MA2262 -PROBABILITY and QUEUEING THEORY |
UNIT I RandOM VARIABLES |
Discrete and continuous random variables - Moments - Moment generating functions
and their properties. Binomial, Poisson ,Geometric ,Negative binomial, Uniform,
Exponential, Gamma, and Weibull distributions . |
UNIT II TWO DIMENSIONAL RandOM VARIABLES |
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and
regression - Transformation of random variables - Central limit theorem. |
UNIT III MARKOV PROCESSES and MARKOV CHAINS |
Classification - Stationary process - Markov process - Markov chains - Transition
probabilities - Limiting distributions-Poisson process |
UNIT IV QUEUEING THEORY |
Markovian models – Birth and Death Queuing models- Steady state results: Single and
multiple server queuing models- queues with finite waiting rooms- Finite source models-
Little’s Formula |
UNIT V NON-MARKOVIAN QUEUES and QUEUE NETWORKS |
M/G/1 queue- Pollaczek- Khintchine formula, series queues- open and closed networks |
REFERENCE |
Text Books |
1. O.C. Ibe, “Fundamentals of Applied Probability and Random Processes”,
Elsevier, 1st Indian Reprint, 2007 (For units 1, 2 and 3).
2. D. Gross and C.M. Harris, “Fundamentals of Queueing Theory”, Wiley
Student edition, 2004 (For units 4 and 5). |
Reference Books |
1. A.O. Allen, “Probability, Statistics and Queueing Theory with Computer
Applications”, Elsevier, 2nd edition, 2005.
2. H.A. Taha, “Operations Research”, Pearson Education, Asia, 8th edition,
2007.
3. K.S. Trivedi, “Probability and Statistics with Reliability, Queueing and
Computer Science Applications”, John Wiley and Sons, 2nd edition, 2002. |
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