Unit-I
Introduction: Probability models, Algebra of events, probability axioms, conditional probability, Baye’s rules, Bernoulli traits.
Discrete Random Variables: Discrete random variables, probability mass functions, discrete distribution functions-Bernoulli, Binomial, geometric, Poisson, hyper geometric & uniform distributions, probability generating function.
Unit-II
Continuous Random variable: Exponential distribution, memory less property, application to reliability, hypo exponential, Erlang, Gamma, hyper exponential & Normal distributions ,order statistics, distribution of sums.
Unit III
Expectation: Expectation, variance, moments of important distribution, Expectation of functions of more than one random variable, Application to the computation of MTTF of series system parallel system, standby redundancy, TMR & NMR system.
Unit IV
Stochastic process: classification of stochastic process, Markov process, Bernoulli process, Poisson process , renewal processes.
Discrete Parameter Markov Chains: Computation of n-step transition probability, state classification & limiting distribution of times between state changes irreducible finite chains with aperiodic states, discrete parameter birth-death processes, Analysis of program execution time, M|G|1 , Queue, pollackek-khinchin formula.
Unit-V
Continuous parameter Markov chains
Birth & death process, M|M|1 Queue, M|M|m Queue, cyclic Queuing model of a multiprogramming system, Machine repairman model, computation of response time in a terminal oriented system. Queuing system with finite populations.
Networks of queues: Introductory concept of open & closed queuing networks.
References:
P.K.S Trivedi,-Probability and Statistics with reliability,
Queuing and computer science applications, PHI, New Delhi
Hisashi Kobayashi: Modeling and Analysis-An Introduction to system performance Evalution Methodology,” Addison Wesley
W.feller-An introduction to probability theory & its application (vol1.)(John Wiley & sons, NY.)
U.N.Bhat-Elements of applied stochastic processes, John Wiley & sons, NY.
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