Department of Industrial and Manufacturing Systems Engineering
Iowa State University

IE 313 Stochastic Analysis

Spring 2000

Recent Announcements

Contact Information

Instructor:	Dr. Siggi Olafsson	Teaching Assistant:	Mr. Chiang-Sheng Lee
Office::	3018 Black Engineering	Office:	Office hours in 0010 Black Engineering
Phone:	294-8908		(OR Teaching Lab)
Email:	olafsson@iastate.edu	Email:	chiang@iastate.edu
Homepage:	http://www.public.iastate.edu/~olafsson
Office Hours:	10:15am - 11:45am MWF or by appointment	Office Hours:	M 3:30-4:30 and T 3:00 - 4:00

Administrative Information

Catalog Description

Development of basic queuing models and related applications. Use of simulation for some applications. Project involving data collection and analysis of a queuing system is required.

Prerequisites

Calculus through differential equations (Math 267), and elementary statistics (Stat 231).

Textbook

Nelson, B.L. 1995. Stochastic Modeling: Analysis and Simulation, McGraw-Hill, New York.
Lecture notes that are made available at the course web site.

Course Objectives

After completing this course a student should:

Understand the behavior of stochastic systems in terms of both sample paths and probability distributions of random variables.
Understand the principles of generating sample paths using simulation.
Know how to model arrival processes using the Poisson process.
Be able to model and analyze stochastic systems using Markov chain models.
Understand and be able to apply basic queuing models and theory.

Topics Covered

Modeling of uncertainty, sample paths, basic probability theory, random variables, joint distributions, expected values, conditional probability, limit distributions, discrete event simulation, generating random variates, arrival processes, the Poisson process, memory-less property, superposition and decomposition property, discrete time Markov chains, transient and steady-state analysis, exponential distribution, continuous time birth-death chains, queuing models, Little’s Law, Markovian queues, queuing approximations.

Class/Laboratory Schedule

This class meets three times a week for a fifty-minute lecture. There are approximately five homework assignments to be completed in small groups (2-3), as well as short (5-10 minute) in-class assignments also to be completed in small groups. Some homework assignments require use of computer software and there are two laboratory session to demonstrate the use of this software. A group project involves data gathering from a real-world system, formulating a model of the system, and analyzing its performance. Each group of 2-4 students gives two in-class presentations: a status report after the data gathering and partial modeling, and a final report presenting the conclusions and recommendations of the project. A written final report is also required. Grading is based on homework (25%), a midterm exam (20%), a final exam (20%), project presentations (10%), project report (15%), in-class participation (5%), and peer evaluations of group work (5%).

Contribution to Professional Component

The students learn how to apply their knowledge in probability and statistics to analyze real-world engineering systems. For their project they will gather data from a real system that then needs to be interpreted and used to formulate a model of the system. The students will then apply the techniques from class to analyze the model in order to improve the design and/or operation of the system. The project, as well as many of the other assignments, will be performed in small groups, encouraging the students to develop their ability of work as part of a team. The students will also enhance their communication skills through oral presentations and a written report.

Relationship to IMSE Program Objective

This course provides tools and experience for modeling of production and service systems as well as integration of processes. An important element of the course is for the students to gain an understanding of how to apply their knowledge of probability and statistics to analyze real-world systems. The students will also gather and analyze real-world data and use this to build a model of the real system. Students work extensively in teams, providing them with valuable experience in working in such environments, and present their results to the class, enhancing their communication skills.

Lecture Notes

Download all the lecture notes for the semester (last 10 pages + cover and index are new)

Introduction to Probability Modeling and Simulation: Modeling of uncertainty, sample paths, basic probability theory, random variables, joint distributions, expected values, conditional probability, limit distributions, discrete event simulation, generating random variates.

Read Chapters 1-4 in the textbook.

The Poisson Process: Arrival processes, the Poisson process, memory-less property, superposition and decomposition property.

Read Chapter 5 excluding 5.8 and 5.9, and Section 7.2.2 in the textbook.

Markov Processes: Discrete time Markov chains, transient and steady-state analysis, the exponential distribution, continuous time birth-death chains.

Read Chapter 6 and pp 182-189 and 197-201 of Chapter 7 in the textbook.

Queueing Processes: Queuing models, Little’s Law, Markovian queues, general service, queuing approximations.

Read Chapter 8 in the textbook.

Project

There will be a group project that will account for a 30% of the final grade:

First presentation 5%
Second presentation 5%
Final Report 15%
Peer reviews 5%

You will complete the project in two phases.

Phase I

Find a simple system that involves some resources or servers that customer need access to. Write up a brief description of the system and what data you are going to collect to model the system (1/2 page) and turn in by February 16th.

I will give you feedback on your proposed system by February 18th and assuming everything is in order the next step is to model the system. This will involve: (1) gathering the necessary data, fitting appropriate distributions, and checking the quality of your fits. After completing this you will, as a group, give a short in-class presentation of your results (10 minutes). I will schedule these presentations for the final week in March (March 27-March 31). This presentation will account for 5% of the final grade.

Phase II

Taking the model you have developed as a starting point, you will then use techniques we learn in the second half of the course to evaluate the performance of the system that you decided to model. This will typically include an evaluation of the current system and a suggestion for system improvement. You will then present the results and recommendations in class (5%) and write a final report (15%). The presentations will be scheduled for April 19th and April 21st, with the final report being due on April 28th. The final 5% of the grade is based on peer evaluations from your group members.

Second Presentation

The second presentation should include at least the following elements:

System Description.
Modeling. How your system can be modeled using a queuing model.
Performance Evaluation. What performance measures are important for your system and how they are obtained (including numerical results).
Performance Improvement. How the performance can be improved and/or what are the key factor that influence the performance.
Model Validation. What approximations are made in the model, that is, how good is the model. For example, if you use a M/M/1 queue, what would the difference be if you were to use a M/G/1 queue model instead? Are heavy traffic or light traffic approximations appropriate for your system? Etc. What data did you collect, or could you have collected to validate the results of the model?
Recommendations. Make recommendations for improving the system and/or further study (analysis and/or data gathering) as appropriate.

Homework

The homework is due before class starts one week after it is assigned. Unless otherwise noted each problem of the homework has equal weight and the entire homework is graded out of 100. The total weight of homeworks is 25% for five homework assignments, so each homework is worth 5% of the final grade. If you have questions about the homework you can send be an email or come and see me during my office hours between 10:15am and 11:45am MWF. You can also contact the TA for help.

Homework 1 due February 4th: Problems 3.2, 3.9, 3.17, 3.18 on pp. 51-55 in the textbook. (Solutions. )
Homework 2 due February 16th: Problems 2.9, 3.12, 3.14, and 4.9 in the textbook.
Homework 3 due Mars 1st: Problems 5.1, 5.3, 5.8, and 5.17 in the textbook.
Homework 4 due April 14th: Problems 6.4, 6.6, 6.11, 6.27, 7.2, and 7.10 in the textbook.
Homework 5 due April 21st: Problems 8.1, 8.4, 8.5, and 8.21 in the textbook.

Last modified April 3, 2000.