Modelling Self-Similar Traffic of Multiservice Networks

Abstract

Simulation modelling is carried out, which allows adequate describing the traffic of multiservice networks with the commutation of packets with the characteristic of burstiness. One of the most effective methods for studying the traffic of telecommunications systems is computer simulation modelling. By using the theory of queuing systems (QS), computer simulation modelling of packet flows (traffic) in modern multi-service networks is performed as a random self-similar process. Distribution laws such as exponential, Poisson and normal-logarithmic distributions, Pareto and Weibull distributions have been considered. The distribution of time intervals between arrivals of packages and the service duration of service of packages at different system loads has been studied. The research results show that the distribution function of time intervals between packet arrivals and the service duration of packages is in good agreement with the Pareto and Weibull distributions, but in most cases the Pareto distribution prevails. The queuing systems with the queues M/Pa/1 and Pa/M/1 has been studied, and the fractality of the intervals of requests arriving have been compared by the properties of the estimates of the system load and the service duration. It has been found out that in the system Pa/M/1, with the parameter of the form a> 2, the fractality of the intervals of requests arriving does not affect the average waiting time and load factor. However, when 𝑎≤2, as in the M/Pa/1 system, both considered statistical estimates differ. The application of adequate mathematical models of traffic allows to correctly assess the characteristics of the quality of service (QoS) of the network.

Evaluating the Functioning Quality of Data Transmission Networks in the Context of Cyberattacks

“…It should be noted that, when we simulate the delivery process, the Hurst index value, close to H ≈ 0.5, is the limiting value for the Pareto flow, because if H ≥ 0.5, dispersion for this distribution is not determined [21] (Figure 9), therefore the simulated results of the delivery process obtained at these H values will be wrong. Analysis of the received results shows that they correspond completely with the data of works published previously by other authors [13,16,17,[19][20][21][22]33] devoted to the development of quality evaluation methods of the functioning of telecommunication networks when self-similar and stationary Poisson traffic is transmitted. This confirms the adequacy of the developed model and the consistency of the received results.…”

“…In the case of the availability and implementation of an information impact by an attacker on network elements, the probability of the successful delivery of data packets in a given time significantly worsens (Figure 10). Analysis of the received results shows that they correspond completely with the data of works published previously by other authors [13,16,17,[19][20][21][22]33] devoted to the development of quality evaluation methods of the functioning of telecommunication networks when self-similar and stationary Poisson traffic is transmitted. This confirms the adequacy of the developed model and the consistency of the received results.…”

“…In [10,[13][14][15][16][17], an approach is proposed for the calculation of the packet loss probability, based on the usage of fundamental expressions, obtained for queuing systems M/M/1, taking into account the flow categorization and the claim operation discipline with the introduction of equalizing coefficients, considering the traffic variability [13], the Hurst index [10,14] and related parameters [15][16][17]. These works surely make a noticeable contribution to the development of the methods of teletraffic theory, but they do not take into account the impact of cyberattacks on packets losses.…”

“…where α v > 0-shape parameter of the Weibull distribution; Γ(*)-gamma-function [27]; H-Hurst exponent; α-distribution shape parameter, which is numerically equal to: -for Weibull distribution [14,16]:…”

Some Aspects of Blockchain-Enabled Radio Access Networks (B-RAN) Modeling: Review and Theoretical Study

“…It is worth mentioning, that the problem of the adequate traffic modeling of mobile networks is not new as well! The related works with the most consistent results can be found in the papers [2,3,[6][7][8][9][10][11][12][13] and the book [14]. For the traffic theory of the networks (see, for example [15,16]) all those works use not only Markov modeling but apply as well the theory of self-similar processes for interpretation of the traffic [17] in wireless communication networks of 5G and beyond.…”