Stochastic Discrete Event Systems
| Numbering Code |
U-ENG29 39096 LJ10 U-ENG29 39096 LJ55 |
Year/Term | 2022 ・ First semester | |
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| Number of Credits | 2 | Course Type | Lecture | |
| Target Year | Target Student | |||
| Language | Japanese | Day/Period | Tue.2 | |
| Instructor name |
HONDA JUNYA (Graduate School of Informatics Associate Professor) TANAKA TOSHIYUKI (Graduate School of Informatics Professor) |
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| Outline and Purpose of the Course | In the analysis of stochastic discrete event systems, the theoretical results on Markov chains are useful mathematical tools. This course covers the fundamental results of Markov chains and their applications to ranking/rating methods and to the analysis methods of basic queuing models. | |||
| Course Goals | This course aims to deepen the understanding of the fundamental results of Markov chains and their applications. | |||
| Schedule and Contents |
Outline of this course and review of fundamental notions,1?2times,The contents of this course are outlined. Furthermore, basic notions, such as random variables, probability distributions and generating function methods, are explained. Discrete-time Markov chains,3?4times,The discrete-time Markov chain is introduced. Topics include the basic notions of the Markov chain, such as irreducibility, period, and recurrence, as well as the condition for the existence of its stationary and limiting distributions. Markov methods for ranking/rating,2～3times,Markov methods for ranking/rating are lectured, focusing on the group of web pages. Continuous-time Markov chains,3～4times,The Poisson process and continuous-time Markov chain are introduced. Furthermore, the properties of a birth-and-death process (a special case of the continuous-time Markov chain) are explained, together with the derivation of its stationary distribution. Exponential-type queueing models,2～3times,Exponential-type queueing models (which are reduced to birth-and-death processes) are lectured, focusing on the derivation of their performance measures, such as the stationary queue length distribution and the waiting time distribution. |
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| Evaluation Methods and Policy | Based on the scores of the term examination. | |||
| Course Requirements | Background knowledge on probability and statistics is helpful to learn this course but it is not prerequisite. | |||
| Textbooks | Textbooks/References | Handouts are provided. | ||
| References, etc. |
P. Bremaud, Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, Springer, 1999. isbn{}{9780387985091} L. Kleinrock, Queueing Systems Vol.1, John Wiley and Sons, 1975. isbn{}{9780471491101} |
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