Probability and Statistical Methods (EK500)
- Develop a solid foundation in probability theory and random processes.
- Learn fundamental modeling and analysis techniques for stochastic systems so you can use them in applications found in various Engineering disciplines, Operations Research, and Computer Science.
- Develop the ability to read technical journals and learn more advanced material based on random processes.
FOUNDATIONS OF PROBABILITY THEORY
- Basic concepts (sample space, event space, probability space)
- Probability measures and probability functions
- Discrete and continuous probability spaces
- Dependent and independent events, conditional probability
- Probability distribution and density functions
- Functions of random variables
- Expectation, moments, characteristic functions
- Sequences of random variables, convergence, laws of large numbers and central limit theorem
- Random process properties (stationarity, ergodicity, correlation)
- Spectral analysis, random process transformations
- Special random processes used in modeling: Gaussian, Poisson, Markov; applications
- Introduction to Estimation
Discrete Event and Hybrid Systems (SE/EC/ME733)
- Learn about Discrete Event Systems (DES) and their applications, as well as recently emerging Hybrid Systems (HS) that combine both continuous (time-driven) and discrete (event-driven) dynamics.
- Develop the ability to conceptualize cutting-edge issues in the DES and HS domain, and formulate problems for potential research purposes.
REVIEW OF SYSTEM THEORY FUNDAMENTALS
- Basic concepts
- Time-driven vs. event-driven systems
- Examples of Discrete Event Systems (DES): computer systems; communication networks; automated manufacturing; traffic systems
- The queueing system model.
UNTIMED MODELS OF DISCRETE-EVENT SYSTEMS.
- State Automata
- Petri Nets
- Analysis: stability, reachability, deadlocks.
TIMED MODELS OF DISCRETE-EVENT SYSTEMS.
- Timed State Automata
- Timed Petri Nets
- Review of probability theory and stochastic processes
- Stochastic Timed State Automata
- The Poisson counting process and Markov chain models
INTRODUCTION TO DISCRETE EVENT (MONTE-CARLO) SIMULATION
- Basic concepts in discrete event simulation
- Model construction and applications
- Introduction to estimation theory
MARKOV DECISION PROCESSES
- Dynamic Programming
- Solving resource contention problems: admission control,routing, scheduling
Introduction to Cyber-Physical Systems