Markov-Modulated On–Off Processes in IP Traffic Modeling

Juraj Smiesko, Martin Kontsek () and Katarina Bachrata
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Juraj Smiesko: Department of InfoComm Networks, Faculty of Management Science and Informatics, University of Zilina, 010 26 Zilina, Slovakia
Martin Kontsek: Department of InfoComm Networks, Faculty of Management Science and Informatics, University of Zilina, 010 26 Zilina, Slovakia
Katarina Bachrata: Department of Software Technologies, Faculty of Management Science and Informatics, University of Zilina, 010 26 Zilina, Slovakia

Mathematics, 2023, vol. 11, issue 14, 1-29

Abstract: 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.

Keywords: IP traffic; Markov-modulated process; regular process; Bernoulli process; distribution of gaps in the process; generation function; fast dimensioning; effective bandwidth (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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