{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:58:48Z","timestamp":1760151528345,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T00:00:00Z","timestamp":1649203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym14040752","type":"journal-article","created":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T22:23:23Z","timestamp":1649370203000},"page":"752","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Study of the Process of Packet Arrival at a Multiservice Node"],"prefix":"10.3390","volume":"14","author":[{"given":"Daniyar","family":"Shingissov","sequence":"first","affiliation":[{"name":"Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Nur-Sultan 010000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5716-4506","authenticated-orcid":false,"given":"Shakhmaran","family":"Seilov","sequence":"additional","affiliation":[{"name":"Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Nur-Sultan 010000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vadim","family":"Goikhman","sequence":"additional","affiliation":[{"name":"Faculty of Infocommunication Networks and Systems, The Bonch-Bruevich Saint-Petersburg State University of Telecommunications, 193232 Saint Petersburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikolai","family":"Sokolov","sequence":"additional","affiliation":[{"name":"LLC Scientific and Technical Center \u201cProtei\u201d, 194044 Saint Petersburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhanar","family":"Akhmetova","sequence":"additional","affiliation":[{"name":"Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Nur-Sultan 010000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gulzhan","family":"Uskenbayeva","sequence":"additional","affiliation":[{"name":"Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Nur-Sultan 010000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leila","family":"Rzayeva","sequence":"additional","affiliation":[{"name":"Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Nur-Sultan 010000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,6]]},"reference":[{"key":"ref_1","first-page":"5","article-title":"L\u00f8sning af nogle Problemer fra Sandsynlighedsregningen af Betydning for de automatiske Telefoncentraler","volume":"13","author":"Erlang","year":"1917","journal-title":"Elektroteknikeren"},{"key":"ref_2","unstructured":"Iversen, V.B. (2003). Teletraffic Engineering Handbook, ITU. ITU-D."},{"key":"ref_3","unstructured":"Akimaru, H., and Kawashima, K. (2012). Teletraffic: Theory and Applications, Springer Science & Business Media. Telecommunication Networks and Computer Systems."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Gross, D., Shortle, J.F., James, M., Thompson, J.M., and Harris, C.M. (2018). Fundamentals of Queueing Theory, Wiley. [5th ed.].","DOI":"10.1002\/9781119453765"},{"key":"ref_5","unstructured":"Korn, G.A., and Korn, T.M. (2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review, Courier Corporation."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Harris, J.W., and Stocker, H. (1998). Handbook of Mathematics and Computational Science, Springer Science & Business Media.","DOI":"10.1007\/978-1-4612-5317-4"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1086\/287954","article-title":"General Black Box Theory","volume":"30","author":"Bunge","year":"1963","journal-title":"Philos. Sci."},{"key":"ref_8","unstructured":"Mix, D.F. (2019). Fourier, Laplace, and z Transforms: Unique Insight into Continuous-Time and Discrete-Time Transforms. Their Definition and Requests, Amazon."},{"key":"ref_9","first-page":"31","article-title":"The choice of a distribution function to describe the process of packet arrival in a router","volume":"3","author":"Ermakov","year":"2021","journal-title":"Inf. Space"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1615\/TelecomRadEng.v78.i6.30","article-title":"Evaluating the Packet Traffic Parameter Measurements","volume":"78","author":"Goikhman","year":"2019","journal-title":"Telecommun. Radio Eng."},{"key":"ref_11","unstructured":"Levakov, A.K., Sokolov, A.N., and Sokolov, N.A. (2019, January 23\u201327). Using a Step Distribution Function to Describe the Incoming Packet Flow. Proceedings of the XXII International Scientific Conference Distributed Computer and Communication Networks: Control, Computation, Communications, Moscow, Russia."},{"key":"ref_12","unstructured":"ITU-T (2006). Network Performance Objectives for IP-Based Services, ITU. Recommendation, Y.1541."},{"key":"ref_13","unstructured":"(2011). 3GPP Technical Report 37.868 (Release 11), ETSI."},{"key":"ref_14","first-page":"91","article-title":"Models of incoming traffic in packet networks","volume":"9","author":"Levakov","year":"2015","journal-title":"T-Comm-Te\u043be\u043ao\u043c\u043cy\u043d\u0438\u043aa\u0446\u0438\u0438 Tpa\u043dcnopm."},{"key":"ref_15","unstructured":"Kr\u00e4mer, W., and Langenbach-Belz, M. (1976, January 10\u201317). Approximate Formulae for the Delay in the Queueing System GI\/G\/1. Proceedings of the 8th International Teletraffic Congress, Melbourne, Australia."},{"key":"ref_16","unstructured":"Kuhn, P. (1976, January 10\u201317). Analysis of Complex Queuing Networks by Decomposition. Proceedings of the 8th International Teletraffic Congress, Melbourne, Australia."},{"key":"ref_17","unstructured":"Levakov, A.K. (2019). Next-Generation Communication Network in Emergency Situations. Analysis of Teletraffic Models, IRIAS."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Cabrera, B.D., Gosar, J., Lee, W., and Mehra, R.K. (2004, January 14\u201317). On the Statistical Distribution of Processing Times in Network Intrusion Detection. Proceedings of the 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas.","DOI":"10.1109\/CDC.2004.1428609"},{"key":"ref_19","unstructured":"Samouylov, K.E., Levakov, A.K., Sokolov, N.A., and Zaitcev, V.S. (2020, January 13\u201317). Method of Arrival Process Description for Packet Switch. Proceedings of the Selected Papers of the X Conference Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems, Moscow, Russia."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1111\/j.2517-6161.1951.tb00080.x","article-title":"Some problems in the Theory of Queues","volume":"13","author":"Kendall","year":"1951","journal-title":"J. R. Stat. Soc. Ser. B."},{"key":"ref_21","unstructured":"Kleinrock, L. (1975). Queueing Systems: Theory, Wiley."},{"key":"ref_22","unstructured":"Vadzinsky, R.N. (2001). Handbook on Probability Distributions, Nauka."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/752\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:49:02Z","timestamp":1760136542000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/752"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,6]]},"references-count":22,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["sym14040752"],"URL":"https:\/\/doi.org\/10.3390\/sym14040752","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,4,6]]}}}