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Digital
Library of the European Council for Modelling and Simulation |
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Title: |
Some ergodicity and truncation bounds for a small scale markovian supercomputer model |
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Authors: |
Rostislav Razumchik, Alexander Rumyantsev |
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Published in:
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(2022). ECMS 2022,
36th Proceedings DOI: http://doi.org/10.7148/2022 ISSN:
2522-2422 (ONLINE) ISSN:
2522-2414 (PRINT) ISSN:
2522-2430 (CD-ROM) ISBN: 978-3-937436-77-7 Communications of the ECMS , Volume 36, Issue 1, June 2022, Ålesund, Norway May 30th - June 3rd, 2022 |
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Citation
format: |
Rostislav Razumchik, Alexander Rumyantsev (2022). Some ergodicity and truncation bounds for a small scale markovian supercomputer model, ECMS 2022 Proceedings Edited By: Ibrahim A. Hameed, Agus Hasan, Saleh Abdel-Afou Alaliyat, European Council for Modeling and Simulation. doi:10.7148/2022-0324 |
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DOI: |
https://doi.org/10.7148/2022-0324 |
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Abstract: |
In this paper we address the transient analysis of a markovian two-server supercomputer model where customers are served by a random number of servers simultaneously. The Markov process, which described the model's evolution, is of quasi-birth-death type. It is shown that, at least under low load conditions, the logarithmic norm method can be used to obtain ergodicity bounds for the model. This allows one to solve both the stability detection problem (i.e. determine when the computations of the time-dependent performance measures can be terminated) and the truncation problem (i.e. locate the level at which the infinite system of Kolmogorov forward equations must be truncated in order to guarantee certain accuracy). An illustrative numerical example is provided. |
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