472 بحث : العمليات العشوائية ونماذج الصفوف

تعريف العمليات العشوائية، الخاصية المار آوفية، سلاسل مارآوف، مصفوفات احتمال الانتقال وحيدة الخطوة ومتعددة الخطوات، معادلة آولموجروف- شامبان، تصنيف الحالات، التوزيعات المستقرة لسلاسل مارآوف، عمليات مارآوف متصلة الزمن (عمليات الولادة والوفاة، العملية البواسونية)، نماذج الصفوف وعناصرها: دراسة وتقييم أنظمة الصفوف باستخدام الرسوم التراآمية، مقاييس الكفاءة، نماذج الصفوف المارآوفية البسيطة (الأحادية، المتعددة، والمحدودة)، بعض الأنظمة الصفية غير المارآوفية، بعض النماذج المارآوفية ذات الوصول الجماعي والخدمة الجماعية.

المتطلب السابق: 213 بحث و 215 إحص

OR-472
 Stochastic Processes and Queueing Models
Course Syllabus
 
Instructor:
            Name: Dr. Khalid A. Alnowibet
            Office: AB 27 Building 4
            Tel. : 011- 4676335
            e-mail: knowibet@ksu.edu.sa Use “OR472” in the subject
 
Lectures:
Sun., Tues., Thur.        10:00 am to 10:50 am
 
Section:
            Tuesday: 1:00pm – 3:00 pm
 
Office Hours:
For any questions or inquiries about the lectures students can email their question and their questions will be answered promptly. For meeting with instructor is available on:
Mon., Wed.   8:00 am to 11:00 am or by appointment
 
Attendance:
Students must attend all lectures on time. Students with absence of more than 25% of total classes will not be legible to attend the final exam. There is no marks designated to attendance, however, students with attendance exceeding 95% may get bonus if needed.
 
Text books:

  1. مقدمة في العمليات العشوائيةتأليف : د. لطفي تاج و د. عمار سرحانمطابع الجامعة
  2. “Introduction to Probability Models “ By Sheldon M. Ross
  3. “Operations Research: Applications and Algorithms|” , By Wayne L. Winston
  4. “Operations Research: An Introduction”, Hamdi Taha, Ch. 10, 14, 15, 16
  5. “An Introduction to Stochastic Modeling “ By Howard Taylor & Samuel Karlin

 
Grading

  1. Attendance, Homework, Quizzes 10%
  2. < >First Midterm Exam20 %
  3. Second Midterm Exam20 %
  4. Final Exam40 %

 
 
Quizzes
Almost every lecture there will be a small quiz on the material presented in the lecture. The purpose of these simple, quick and frequent quizzes is to keep students focused and grasp their attention throughout the lecture.
 
Projects
There will 2 projects on the semester that requires student accumulated knowledge during the course. The projects are intended to be applied to help students see the impact of what they learn in the real life problems. These project should be performed independent be the student with the aid of the instructor or the TA.
 
Course Outline and Tentative Schedual:
 

Topics Expected Lectures
1 Review of basics in probability theory 2
2 Introduction to Stochastic Processes and their types 2
3 Discrete time Markov Chain : Definitions and Examples 2
4 Classification of States in Markov Chains 2
5 Long Run Distribution of Markov Chains 3
6 Continuous time Markov Chain: Definitions and Examples 1
7 Poisson Process and its properties 2
8 Exponential distribution and its properties 2
9 Birth and death processes 2
10 Introduction to queueing systems and modeling 2
11 Measures of performance in queueing systems 3
12 Single-server Markovian queue  M/M/1 3
13 Multi-server Markovian queue  M/M/s 3
14 Queueing models with zero buffer :
Infinite-Server Markovian queue  M/M/∞ and Erlang loss queue  M/M/s/s
2
15 Multi-Server Markovian queue with finite source 2
16 Some none Markovian queues 2
17 Markovian queueing models with impatient and discouraged arrivals 2
18 Markovian models with bulk arrivals and service 2