MA 6453 PROBABILITY AND QUEUEING THEORY | syllabus

 

                    MA 6453 PROBABILITY AND QUEUEING THEORY L T P C 3 1 0 4

                                                                                                                    
OBJECTIVE:

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.

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

 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",
Springer, 3rd Edition, 2006.
2. Taha. H.A., "Operations Research", Pearson Education, Asia, 8th Edition, 2007.
3. Trivedi.K.S., "Probability and Statistics with Reliability, Queueing and Computer Science
Applications", John Wiley and Sons, 2nd Edition, 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", Wiley India Pvt. Ltd.,
Bangalore, 2nd Edition, 2012.

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