MA1252 PROBABILITY AND QUEUEING THEORY 3 1 0 100

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 fundamental knowledge of the basic probability concepts.

• 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 PROBABILITY AND RANDOM VARIABLE 9 + 3

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 +3

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 9 + 3

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 + 3

Classification - Stationary process - Markov process - Poisson process - Birth and death process - Markov chains - Transition probabilities - Limiting distributions.

UNIT V QUEUEING THEORY 9 + 3

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.

TUTORIAL 15

TOTAL : 60

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.

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 fundamental knowledge of the basic probability concepts.

• 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 PROBABILITY AND RANDOM VARIABLE 9 + 3

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 +3

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 9 + 3

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 + 3

Classification - Stationary process - Markov process - Poisson process - Birth and death process - Markov chains - Transition probabilities - Limiting distributions.

UNIT V QUEUEING THEORY 9 + 3

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.

TUTORIAL 15

TOTAL : 60

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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