MA1252 PROBABILITY AND QUEUEING THEORY Syllabus

SEMESTER IV
MA1252 –PROBABILITY AND QUEUEING THEORY

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UNIT I PROBABILITY AND RANDOM VARIABLE 9

Axioms of Probability – Conditional Probability – Total Probability – Baye’s Theorem– Random

variable – Probability mass function – Probability density function – Properties – Moments – Moment

generating functions and their properties.

UNIT II STANDARD DISTRIBUTIONS 9

Binomial – Poisson – Uniform – Exponential – Gamma – Normal distributions and their properties –

Functions of a random variable – Chebyshev inequality.

UNIT III TWO DIMENSIONAL RANDOM VARIABLES 9

Joint distributions – Marginal and conditional distributions – Covariance – Correlation and regression –

Transformation of random variables – Central limit theorem.

UNIT IV RANDOM PROCESSES AND MARKOV CHAINS 9

Classification – Stationary process – Markov process – Poisson process – Birth and death process –

Markov chains – Transition probabilities – Limiting distributions.

UNIT V QUEUEING THEORY 9

Markovian models – M/M/1 – M/M/C – finite and infinite capacity – M/M/∞ queues – Finite source

model – M/G/1 queue (steady state solutions only) – Pollaczek – Khintchine formula – Special cases.



L: 45 T: 15 Total: 60



TEXT BOOKS



1. Ross S, “A first course in probability”, Sixth Edition, Pearson Education, 2006.

2. S.Karlin and H.M. Taylor., “An Introduction to Stochastic Modeling” Academic Press,

2007

3. Taha, H. A., “Operations Research-An Introduction”, Seventh Edition, Pearson Education,

2007.

REFERENCES

1. Veerarajan T, “Probability, Statistics and Random Processes”, Second Edition, Tata McGraw

Hill, 2003.

2. Richard A Johnson, “Probability and Statistics for Engineers”, Seventh Edition,

Pearson Education, 2005.

3. Gross D. and Harris, C.M., “Fundamentals of Queuing Theory”, Third Edition, John Wiley and

Sons, 1998.