181404 PROBABILITY AND QUEUEING THEORY B.E Computer Science And Engineering SYLLABUS 4th Semester Anna University of Technology

181404               Probability and queueing Theory                             3  1  0  4

(Common to CSE & IT)

AIM

The probabilistic models are employed in countless applications in all areas of science and engineering. Queuing theory provides models for a number of situations that arise in real life. The course aims at providing necessary mathematical support and confidence to tackle real life problems.

OBJECTIVES

At the end of the course, the students would

·                     Have a well – founded knowledge of standard distributions which can describe real life phenomena.

·                     Acquire skills in handling situations involving more than one random variable and functions of random variables.

·                     Understand and characterize phenomena which evolve with respect to time in a probabilistic manner.

·                     Be exposed to basic characteristic features of a queuing system and acquire skills in analyzing queuing models.

UNIT I             RANDOM VARIABLES                                                                      9 + 3

Discrete and continuous random variables - Moments - Moment generating functions and their properties. Binomial, Poisson ,Geometric ,Negative binomial, Uniform, Exponential, Gamma, and Weibull  distributions .

UNIT II            TWO DIMENSIONAL RANDOM VARIABLES                                  9 + 3

Joint distributions - Marginal and conditional distributions – Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.

UNIT III           MARKOV processes AND Markov chains                                      9 + Classification - Stationary process - Markov process -  Markov chains - Transition probabilities - Limiting distributions-Poisson process

 

UNIT IV           QueuEing Theory                                                                                     9 + 3

Markovian models – Birth and Death Queuing models- Steady state results: Single and multiple server queuing models- queues with finite waiting rooms- Finite source models- Little’s Formula

UNIT V           NON-MARKOVIAN QUEUES AND QUEUE NETWORKS                          9 + 3

M/G/1 queue- Pollaczek- Khintchine formula, series queues- open and closed networks

TUTORIAL     15                                                                                              TOTAL : 60

TEXT BOOKS

 1.    O.C. Ibe, “Fundamentals of Applied Probability and Random Processes”,

  Elsevier,  1^st Indian Reprint, 2007 (For units 1, 2 and 3).

2.      D. Gross and C.M. Harris, “Fundamentals of Queueing Theory”, Wiley

         Student edition, 2004 (For units 4 and 5).  

 

Books for ReferenceS:

1.      A.O. Allen, “Probability, Statistics and Queueing  Theory with Computer

         Applications”, Elsevier, 2^nd edition, 2005.

2.      H.A. Taha, “Operations Research”, Pearson Education, Asia, 8^th edition, 2007.

3.      K.S. Trivedi, “Probability and Statistics with Reliability, Queueing and  

         Computer Science Applications”,  John Wiley and Sons,  2^nd edition, 2002.