Research Article Optimization of Data Distributed Network System under Uncertainty Laxminarayan Sahoo , 1 Supriyan Sen , 1 Kalishankar Tiwary , 2 Sovan Samanta , 3 and Tapan Senapati 4 1 Department of Computer and Information Science, Raiganj University, Raiganj 733134, India 2 Department of Mathematics, Raiganj University, Raiganj 733134, India 3 Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk 721636, India 4 School of Mathematics and Statistics, Southwest University, Beibei, Chongqing 400715, China Correspondence should be addressed to Sovan Samanta; ssamantavu@gmail.com Received 26 January 2022; Accepted 2 March 2022; Published 8 April 2022 Academic Editor: Fahad Al Basir Copyright © 2022 Laxminarayan Sahoo et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e major network design or data distributed problems may be described as constrained optimization problems. Constrained optimization problems include restrictions imposed by the system designers. ese limitations are basically due to the system design’s physical limitations or functional requirements of the network system. Constrained optimization is a computationally challenging job whenever the constraints/limitations are nonlinear and nonconvex. Furthermore, nonlinear programming methods can easily deal same optimization problem if somehow the constraints are nonlinear and convex. In this paper, we have addressedadistributednetworkdesignprobleminvolvinguncertaintythattransmitsdataacrossaparallelrouter.isdistributed network design problem is a Jackson open-type network design problem that has been formulated based on the M/M/1 queueing system. Because our network design problem is a nonlinear, convex optimization problem, we have employed a well-known Kuhn–Tucker (K-T) optimality algorithm to solve the same. Here, we have used triangular fuzzy numbers to express uncertain traffic rates and data processing rates. en, by applying α-level interval of fuzzy numbers and their corresponding parametric representation of α-level intervals, the associated network design problem has been transformed to its parametric form and later hasbeensolved.Toobtaintheoptimaldatastreamrateintermsofintervalandtoillustratetheapplicabilityoftheentireapproach, a hypothetical numerical example has been exhibited. Finally, the most important results have been reported. 1.Introduction Aqueueisasetofindividualsorthingsthatmustbehandled inaspecificway.Erlang[1],aDanishengineerknownasthe “Father of Queueing eory,” had published articles on the study of telephone traffic congestion in 1909. A queueing networkconsistsofnodes,eachofwhichrepresentsaservice facility. In 1957, Jackson [2] found the use of queueing networks. Jackson’s network [3] has the most significant contributions to the queueing network service centres, digital communications, communications infrastructure, processing and flexible automation systems, transportation hubs, and healthcare systems which are just a few areas of use for queueing frameworks. Queueing networks are cat- egorized into three types: open, closed, and mixed networks. Users begin receiving from an external device and for- warding to an external destination via open networks. Closednetworkshaveaconstantmajorityofindividualswho stream between queues but never leave the same process. Some working phases are created by combining networks in order for them to be open, while others require them to be closed, which are referred to as mixed networks. Retrial queues or queues with frequent orders are queueing con- cepts that are expected to arrive to the clients who find the host engaged could sometimes retry for which service after quiteperiodoftime.Betweenretrials,thestuckuserneedsto Hindawi Discrete Dynamics in Nature and Society Volume 2022, Article ID 7806083, 12 pages https://doi.org/10.1155/2022/7806083