Markov-Modulated On–Off Processes in IP Traffic Modeling
This paper deals with the modeling of real IP flows using Markov-modulated On–Off processes. In the first section of the paper, we summarize the knowledge found so far about the Markov modulated On–Off regular process model, which has already been published in our previous papers. For the sake of co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/14/3089 |
| _version_ | 1797588408848089088 |
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| author | Juraj Smiesko Martin Kontsek Katarina Bachrata |
| author_facet | Juraj Smiesko Martin Kontsek Katarina Bachrata |
| author_sort | Juraj Smiesko |
| collection | DOAJ |
| description | This paper deals with the modeling of real IP flows using Markov-modulated On–Off processes. In the first section of the paper, we summarize the knowledge found so far about the Markov modulated On–Off regular process model, which has already been published in our previous papers. For the sake of completeness, we also summarize the well-known facts regarding the Bernoulli process. In the second section, we deal with the continuation of modeling using the Markov-modulated On–Off Bernoulli process. Our own derivation of the hitherto-unknown probability distribution of time spaces (tail distribution) is completely new. For its derivation, we used the tail distribution generating function, and then, using its derivation, we calculated the hitherto-unknown moments of the distribution (mean, variation, and third initial moment). This knowledge will allow us to create a new numerical procedure for estimating MMBP parameters from measured IP traffic. Finally, we present a formula for the sizing of network resources for a given flow using effective bandwidth with respect to QoS based on a given level of IP traffic. |
| first_indexed | 2024-03-11T00:51:33Z |
| format | Article |
| id | doaj.art-2e092c8c2b114ba5a211643c508e8c3b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:51:33Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2e092c8c2b114ba5a211643c508e8c3b2023-11-18T20:20:23ZengMDPI AGMathematics2227-73902023-07-011114308910.3390/math11143089Markov-Modulated On–Off Processes in IP Traffic ModelingJuraj Smiesko0Martin Kontsek1Katarina Bachrata2Department of InfoComm Networks, Faculty of Management Science and Informatics, University of Zilina, 010 26 Zilina, SlovakiaDepartment of InfoComm Networks, Faculty of Management Science and Informatics, University of Zilina, 010 26 Zilina, SlovakiaDepartment of Software Technologies, Faculty of Management Science and Informatics, University of Zilina, 010 26 Zilina, SlovakiaThis paper deals with the modeling of real IP flows using Markov-modulated On–Off processes. In the first section of the paper, we summarize the knowledge found so far about the Markov modulated On–Off regular process model, which has already been published in our previous papers. For the sake of completeness, we also summarize the well-known facts regarding the Bernoulli process. In the second section, we deal with the continuation of modeling using the Markov-modulated On–Off Bernoulli process. Our own derivation of the hitherto-unknown probability distribution of time spaces (tail distribution) is completely new. For its derivation, we used the tail distribution generating function, and then, using its derivation, we calculated the hitherto-unknown moments of the distribution (mean, variation, and third initial moment). This knowledge will allow us to create a new numerical procedure for estimating MMBP parameters from measured IP traffic. Finally, we present a formula for the sizing of network resources for a given flow using effective bandwidth with respect to QoS based on a given level of IP traffic.https://www.mdpi.com/2227-7390/11/14/3089IP trafficMarkov-modulated processregular processBernoulli processdistribution of gaps in the processgeneration function |
| spellingShingle | Juraj Smiesko Martin Kontsek Katarina Bachrata Markov-Modulated On–Off Processes in IP Traffic Modeling Mathematics IP traffic Markov-modulated process regular process Bernoulli process distribution of gaps in the process generation function |
| title | Markov-Modulated On–Off Processes in IP Traffic Modeling |
| title_full | Markov-Modulated On–Off Processes in IP Traffic Modeling |
| title_fullStr | Markov-Modulated On–Off Processes in IP Traffic Modeling |
| title_full_unstemmed | Markov-Modulated On–Off Processes in IP Traffic Modeling |
| title_short | Markov-Modulated On–Off Processes in IP Traffic Modeling |
| title_sort | markov modulated on off processes in ip traffic modeling |
| topic | IP traffic Markov-modulated process regular process Bernoulli process distribution of gaps in the process generation function |
| url | https://www.mdpi.com/2227-7390/11/14/3089 |
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