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MA1252 PROBABILITY AND QUEUEING THEORY
UNIT I PROBABILITY AND RANDOM VARIABLE
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 DISTRIBUTION
Binomial, Poisson, Geometric, Negative Binomial, Uniform, Exponential, Gamma, Weibull and Normal distributions and their properties - Functions of a random variable.
UNIT III TWO DIMENSIONAL RANDOM VARIABLES
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.
UNIT IV RANDOM PROCESSES AND MARKOV CHAINS
Classification - Stationary process - Markov process - Poisson process - Birth and death process - Markov chains - Transition probabilities - Limiting distributions.
UNIT V QUEUEING THEORY
Markovian models – M/M/1, M/M/C , finite and infinite capacity - M/M/8 queues - Finite source model - M/G/1 queue (steady state solutions only) – Pollaczek – Khintchine formula – Special cases.
TEXT BOOKS
1. Ross, S., “A first course in probability”, Sixth Edition, Pearson Education, Delhi, 2002.
2. Medhi J., “Stochastic Processes”, New Age Publishers, New Delhi, 1994. (Chapters 2, 3, & 4)
3. Taha, H. A., “Operations Research-An Introduction”, Seventh Edition, Pearson Education Edition Asia, Delhi, 2002.
REFERENCES
1. Veerarajan., T., “Probability, Statistics and Random Processes”, Tata McGraw-Hill, Second Edition, New Delhi, 2003.
2. Allen., A.O., “Probability, Statistics and Queuing Theory”, Academic press, New Delhi, 1981.
3. Gross, D. and Harris, C.M., “Fundamentals of Queuing theory”, John Wiley and Sons, Second Edition, New York, 1985.
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