MA2262 PROBABILITY AND QUEUEING THEORY
(Common to CSE & IT)
AIM
The probabilistic models are employed in countless applications in all areas of science and engineering. Queuing theory provides models for a number of situations that arise in real life. The course aims at providing necessary mathematical support and confidence to tackle real life problems.
OBJECTIVES
At the end of the course, the students would
• Have a well – founded knowledge of standard distributions which can describe real life phenomena.
• Acquire skills in handling situations involving more than one random variable and functions of random variables.
• Understand and characterize phenomena which evolve with respect to time in a probabilistic manner.
• Be exposed to basic characteristic features of a queuing system and acquire skills in analyzing queuing models.
UNIT I RANDOM VARIABLES 9+3
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 9+3
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.
UNIT III MARKOV PROCESSES AND MARKOV CHAINS 9+3
Classification - Stationary process - Markov process - Markov chains - Transition probabilities - Limiting distributions-Poisson process
UNIT IV QUEUEING THEORY 9+3
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 9+3
M/G/1 queue- Pollaczek- Khintchine formula, series queues- open and closed networks
TUTORIAL 15 TOTAL : 60 PERIODS
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).
REFERENCES:
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.
(Common to CSE & IT)
AIM
The probabilistic models are employed in countless applications in all areas of science and engineering. Queuing theory provides models for a number of situations that arise in real life. The course aims at providing necessary mathematical support and confidence to tackle real life problems.
OBJECTIVES
At the end of the course, the students would
• Have a well – founded knowledge of standard distributions which can describe real life phenomena.
• Acquire skills in handling situations involving more than one random variable and functions of random variables.
• Understand and characterize phenomena which evolve with respect to time in a probabilistic manner.
• Be exposed to basic characteristic features of a queuing system and acquire skills in analyzing queuing models.
UNIT I RANDOM VARIABLES 9+3
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 9+3
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.
UNIT III MARKOV PROCESSES AND MARKOV CHAINS 9+3
Classification - Stationary process - Markov process - Markov chains - Transition probabilities - Limiting distributions-Poisson process
UNIT IV QUEUEING THEORY 9+3
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 9+3
M/G/1 queue- Pollaczek- Khintchine formula, series queues- open and closed networks
TUTORIAL 15 TOTAL : 60 PERIODS
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).
REFERENCES:
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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