MA4156 Linear Algebra, Probability and Queueing Theory Syllabus:

MA4156 Linear Algebra, Probability and Queueing Theory Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES:

The objective of this course is to enable the student to
 grasp the basic concepts of Probability, Random variables, correlation and regression.
 characterize the phenomena which evolve with respect to time in a probabilistic manner.
 encourage students to develop a working knowledge of the ventral ideas of linear algebra.
 acquire skills in analyzing Queueing Models.
 develop a fundamental understanding of linear programming models and apply the simplex method for solving linear programming problems.

UNIT – I LINEAR ALGEBRA

Vector spaces – Norms – Inner products – Eigenvalues using QR transformations – QR factorization – Generalized eigenvectors – Jordan Canonical forms – Singular value decomposition and applications – Pseudo inverse – Least square approximations.

UNIT – II PROBABILITY AND RANDOM VARIABLES

Probability Concepts – Axioms of probability – Conditional probability – Bayes theorem – Random variables – Probability functions – Two-dimensional random variables – Joint distributions – Marginal and conditional distributions – Correlation – Linear Regression.

UNIT – III RANDOM PROCESSES

Classification – Stationary random process – Markov process – Markov chain – Poisson process – Gaussian process – Auto correlation – Cross correlation.

UNIT – IV QUEUEING THEORY

Markovian queues – Single and multi-server models – Little’s formula – Steady state analysis – Self-service queue.

UNIT – V LINEAR PROGRAMMING

Formulation – Graphical solution – Simplex method – Big M method – Variants of Simplex method – Transportation problems – Assignment models.

TOTAL: 60 PERIODS

COURSE OUTCOMES:

After the completion of the course, the student will be able to
 apply various methods in Linear Algebra to solve the system of linear equations.
 use two-dimensional random variables, correlations and regression in solving application problem.
 apply the ideas of Random Processes.
 understand the basic characteristic features of a queueing system and acquire skills in analyzing queueing models.
 apply the Simplex method for solving linear programming problems.

REFERENCES:

1. Miller,S.L. and Childers D.G., “Probability and Random Processes with Applications to Signal Processing and Communications”, Academic Press,2004.
2. Friedberg A.H, Insel A.J. and Spence L, “Linear Algebra”, Prentice Hall of India, New Delhi, 2004.
3. Gross, D., Shortie, J.F., Thompson, J.M and Harris, C.M., “Fundamentals of Queueing Theory”, 4th Edition, Wiley,2014.
4. T. Veerarajan, “Probability, Statistics and Random Process with Queueing Theory and Queueing Network, Tata McGraw Hill, 4th Edition,2017.
5. Taha H.A., “Operations Research: An Introduction”, 9th Edition, Pearson Education Asia, New Delhi,2016.
6. Richard Bronson, ”Matrix Operations” Schaum’s outline series, McGraw Hill, 2nd Edition, New York,2011.
7. Oliver C. Ibe, “ Fundamentals of Applied Probability and Random Processes”, Academic Press, (An Imprint of Elsevier), Boston,2014.