Jordan University of Science and Technology

Department of Mathematics and Statistics

Math 470 (Probabilistic Models in Operations Research)

 Instructor: Dr. Mahmoud Alrefaei    


                 Second Semester                                         Year: 2004/2005
                   

Week Section Subject Assignments
1 19.1,2 Stochastic Processes, Markov Chains, examples 1, 3, 6
2 19.3 n-step transition probabilities 1, 2, 3
  classification of states in a Markov chain  
3   Steady-state probability and mean first passage times 3, 4, 5, 7, 10
    Absorbing chains 1, 3, 5
4 22.1 Queuing Theory: Some queuing terminology  
22.2 Modeling arrival and service processes  
5 22.3 Birth-Death processes 2, 3
22.4 The M/M/1 queuing systems 1-5, 7, 8
6   First Exam: Monday 28/3/2005 at 8:15   
  22.5 The M/M/1/k queuing systems 5
722.6 The M/M/s queuing systems 1-9
 22.9 Finite source models: The machine repair model 1, 2, 3, 7
8 22.10 Exponential queues in series and open queuing network 2, 4, 6
  22.7, 8 The M/G/ ¥ and GI/G/ ¥ queuing systems and the M/G/1 queue 3, 4
9 22.11 The M/G/s system (Blocked customers cleared) 1, 2
  22.12 How to tell whether the IAT's and ST's are Exponential 1
  22.13 What to do if not exponential 1
10 22.14 Priority queuing models 3, 4
11   Simulation: Basic terminology  
  Discrete event simulation  
12   Second Exam: Monday 9/5/2005  
    Random numbers generations  
  Monte Carlo simulation  
13  Simulation with continuous random variables:  
  The inverse transformation method  
  Accept-rejection method and the convolution method  
14   Examples of stochastic simulation  
  Statistical analysis in simulation; transient and steady-state  
  Simulation languages  
15   simulating a single server queuing system  
16   Final exams starts  

Grading Policy:

First Exam
25%
Second Exam
25%
Assignments and a Project
10%
Final Exam
40%

Text Book:

Winston W. L. Operations Research Applications and Algorithms, third edition. Duxbury Press, Belmont, California, 1994.

References:

  1. Hoel P. G., S. C. Port, and C. J. Stone Introduction to Stochastic Processes. Waveland Press, Prospect Height, Illinois, 1987.
  2. Hillier F. S. and G. J. Lieberman. Introduction to Stochastic Models in Operations Research. McGrow Hill, New York, 1990.
  3. Taha H. A. Operations Research an Introduction sixth ed. Prentice Hall, London, 1997.

Links: 

 

Examples:

M/ M/ S Example

Simulating single server 

Monte Carlo

Exercise 7 pp 1154

File translated from TEX by TTH, version 2.51.