Possibility of fractional calculus application for telecommunication traffic modelling
Branka D. Mikavica, Aleksandra M. Kostic-Ljubisavljevic, Vesna Radonjić-Đogatović · Vojnotehnicki glasnik · 2015
Fractional calculus is a field of mathematical analysis concerned with research and application of derivatives and integrals of an arbitrary order. Many famous mathematicians studied the theory of fractional calculus such as Euler, Riemann, Liouville, Abel, Fourier and others. There are many proposed definitions for calculating derivatives and integrals of non-integer order. In this paper, several proposed definitions along with basic statements of fractional calculus are presented with an emphasis on a possibility of fractional calculus application in telecommunication traffic modelling. The fact is that fractional calculus is widely used in various scientific disciplines in recent decades. Models based on fractional calculus have proved to be very useful in physics, mechanics, electrical engineering, biochemistry, medicine, economy, and probability theory. This paper analyses a possibility of application of fractional calculus for modelling telecommunication traffic. Many research studies have shown that traffic characteristics at a local and global level, such as self-similarity and long range dependence, can efficiently be described by fractional calculus instead of using conventional stochastic processes. Some proposed models based on fractional calculus that describe phenomena present in modern telecommunication networks are presented in this paper.