# 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.

### 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:

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

### REFERENCES :

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