EMIS 8372 QUEUEING THEORY
2:00 - 3:20 p.m. TTh (Fall 2005)
228 Caruth Hall
 

Instructor: Dr. U. Narayan Bhat  
111A Heroy Hall
214-768-3268
Email: nbhat@smu.edu
Office hours by appointment

Text: D. Gross and C. M. Harris, Fundamentals of Queueing Theory, Wiley, 3rd Ed., 1998.
         Lecture Notes: Introduction to Queueing Theory (Chapters available here)

Grading: Final grade will be based on performance in the following (approximately equal weights)
    1. Midterm exam (in class), Oct. 6, 2005
    2. Final exam (take home):  Due Dec. 9, 2005
    3. Term paper.
The term paper (15 - 25 pages) will be due on Dec. 9, 2005. Topics for the term paper are to be selected with the consent of the instructor. It can be of three types:
    (a) New method for the analysis of a problem
    (b) Illustrating a model of significant complexity using real data
    (c) Survey of research on a topic not covered in class.

DEPARTMENT OF ENGINEERING MANAGEMENT,
INFORMATION AND SYSTEMS

Course Number: EMIS 8372
Title: Queueing Theory

Catalog Description:  Queueing theory provides the theoretical basis for the analysis of a wide variety of stochastic service systems.  The underlying stochastic processes are Markov and renewal processes.  The course has two objectives: to cover the fundamentals of stochastic processes necessary to analyze such systems and to provide the basics of formulation and analysis of queueing models with emphasis on their performance characteristics.

Prerequisite: EMIS 7370 or equivalent, or permission of instructor.

Textbook(s): Introduction of Queueing Theory (Lecture Notes)
                      D. Gross and C. M. Harris, Fundamentals of  Queueing Theory, Wiley, 3rd Ed., 1998.

Goals:  Providing students with the necessary background to model and analyze queueing systems.  The fundamentals of stochastic processes necessary for such capability will be covered while discussing specific queueing models.

Course Outline and Approximate Schedule
(Class periods are 80 minutes in length)

TOPIC No of class periods Text reference
1. Introduction; system elements; objectives and modes of analysis; Markov processes.  

3

 Chapters 1-3 (LN); Chapter 1 (GH)
2. Simple Markovian birth-death models; transient and steady state behavior; methods of analysis; performance measures; variants of  models.              5 Chapter 4 (LN); Chapter 2 (GH)
3. Markov chains; non-Markovian systems; imbedded Markov chains 6 Chapter 5 (LN); Chapter 4 (GH)
4. Queueing Networks 3 Chapter 7 (LN); Chapter 4 (GH)
5.  Extended Markov Models 3 Chapter 6 (LN); Chapter 3 (GH)
6.  The general queue G/G/1; approximations and bounds. 3 Chapter 8 (LN); Chapter 6 & 7 (GH)
7.  Inference in queues 2 Chapter 9 (LN); Chapter 6 (GH)
8.  General Issues 2  

 

Gross and Harris Chapter 2

 Answers to selected numerical problems

2.11    (a) 1 - 0.33 - 0.22 = 0.45

(b)    1.33  (c) 12 min  (d) 0.44  (e) 7.26

 2.12     $475

 2.16   (a) 15    (b) 6.01

 2.21      24 days

 2.22      c = 2

 2.24   a) 0.6 trucks  (b) 24 mins.  (c) $1.54/min.

 2.25   cost with M/M/2: $1896764

                         M/M/1:    1788400

 

 2.34      (a) 4.35  (b) 12.33 hrs  (c) 0.147  (d) X  < 113.88 Y

 2.35      5

 2.37   8.46

 2.39   9

 2.43      L with 3 repairman: 1.8765; with 1 repairman: 1.1624

 2.44      (a) 0.103627                (c) 0.0864

(b) mWq = 0.327586          0.552677

Gross & Harris Chapter 3

Answers to Selected Problems.

[Note: Skip problems 3.6, 3.12, 3.19, 3.20, 3.22, 3.29]

3.3                 M(X)/M/1                                            M/M/1

po             0.333                                               0.333

L              3.333                                               2.000

Lq            2.667                                               1.333

W            0.333                                               0.200

Wq          0.267                                               0.133

 

3.4                (a) L = 0.75; Lq = 0.417; W = 0.75; Wq = 0.417

3.7                Lq = 14.845

3.14     (a) Mean Service Rate = 1.3 min          (b) same as (a).

3.16          po = 0.167; L = 3.125; Wq = 27.5; W = 27.5

3.17           L = 2; W = 0.5; with M/M/1 model

 L = 2.2; W = 0.8; with M/Ek/1 model

3.18           Use k = 4 in M/Ek/1 model.

             [k obtained using by equating sample value of coefficient of variation with ].

3.28      M/M/1/¥/PR:  

             M/M/1/¥/FIFO: 

             M/M/1/¥/PR (with interchanged service rates):

Introduction to Queueing Theory

by

U. Narayan Bhat

 

Copyright© reserved by the author.  The material in this manuscript may not be copied, or emailed to multiple sites, or posted to a list serve without the author's express written permission.  However, users may download and print it for individual use.

 

Contents (tentative)

 

Chapter 1    Introduction    (Chapter 1 pdf file)

Chapter 2    System Element models (Chapter 2 pdf file)

Chapter 3    An introduction to stochastic processes (Chapter 3 pdf file)

Chapter 4    Simple Markovian queueing systems  (Chapter 4 pdf file)

Chapter 5    Imbedded Markov chain models (Chapter 5 pdf file)

Chapter 6    Extended Markovian models

Chapter 7    Queueing networks

Chapter 8    General queueing models

Chapter 9    Statistical inference

Chapter 10  Others topics