| Presentation | 2010-12-16 Ergodic Markov Chain and Its Implication in Performance Evaluation of Network Systems Shoji KASAHARA, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In ergodic stochastic processes, the time-dependent state probability converges to the limiting probability, independently of initial distributions, and the limiting probability is eventually equal to the steady-state probability. Ergodic Markov chains have the ergodicity, and ergodic Markov chain is a fundamental theory for performance evaluation of computer/communication network systems. In most of elementary books for performance evaluation of computer/communication network systems, the system of differential-difference equations for state probabilities are considered first, and then those equations are simplified to difference equations by assuming that the system is in steady state or in equilibrium. In this approach, however, it is not clear why we can consider the system in steady state, and even the notion of steady state may be vague. The notion of steady state is important for Monte Carlo simulation experiments to obtain accurate estimates of performance measures. In this tutorial, fundamentals of ergodic Markov chain with finite states, such as steady state probabilities, limiting probabilities, and the convergence of time-dependent state probabilities, are presented. In addition, some remarks on discrete-event simulation are also provided. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Ergodic Markov chain / steady state probability / limiting probability / discrete-event simulation / network system / performance evaluation |
| Paper # | NS2010-125,RCS2010-179 |
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| Conference Information | |
| Committee | NS |
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| Conference Date | 2010/12/9(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Network Systems(NS) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Ergodic Markov Chain and Its Implication in Performance Evaluation of Network Systems |
| Sub Title (in English) | |
| Keyword(1) | Ergodic Markov chain |
| Keyword(2) | steady state probability |
| Keyword(3) | limiting probability |
| Keyword(4) | discrete-event simulation |
| Keyword(5) | network system |
| Keyword(6) | performance evaluation |
| 1st Author's Name | Shoji KASAHARA |
| 1st Author's Affiliation | Graduate School of Informatics, Kyoto University() |
| Date | 2010-12-16 |
| Paper # | NS2010-125,RCS2010-179 |
| Volume (vol) | vol.110 |
| Number (no) | 339 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |