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University: Ryerson University
Name of sponsoring Professor: Dr. Bobby Ma
Department: Department of Electrical and Computer Engineering

Teaching: CN8814 Network Mathematics and Simulations

COURSE DESCRIPTION

This course provides foundations in probability and random processes, and develops the understanding of Markov processes and the simulation of Markov Chains. The course also covers queuing systems and applications of queueing systems to traffic management in a network. The course will conclude with a discussion of basic simulation and modeling techniques. The course project will involve the simulation and performance analysis of a computer communications network using OPNET.

MAJOR TOPICS:

·         Probability Theory and Random Processes (6 hours)

Review of probability theory: axioms, random variables, expected values, transforms, and limit theorems. Random processes: introduction, definition and characteristics of random processes, stationary and wide-sense stationary processes, ergodicity, autocorrelation functions.

·         Markov Processes (6 hours)

Discrete-time Markov chains, continuous-time Markov chains, birth-death processes.

·         Queuing Systems (12 hours)

Arrival rates and traffic load definitions, basic queueing models: arrival processes, service times, queueing system classifications: M/M/1, M/M/m, etc. models.

·         Traffic Management (6 hours)

Traffic Management and QoS, differentiated services, queue scheduling disciplines, priority queueing, fair queueing, weighted fair queueing, custom queueing, queue memory management, traffic regulation. 

·         Simulation and Modeling Techniques (3 hours)

Random number generators, general approaches to generating random sequences, testing random number generators, estimation of performance measures from simulation, quality of an estimator: bias, variance and confidence interval.  Monte Carlo simulation, modeling techniques and examples.

RECOMMENDED TEXTS:

·         L. Kleinrock, Queueing Systems, Volume 1: Theory, John Wiley & Sons, 1975.

·         J. Walrand and P. Varaiya, High Performance Communication Networks, 2^nd Edition, Morgan Kaufmann, 2000.

·         A. Leon-Garcia and I. Widjaja, Communication Networks, 2^nd Edition, McGraw Hill, 2004.

PROJECT:

The course project will involve the simulation and performance analysis of a computer network using OPNET.  Additional information about the project will be provided.  Please note there will be an OPNET tutorial by A. Taranenko.  The tutorial will be presented in two parts and is scheduled for Friday, January 18 and Friday, January 25 starting at 5:00 pm.

COURSE EVALUATION:

OPNET Technologies, Inc. is a leading provider of solutions for managing networks and applications. OPNET's best-in-class solutions address application troubleshooting, application monitoring, network monitoring, network configuration management, capacity management, and network simulation. OPNET’s solutions have been operationally proven in thousands of customer environments worldwide, including corporate and government enterprises, government and defense agencies, network service providers, and network equipment manufacturers. For more information about OPNET and its products, visit www.opnet.com.