JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Probability Theory & Stochastic Processes

Course Objectives

The main objectives of the course are:

• 1. To explore in the random process and queuing theory useful for Computer and communication Networks.
• 2. Understand Random variables as an intrinsic need for the analysis of random phenomena.
• 3. To understand the modeling of telecommunication networks using appropriate queuing process.
• 4. To know the need of Markov chains and queuing theory in communication networks.

Course Outcomes

Students will be able to:

• 1. Evaluate and apply moments and Characteristics functions.
• 2. Understand the concept of random process spectral density of stationary process.
• 3. Understand the concepts of Markov Chains and queuing theory.
• 4. Understand the concepts of M| M|1, M|M|1|K, M|G|1 queuing Process.

UNIT - I

Random Variable: Random Variables-Basic Definitions and properties, Sum of independent random variables, Minimum and Maximum of random variables, Comparisons between random variables, Moments of the random variables, Random variables in the field of telecommunications, Transformations of random variables-The probability generating function, the characteristic function of a pdf, The Laplace Transform of a pdf, Methods for the generation of random variables- Method of the inverse of the distribution function, Method of the transformation.

UNIT - II

Random Processes: The Random Process Concept, Concept of Stationarity and Statistical Independence, First Order Stationary Processes, Second Order and Wide Sense Stationary, (N- Order) and Strict Sense Stationarity, Time Averages and Ergodicity, Mean Ergodic Processes, Correlation Ergodic Processes, Autocorrelation Function and its Properties, Cross Correlation function and its properties, Covariance Functions, The Power Spectrum- Properties, Relationship between Power spectrum and Autocorrelation function.

UNIT - III

Markov Chains and Queuing Theory: Queues, Poisson arrival process- Sum of independent Poisson processes, Random splitting of a Poisson process, Compound Poisson processes, Birth death Markov chains, Formulation of Hidden Markov Model (HMM), building, evaluation and decoding of HMM, Notations for Queuing systems, The Little Theorem, M/M/1 queue analysis, M/M/1/K queue analysis, M/M/S queue analysis, M/M/S/S queue analysis, The M/M/∞ queue analysis, Distribution of the queuing delays in the FIFO case- M/M/1 case, M/M/S case.

UNIT - IV

M/G/1 Queuing Theory: M/G/1 queue, M/G/1 system delay distribution in the FIFO case, Laplace Transform numerical inversion method, Generalizations of the M/G/1 theory, Different imbedding instants in the M/G/1 theory, M/G/1 with geometrically distributed messages.

R19 M.TECH. SYSTEMS AND SIGNAL PROCESSING

UNIT - V

Local Area Network Analysis: Introduction, Contention based protocols- Aloha, Slotted Aloha, Aloha Protocol with ideal capture effect, CSMA Schemes, Demand assignment protocols-Polling protocol, Token passing protocol, Analysis of token and polling Schemes, R-Aloha, PRMA protocol, Comparisons between CSMA/CD and Token Protocols, Fixed assignment Protocols- FDMA, TDMA, Resource reuse in cellular systems, CDMA.

TEXTBOOKS:

• 1. Probability, Random Variables & Random Signal Principles-Peyton Z. Peebles, TMH, 4th Edition,2001.
• 2. Queuing Theory and Telecommunications Networks and Applications, Springer, Giovanni Giambene, 2014.

REFERENCES:

• 1. Probability, Random Variables and Stochastic Processes – Athanasios Papoulis, S. Unnikrishna Pillai – TMH, 2008
• 2. Probability and Random Processes with Applications to Signal Processing – Henry Stark, John W. Woods, 3rd Edition, Pearson, 2003
• 3. Probability and Stochastic Processes – A Friendly Introduction for Electrical and Computer Engineers – Roy D. Yates, David J. Goodman.2014
• 4. Digital Processing of Speech Signals. L. R Rabinar and R W Jhaung, 1978, PHI. R19 M.TECH. SYSTEMS AND SIGNAL PROCESSING M.TECH.- I YEAR- I SEMESTER SYSTEMS AND SIGNAL PROCESSING