Discrete and continuous random variables - Moments - Moment generating functions and their properties. Binomial, Poisson ,Geometric ,Negative binomial, Uniform, Exponential, Gamma, and Weibull distributions .
TWO DIMENSIONAL RANDOM VARIABLES
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.
MARKOV PROCESSES AND MARKOV CHAINS
Classification - Stationary process - Markov process - Markov chains - Transition probabilities - Limiting distributions-Poisson process
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
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.