# MA8402 PROBABILITY AND QUEUING THEORY NOTES 2017 REGULATION

__MA8402 PROBABILITY AND QUEUING THEORY NOTES 2017 REGULATION__

In this post we have posted some notes on

**MA8402 PROBABILITY AND QUEUING THEORY**for**ANNA UNIVERSITY AFFILIATED COLLEGES STUDENTS**.Here We have listed the the notes whichever we could collect for

**MA8402 PROBABILITY AND QUEUING THEORY**subject, We think that it will be helpful for your exam preparation.__OBJECTIVES__:

- To provide necessary basic concepts in probability and random processes for applications such as random signals, linear systems in communication engineering.
- To understand the basic concepts of probability, one and two dimensional random
- variables and to introduce some standard distributions applicable to engineering which can describe real life phenomenon.
- To understand the basic concepts of random processes which are widely used in IT fields.
- To understand the concept of queueing models and apply in engineering.
- To understand the significance of advanced queueing models.
- To provide the required mathematical support in real life problems and develop probabilistic models which can be used in several areas of science and engineering.

#### UNIT I PROBABILITY AND RANDOM VARIABLES

Probability – Axioms of probability – Conditional probability – Baye‘s theorem – Discrete and

continuous random variables – Moments – Moment generating functions – Binomial, Poisson,

Geometric, Uniform, Exponential and Normal distributions.

#### UNIT II TWO – DIMENSIONAL RANDOM VARIABLES

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

regression – Transformation of random variables – Central limit theorem (for independent and

identically distributed random variables).

#### UNIT III RANDOM PROCESSES

Classification – Stationary process – Markov process – Poisson process – Discrete parameter

Markov chain – Chapman Kolmogorov equations – Limiting distributions.

#### UNIT IV QUEUEING MODELS

Markovian queues – Birth and death processes – Single and multiple server queueing models –

Little‘s formula – Queues with finite waiting rooms – Queues with impatient customers : Balking

and reneging.

#### UNIT V ADVANCED QUEUEING MODELS

Finite source models – M/G/1 queue – Pollaczek Khinchin formula – M/D/1 and M/EK/1 as special

cases – Series queues – Open Jackson networks.

### TOTAL : 60 PERIODS

__OUTCOMES__:

Upon successful completion of the course, students should be able to:

- Understand the fundamental knowledge of the concepts of probability and have knowledge
- of standard distributions which can describe real life phenomenon.
- Understand the basic concepts of one and two dimensional random variables and apply in
- engineering applications.
- Apply the concept of random processes in engineering disciplines.
- Acquire skills in analyzing queueing models.
- Understand and characterize phenomenon which evolve with respect to time in a
- probabilistic manner

__TEXTBOOKS__:

- Gross, D., Shortle, J.F, Thompson, J.M and Harris. C.M., ―Fundamentals of Queueing Theory”, Wiley Student 4th Edition, 2014.
- Ibe, O.C., ―Fundamentals of Applied Probability and Random Processes”, Elsevier, 1st Indian Reprint, 2007.

__REFERENCES__ :

- Hwei Hsu, “Schaum‘s Outline of Theory and Problems of Probability, Random Variables and Random Processes”, Tata McGraw Hill Edition, New Delhi, 2004.
- Taha, H.A., “Operations Research”, 9th Edition, Pearson India Education Services, Delhi, 2016.
- Trivedi, K.S., “Probability and Statistics with Reliability, Queueing and Computer Science Applications”, 2nd Edition, John Wiley and Sons, 2002.
- Yates, R.D. and Goodman. D. J., “Probability and Stochastic Processes”, 2nd Edition, Wiley India Pvt. Ltd., Bangalore, 2012.

__MA8402 PROBABILITY AND QUEUING THEORY NOTES __

If you have any queries or comments on this post, kindly contact us through contact form or telegram

To contact us through telegram – Click here