MA6453 PROBABILITY AND QUEUEING THEORY Syllabus Semester IV IT BTECH Anna University-Regulation-2013

MA6453                                PROBABILITY AND QUEUEING THEORY                               L  T  P  C
3   1 0 4
OBJECTIVES:
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         RANDOM VARIABLES                                                                                                  9+3
Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions.

UNIT II       TWO - DIMENSIONAL RANDOM VARIABLES                                                            9+3
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and Linear regression – Transformation of random variables.

UNIT III         RANDOM PROCESSES                                                                                               9+3
Classification – Stationary process – Markov process - Poisson process – Discrete parameter Markov chain – Chapman Kolmogorov equations – Limiting distributions.

UNIT IV       QUEUEING MODELS                                                                                                    9+3
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                                                                              9+3
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:

TOTAL (L:45+T:15): 60 PERIODS

• The students will have a fundamental knowledge of the probability concepts.
• Acquire skills in analyzing queueing models.
• It also helps to understand and characterize phenomenon which evolve with respect to time in a probabilistic manner.

TEXT BOOKS:

1. Ibe. O.C., “Fundamentals of Applied Probability and Random Processes", Elsevier, 1st Indian

Reprint, 2007.

2. Gross. D. and Harris. C.M., "Fundamentals of Queueing Theory", Wiley Student edition, 2004.

REFERENCES:

1. Robertazzi, "Computer Networks and Systems: Queueing Theory and Performance Evaluation", ,

3rd Edition, Springer, 2006.

2. Taha. H.A., "Operations Research", 8th Edition,  Pearson Education, Asia, 2007.
3. Trivedi.K.S.,  "Probability  and  Statistics  with  Reliability,  Queueing  and  Computer  Science

Applications", 2nd Edition, John Wiley and Sons, 2002.

4. Hwei Hsu, "Schaum?s Outline of Theory and Problems of Probability, Random Variables and

Random Processes", Tata McGraw Hill Edition, New Delhi, 2004.

5. Yates. R.D. and Goodman. D. J., "Probability and Stochastic Processes", 2nd Edition, Wiley India

Pvt. Ltd., Bangalore, 2012.



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