Random Processes and Queuing Theory
 
 
Subject Code: EEM3066
Aim of Subject: To develop the understanding of basic concepts and theories in signal processing, stochastic processes, detection and estimation, all of which are necessary for communications signal analysis.
Learning Outcome of Subject: At the completion of the subject, students should be able to:
  • Understand the concepts of random variables and transformation.
  • Understand the concepts of random processes and spectral analysis.
  • Understand the concepts of noise.
  • Design optimum linear systems that include Wiener filter, and matched filter.
  • Carry out optimization by parameter selection.
  • Understand the concepts of queueing theory.
  • Analyze the performance of various communication systems in the presence of noise.
Programme Outcomes:
  • Capability to communicate effectively(5%)
  • Acquisition of technical competence in specialised areas of engineering discipline(45%)
  • Ability to identify, formulate and model problems and find engineering solutions based on a systems approach(45%)
  • Ability to work independently as well as with others in a team(5%)
Assessment Scheme:
  • Tutorial / Assignment - Group assignment Focus group discussion at tutorial To enhance understanding of basic concepts in lecture (20% )
  • Test Quiz - Written exam(20% )
  • Final Exam - Written exam(60% )
Teaching and Learning Activities: 50 hours (lectures and tutorials)
Credit Hours: 3
Pre-Requisite: EEM2046: Engineering Mathematics IV
References:
  • Sim Moh Lim and Rakesh Ranjan, "Random Processes & Queueing Theory", Pearson Prentice Hall, 2003. (Textbook)
  • Peyton Z. Peebles, Jr, "Probability, Random Variables, and Random Signal Principles", McGrawHill, 2001.
  • L. Kleinrock , "Queueing System vol. 1", Wiley-Interscience, 1975.
  • Alberto Leon-Garcia, "Probability and Random Processes for Electrical Engineering", Addison Wesley 1994.
  • Athanasios Papoulis, "Probability & statistics", Englewood Cliffs, NJ., Prentice Hall, 1990.
  • Bunday, Brian D., "An introduction to queueing theory", London: Arnold, New York: Halsted Press, 1996.

Subject Contents

  • Review of Probability and Random Variable Concepts

    • Basic concepts. Conditional and total probability. Distribution and density functions. Random variables: single and multiple variables. Mean variance and moments
     
  • Random Processes

    • Basic concepts and definition. Classification of random processes. Stationary process and independence property. Autocorrelation and correlation functions. Ergodicity.
     
  • Spectral Analysis

    • Power density spectrum. Linear systems Noise modelling. Linear system response to random signal. Narrowband, bandlimited and bandpass processes. Hilbert Transforms
     
  • Optimum linear systems

    • Matched filter for white noise and coloured noise, Wiener filters, minimum mean-squared error. Optimization by parameter selection.
     
  • Queueing theory

    • Poisson points and renewals, queueing systems, birth-death systems: M/M/m/K/M, M/M/m systems, Erlang B formula, and markov processes.
     
  • Selected Topics

    • Applications of random signal theory in communications: Radar detection: false alarm probability and threshold detection probability. Performance of digital and analog communication systems.