Testing the Semi Markov Model Using Monte Carlo Simulation Method for Predicting the Network Traffic

Shirin Kordnoori; Hamidreza Mostafaei; Shaghayegh Kordnoori; Mohammadmohsen Ostadrahimi

doi:10.18187/pjsor.v16i4.3394

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Testing the Semi Markov Model Using Monte Carlo Simulation Method for Predicting the Network Traffic

Author(s)

Shirin Kordnoori Department of Computer Engineering-Artificial Intelligence, North Tehran Branch, Islamic Azad University, Tehran, Iran

Hamidreza Mostafaei Department of Statistics, North Tehran Branch, Islamic Azad University, Tehran, Iran

Shaghayegh Kordnoori Ph.D. of Statistics, IRAN Telecommunication Research Center (ITRC), Tehran, Iran

Mohammadmohsen Ostadrahimi Department of Mathematics, North Tehran Branch, Islamic Azad University,Tehran, Iran

Abstract

Semi-Markov processes can be considered as a generalization of both Markov and renewal processes. One of the principal characteristics of these processes is that in opposition to Markov models, they represent systems whose evolution is dependent not only on their last visited state but on the elapsed time since this state. Semi-Markov processes are replacing the exponential distribution of time intervals with an optional distribution. In this paper, we give a statistical approach to test the semi-Markov hypothesis. Moreover, we describe a Monte Carlo algorithm able to simulate the trajectories of the semi-Markov chain. This simulation method is used to test the semi-Markov model by comparing and analyzing the results with empirical data. We introduce the database of Network traffic which is employed for applying the Monte Carlo algorithm. The statistical characteristics of real and synthetic data from the models are compared. The comparison between the semi-Markov and the Markov models is done by computing the Autocorrelation functions and the probability density functions of the Network traffic real and simulated data as well. All the comparisons admit that the Markovian hypothesis is rejected in favor of the more general semi Markov one. Finally, the interval transition probabilities which show the future predictions of the Network traffic are given.

Publication Details

Page(s) 713-720

DOI 10.18187/pjsor.v16i4.3394

Published Journal: Pakistan Journal of Statistics and Operation Research, Volume: 16, Issue: 4, Year: 2020

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Keywords

Monte Carlo simulation, Synthetic time series, Hypothesis test, Semi-Markov processes, Network Traffic

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