The objective of this course is to gain insight, through the use of simple models, into the performance and dimensioning of computer systems, in particular concurrent multithreaded programs. To that aim, basic performance models are studied and used for the analysis and evaluation of programs, to understand the impact of resource sharing, conflicts, scheduling, tex. Differen modelling approaches are considered, such as Markov chains, queuing networks, stochastic Petri Nets, and simulation. Various solution methods (such as analytical, numerical and simulation) and approximations are used to evaluate these models and to understand the behaviour of the systems being investigated.

The course material is not completely fixed, but may adapted (even dynamically) to the interest and importance.

Major sequence of topics will be

- Basic probability theory, discrete and continuous distributions
- Stochastic processes, continuous time Markov chains
- Little's result and the PASTA principle
- Birth-death processes, single-queue systems (M/M/1), M/G/1 systems
- Queueing networks (Jackson systems)
- Stochastic Petri Nets
- Case studies (from books or papers)

W | Date | Time | Place | What | |
---|---|---|---|---|---|

43 | Tue | 26/10 | 13-15 | 1146 | Basic probability theory |

44 | Tue | 2/11 | 13-15 | 1146 | stochastic processes, Markov chains slides |

45 | Tue | 9/11 | 15-17 | 1146 | Markov Processes, Birth-death-processes, M/M/1 queues slides |

46 | Tue | 16/11 | 15-17 | 1146 | general queues (M/G/1), Little's law, PASTA slides |

47 | Tue | 23/11 | 13-15 | 1146 | , Queueing Networks, Jackson Networks, Closed Networks, Mean Value Analysisslides, Example (by Pan Xiaoyue) |

48 | Tue | 30/11 | 13-15 | 1146 | Problem solving session |

49 | Tue | 7/12 | 13-15 | 2344 | Stochastic Petri Nets slides (by Jonathan Linden) (see the paper M. Ajmone Marsan: Stochastic Petri Nets: an Elementary Introduction, which is referenced below) |

50 | Tue | 14/12 | 13-15 | no | Cancelled (no meeting) |

51 | Tue | 21/12 | 13-15 | no | Cancelled |

Here is more detail about what will be/has been covered in each lecture (each bullet should be approximately one lecture).

- Basic probability theory, including:
Probability spaces,
Conditional probability and independence,
Random variables (discrete and continuous),
pdf (probability mass/density function),
cdf (cumulative distribution function),
Conditional random variables,
Independence of random variable,
Expected Value,
Variance,
laws for addition and multiplication,
SOME COMMON Distributions:
Bernoulli Distribution,
Binomial Distribution,
Negative Binomial distribution,
Geometric Distribution,
Possion Distribution,
Exponential Distribution.

**Material:**I will use the structure of the first lecture from Hillston's course, extended with the slides of Virtamo (first 3 lectures), but skip the material on generating functions. - Stochastic processes, Markov Chains, transient and stable properties of Markov chains, balance equations, birth-death-processes,

Here are some random exercises, which you can do (or find others)

- B.R. Haverkort, Performance of Computer Communication Systems, John Wiley & Sons, 1998. For sale in the Campus bookstore
- Gross, harris: Fundamentals of Queueing Theory

- Lecture Notes on Probability Theory and Random Processes, by Jean
Walrand, Department of Electrical Engineering and Computer Sciences,
University of California, Berkeley, CA 94720. August 25, 2004

http://walrandpc.eecs.berkeley.edu/126notes.pdf
This is a very nice to read personal introduction to the topic.
- Introduction to Queueing Theory and Stochastic Teletraffic Models, by Moshe Zukerman. 2008. 165 pp.

- Performance Modeling given by Jane Hilsson, Univ. Edinburgh. This is a good, short introduction aiming to present Process algebra for Performance analysis
- Jorma Virtamo, Lecture Notes on Queueing
- M. Ajmone Marsan: Stochastic Petri Nets: an Elementary Introduction
- (this list is to be extended)