes. Time permitting, we shall also introduce discrete-time martingales, Brownian motion, and other diffusion processes. Students will be expected to perform some numerical analyses in the MATLAB computing environment. Text: Kulkarni, V.G., Modeling & Analysis of Stochastic Systems, Chapman-Hall, 1995.

OPER 647: Queueing Systems Analysis
The main objective of this course is to develop fundamental techniques for the performance analysis of single-station queueing systems and is intended for students in operations research, electrical engineering, computer science, or mathematics. Queueing systems arise in a wide range of real-world settings such as telecommunications, manufacturing, and transportation systems. Upon completion of the course, the student will comprehend the fundamentals of classical queueing theory, its limitations, and areas of applicability. Additionally, modern topics in queueing theory will be introduced. Text: Kleinrock, L. Queueing Systems, Volume I: Theory, Wiley, 1975.

OPER 741: Advanced Stochastic Modeling
This doctoral-level course first develops the rudimentary concepts of measure-theoretic probability necessary for advanced stochastic modeling. Subsequently, we shall study discrete- and continuous-time martingale theory followed by Brownian motion processes and stochastic integration. Applications in operations research, finance, and engineering will also be discussed. Reference Texts: (i) Billingsley, P., Probability and Measure, Wiley, 1995; (ii) Resnick, S.I., A Probability Path, Birkhauser, 2001; (iii) Ross, S.M., Stochastic Processes, Wiley, 1996.

OPER 747: Queueing Networks
The main objective of this course is to develop fundamental techniques for the performance analysis of multi-station queueing systems and is intended for students in operations research, electrical engineering, computer science, or mathematics. Queueing networks arise in a wide range of real-world settings such as telecommunications, manufacturing, and transportation systems. Upon completion of the course, the student will comprehend the fundamentals of classical queueing network theory, exact algorithms, approximate algorithms, and some modern theories. Special emphasis will be placed on algorithmic implementation of main results using the MATLAB computing environment. Text: Bolch, Greiner, de Meer, Trivedi, Queueing Networks and Markov Chains, Wiley & Sons, 1997.