Principal lecturer:
Students:
Part II CST 75%
Term:
Lent term
Course code:
CSM
Prerequisite course:
Hours:
16
Class limit:
20
- Overview of computer systems modeling using both analytic techniques and simulation.
- Stochastic processes (builds on starred material in Foundations of Data Science)
- Discrete and continuous stochastic processes.
- Markov processes and Chapman-Kolmogorov equations.
- Discrete time Markov chains.
- Ergodicity and the stationary distribution.
- Continuous time Markov chains.
- Birth-death processes, flow balance equations.
- The Poisson process.
- Queueing theory
- The M/M/1 queue in detail.
- The equilibrium distribution with conditions for existence and common performance metrics.
- Extensions of the M/M/1 queue: the M/M/k queue, the M/M/infinity queue.
- Queueing networks. Jacksonian networks.
- The M/G/1 queue.
- Signals, systems, and transforms
- Discrete- and continuous-time convolution.
- Signals. The complex exponential signal.
- Linear Time-Invariant Systems. Modeling practical systems as an LTI system.
- Fourier and Laplace transforms.
- Control theory.
- Controlled systems. Modeling controlled systems.
- State variables. The transfer function model.
- First-order and second-order systems.
- Feedback control. PID control.
- Stability. BIBO stability. Lyapunov stability.
- Introduction to Model Predictive Control.
- Introduction to discrete event simulation.
- Simulation techniques
- Random number generation methods
- Statistical aspects: confidence intervals, stopping criteria
- Variance reduction techniques.
Objectives
At the end of the course students should
- Be aware of different approaches to modeling a computer system; their pros and cons
- Understand the concept of a stochastic process and how they arise in practice
- Be able to build simple Markov models and understand the critical modelling assumptions
- Be able to solve simple birth-death processes
- Understand and use M/M/1 queues to model computer systems
- Be able to model a computer system as a linear time-invariant system
- Understand the dynamics of a second-order controlled system
- Design a PID control for an LTI system
- Understand what is meant by BIBO and Lyapunov stability
- Be aware of the issues in building a simulation of a computer system and analysing
the results obtained
Assessment
There will be three in-person assessments for the course: Stochastic processes and Queueing theory: 45%; Signals, Systems, Transforms, and Control Theory: 45%; Simulation: 10%.
Reference books
- Keshav, S. (2012)*. Mathematical Foundations of Computer Networking. Addison-Wesley.
- Kleinrock, L. (1975). Queueing systems, vol. 1. Theory. Wiley.
- Kraniauskas, Peter. Transforms in signals and systems. Addison-Wesley Longman, 1992.
- Jain, R. (1991). The art of computer systems performance analysis. Wiley.