Study of the Process of Packet Arrival at a Multiservice Node

• Published in: Symmetry (Basel) 2022-04, Vol.14 (4), p.752
• Main Authors: Shingissov, Daniyar, Seilov, Shakhmaran, Goikhman, Vadim, Sokolov, Nikolai, Akhmetova, Zhanar, Uskenbayeva, Gulzhan, Rzayeva, Leila
• Format: Article
• Language: English
• Subjects: Approximation; Control algorithms; Distribution functions; Error analysis; function; histogram; Histograms; Mathematical analysis; Nodes; packet; quality of service; Queuing theory; Random variables; scale; Switching; symmetry
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym14040752

The paper considers the main ways of describing the process that characterizes the arrival of packets to a multiservice node of a telecommunications network. The features of the process under consideration are best represented by the cumulative distribution function A(t). It determines the distribution of the interval size between the moments of arrival of neighboring packets to the multiservice node. These intervals are random values. If it is not possible to perform measurements that allow the choosing of the A(t) function, then the distribution law of random variables is selected based on reasonable assumptions. For telephone switching nodes, the Poisson flow hypothesis was used, which is often similar to the symmetric distribution of the number of calls at time interval t. The results of traffic measurements for multiservice switching nodes showed that the studied distribution is inherently asymmetric. This paper mainly considers the possibility of choosing the A(t) function based on the measurement results presented in a form of the histogram a(t), which contains a series of values. This histogram allows us to obtain the desired distribution as a stepwise function by integration of the a(t). Practical interest is associated with the possibility of reducing the number of readings used to assess the A(t) function. The methods used by some authors are based on the application of arbitrarily chosen functions A(t) with so-called heavy tails. The proposed approach is based on real distributions defined at a finite time interval. As a result of this research, a methodology has been developed to accurately describe the process of packet arrival at the input of the multiservice node. The proposed methodology is based on analytical methods. It guarantees error minimization when investigating the probabilistic characteristics of a switching node in a multiservice network.