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You are here:Open notes-->VTU-->STOCHASTIC-MODELS-AND-APPLICATIONS-10CS665-

**STOCHASTIC MODELS AND APPLICATIONS 10CS665 **

# How to study this subject

Subject Code: 10CS665 I.A. Marks : 25

Hours/Week : 04 Exam Hours: 03

Total Hours : 52 Exam Marks: 100

PART A

**UNIT 1 6 Hours**

Introduction 1: Axioms of probability; Conditional probability and

independence; Random variables; Expected value and variance; MomentGenerating

Functions and Laplace Transforms; conditional expectation;

Exponential random variables.

**UNIT 2 6 Hours**

Introduction 2: Limit theorems; Examples: A random graph; The

Quicksort and Find algorithms; A self-organizing list model; Random

permutations.

**UNIT 3 7 Hours**

Probability Bounds, Approximations, and Computations: Tail probability

inequalities; The second moment and conditional expectation inequality;

probability bounds via the Importance sampling identity; Poisson random

variables and the Poisson paradigm; Compound Poisson random variables.

**UNIT 4 7 Hours**

Markov Chains: Introduction; Chapman-Kologorov Equations;

Classification of states; Limiting and stationary probabilities; some 62

applications; Time-Reversible Markov Chains; Markov Chain Monte Carlo

methods.

PART B

**UNIT 5 6 Hours**

The Probabilistic Method: Introduction; Using probability to prove

existence; Obtaining bounds from expectations; The maximum weighted

independent set problem: A bound and a ranom algorithm; The set covering

problem; Antichains; The Lovasz Local lemma; A random algorithm for

finding the minimal cut in a graph.

**UNIT 6 6 Hours**

Martingales: Martingales: Definitions and examples; The martingale

stopping theorem; The Hoeffding-Azuma inequality; Sub-martingales.

**UNIT 7 7 Hours**

Poisson Processes, Queuing Theory 1: The non-stationary Poisson

process; The stationary Poisson process; Some Poisson process

computations; Classifying the events of a non-stationary Poisson process;

Conditional distribution of the arrival times

Queuing Theory: Introduction; Preliminaries; Exponential models

**UNIT 8 7 Hours**

Queuing Theory 2: Birth-and-Death exponential queuing systems; The

backwards approach in exponential queues; A closed queuing network; An

open queuing network; The M/G/1 queue; Priority queues.

**Text Books:**

1. Sheldon M. Ross: Probability Models for Computer Science,

Elsevier, 2002.

**Reference Books:**

1. B. R. Bhat: Stochastic Models Analysis and Applications, New Age

International, 2000.

2. Scott L. Miller, Donald G. Childers: Probability and Random

Processes with Applications to Signal Processing and

Communications, Elsevier, 2004.

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