Internet traffic prediction analog to solitons propagation in optical fibers via the concatenation model and stability analysis

Abstract

AbstractInternet traffic (IT) is a measure of data transfer across devices. In this paper, an analogy is made between data transfer and soliton propagation in optical fibers. This is achieved by employing the concatenation model (CM) that describes soliton propagation in optical fibers, which is presented recently in the literature. The CM contains nonlinear space-time dispersion effect, that may lead to bottleneck soliton shape (BNSS). Thus, in view of this model, BNSS effect of soliton propagation may occur, which is analogous to a possible BN in IT. So, the prediction of the characteristics of internet traffic can be depicted via the CM, which is studied here with Caputo-q time derivative. Also, a variety of exact solutions of the CM are derived. These solutions are represented graphically and they show multiple shapes of concatenated solitons. Among them, bottleneck, M-shaped, hybrid M shaped, chirped solitons and vector of dromian patterns. On the other side, the speed of IT and chips heating are estimated. It is found that the speed of IT is constant with time and the effects of distributed time delay (recent memory (RM)) is to slow the traffic speed. This is done via varying the fractional order. Also, it is observed, when accounting for RM, that the chip heating is too small. We think that the results for the speed of IT and chip heat are, qualitatively, realistic. The stability of a steady state solution is analyzed and the controlled parameters for stability is determined.