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MA6453 / MA2262 Probability and Queueing Theory Scanned Lecture Notes - Kamalapriya
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Anna University , Chennai
Department of B.E-Computer Science and Engg
Fourth Semester
MA6453 / MA2262 Probability and Queueing Theory
Scanned Lecture Notes (All Units)
(Regulation 2013 / 2008)
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Syllabus :

UNIT-1

RANDOM VARIABLES
UNIT-2
TWO DIMENSIONAL RANDOM VARIABLES
UNIT-3
RANDOM PROCESSES / MARKOV PROCESS AND MARKOV CHAIN
UNIT-4
QUEUEING MODELS / THEORY
UNIT-5
ADVANCED QUEUEING MODELS / NON-MARKOVIN MODELS AND NETWORK MODELS

Content :
UNIT-1
RANDOM VARIABLES
1. Deterministic
2. Random
Sample space
Types of random variables
1. Discrete rv
2. Continuous rv
Probability mass function
Probability density function
Cumulative distribution function
Probability distribution
Mathematical expectation
Moment about origin
Moment about mean
Binomial distribution
Poisson distribution
Geometric distribution
Exponential distribution
Wribull distribution

UNIT-2
TWO DIMENTIONAL RANDOM VARIABLES
Discrete random variable
Marginal distribution
Conditional probability
Two dimensional continuous RV
Marginal PDF
Correlation
Correlation co efficient
Procedure
Correlation coefficient if table value is given
Regression
Transformation of one RV
Transformation of two RV
Central limit theorem
Liapounoff’s form
Lindberg-levy’s form

UNIT-3
MARKOV PROCESSES AND MARKOV CHAIH
Random process
Classification of random process
1. Discrete random sequence
2. Discrete random processs
3. Continuous random sequence
Auto correlation
Stationary random process
First order stationary
Second order stationary process
Wide sense stationary
Markov process
Poisson process
Probability law of poisson process
Mean of poisson process
Varience of poisson process

UNIT 4
QUEUEUING THEORY
Queue
Characteristics of queueing system
1. Input or arrival pattern
2. Service pattern
3. No of service channel System
4. Capacity
5. Queue discipline
Kendall’s notation of a queueing system

UNIT-5
NON MORKOVIAN QUEUES AND QUEUE NETWORK
Queue network
1. Open queueing network
2. Closed queueing network
Series queues
Two stage series queues
Series queue with blocking
Open Jackson network

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