Course

Unit 1

Selected Topics in Probability and Random Variables -Memoryless property of exponential and geometric randomVariables -Moment generating function – Laplace-Stieljes transform (LST) of random variables -Selected Topics in Stochastic Processes –Stationarity –Ergodicity –Independence –Correlation – Stationary Increment and Independent Increment Processes – Bernoulli trials – Poisson processes – Gaussian processes.

Unit 2

Markov Processes -Discrete time Markov chains (DTMCs) -Continuous time Markov chains (CTMCs) – Recurrence –Transience –Stability – Renewal Processes and Markov Renewal Processes – Queueing Theory – Common queueing models (M/M/1, M/M/1/K, M/M/K/K, M/G/1, M/G/1/K, G/M/1, Geo/Geo/1, M/G/) – Vacation models -Loss networks and delay networks -Multiclass queueing models with priority -Open and closed networks of queues.

Unit 3

Discrete-Event Simulation of Queueing Systems – Applications to Telecommunications and Computer Communication Networks -Capacity design, Dynamic channel allocation in cellular networks and telecommunication switching -Throughput and delay analysis in wireless local area networks (WLANs) -Coverage analysis in wireless sensor networks (WSNs).

• Vidyadhar G. Kulkarni, “Modeling and Analysis of Stochastic Systems”, CRC Press, 2016.
• Anurag Kumar, “Discrete EventStochastic Processes”, available online

• Dimitri P. Bertsekas, and Robert G. Gallager, “Data Networks”, PrenticeHall International, 1987.
• Alberto Leon-Garcia, “Probability, Statistics, and Random Processes for Electrical Engineering”, 3^rd ed. Pearson/Prentice Hall, 2008.

Evaluation Pattern

Objectives

• To provide a thorough understanding of the mathematical foundations of telecommunication and computer communication networks
• To teach the application of Markov processes and queueing theory to analyze the performance of and address the design questions in circuit- and packet-switching networks
• To gain hands-on experience of discrete-event simulations of queueing systems

Course Outcomes

• CO1: Able to map frequently occurring scenarios in telecommunication and computer networking into standard stochastic models, i.e., able to construct mathematical models from the physical description of the problems
• CO2: Able to identify appropriate solution methods and physically interpret themathematical results
• CO3: Able to analyze and compare the performance of queueing systems by discrete-event simulations
• CO4: Gain professional knowledge and skills by term projects

CO – PO Mapping