WELCOME. SUBJECT CODE - MA1252 SUBJECT - PROBABILITY AND SUBJECT CODE - MA1252 SUBJECT - PROBABILITY AND QUEUEING THEORY.

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Presentation transcript:

WELCOME

SUBJECT CODE - MA1252 SUBJECT - PROBABILITY AND SUBJECT CODE - MA1252 SUBJECT - PROBABILITY AND QUEUEING THEORY

OBJECTIVES  By the end of this paper, the student should be able to:  Recognize and understand Probability distribution functions, in general.  Calculate and interpret expected values.  Recognize the probability distribution and apply it appropriately.  Recognize the joint probability distribution and apply it appropriately (optional).  Recognize the queues and queueing network apply it appropriately (optional).

TEACHING PLAN UNIT-I - 14 HRS UNIT-II - 12 HRS UNIT-III - 13 HRS UNIT-IV - 14 HRS UNIT-V - 14 HRS TOTAL - 67 HRS

UNIT-I RANDOM VARIABLE & DISTRIBUTION FUNCTION UNIT-I RANDOM VARIABLE & DISTRIBUTION FUNCTION  RANDDOM VARIABLE  CONTINUOUS RANDOM VARIABLE  PROBABILITY DENSITY FUNCTION  CUMULATIVE DISTRIBUTION FUNCTION  DISCRETE RANDOM VARIABLE  PROBABILITY DISTRIBUTION FUNCTION  CUMULATIVE DISTRI BUTION FUNCTION  MOMENT GENERATING FUNCTION  PROPERTIES

DISTRIBUTION FUNCTION  BINOMIAL  GEOMETRIC  NEGATIVE BINOMIAL  UNIFORM  EXPONENTIAL  GAMMA  WEIBULL

UNIT-II TWO DIMENSIONAL R.V’S UNIT-II TWO DIMENSIONAL R.V’S  TWO DIMENSIONAL RANDOM VARIABLES  JOINT PROBABILITY DISTRIBUTION  MARGINAL PROBABILITY DISTRIBUTION  COVARIANCE  CORRELATION AND REGRESSION  TRANSFORMATION OF RANDOM VARIABLES  CENTRAL LIMIT THEOREM

UNIT-III MARKOV PROCESSES & MARKOV CHAIN UNIT-III MARKOV PROCESSES & MARKOV CHAIN  RANDOM PROCESSES  STATIONARY PROCESSES  MARKOV CHAIN  KOLMOGROV DIFFERENTIAL EQUATION  TRANSISTION PROBABILITY  POISSON PROCESSES

UNIT-IV QUEUEING THEORY  MARKOVIAN MODELS  SIMPLE QUEUE  KENDALL’S NOTATION  SINGLE SERVER QUEUEING MODEL  MULTI SERVER QUEUEING MODEL  FINITE SOURCE QUEUEING MODEL

SIMPLE QUEUE

MULTIPLEQUEUE MULTIPLE QUEUE

UNIT-V NON-MARKOVIAN QUEUE & QUEUE NETWORK  NON-MARKOVIAN QUEUEING MODEL  POLLACZEK-KHINTCHINE FORMULA  QUEUEING NETWORK  OPEN QUEUEING NETWORK  CLOSED QUEUEING NETWORK

CLOSED QUEUEING NETWORK

OPEN QUEUEING NETWORK

TEXT & REFERENCE BOOKS:

THANK YOU