The major network design or data distributed problems may be described as constrained optimization problems. Constrained optimization problems include restrictions imposed by the system designers. These 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 addressed a distributed network design problem involving uncertainty that transmits data across a parallel router. This distributed 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. Then, 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 has been solved. To obtain the optimal data stream rate in terms of interval and to illustrate the applicability of the entire approach, a hypothetical numerical example has been exhibited. Finally, the most important results have been reported.

The main objective of this paper is to find the duration of maximum time connectivity of sensor nodes under uncertainty utilizing the prespecified voltage/power of each sensor node. Wireless sensor networks (WSNs) are composed of nodes that transmit data between each other over routing. A variety of routing protocols and algorithms exist, each related to a particular set of conditions. There are a variety of routing algorithms available, some of which can be used in WSNs for routing. The goal of the fastest distance routing algorithms in a WSN is to use the least amount of energy possible. In a WSN, Dijkstra’s algorithm is typically used for shortest path routing. The Floyd–Warshall’s algorithm is used to compute the shortest paths between distinct nodes in a regular graph, but due to the absence of a communication mode, this algorithm is not ideal for routing in wireless networks. In this research work, we have considered a WSN to find out the maximum connectivity time utilizing optimum voltage. On the other hand, duration of connectivity and energy/voltage are two vital parameters that are difficult to manage. Because of limited resources and safety concerns, safety implementation is limited. Also, due to the irregular/hazardous environmental situations, the distance between sensor nodes and its voltage to link up the nodes are totally unpredictable. In this work, we employ triangular fuzzy numbers to express unpredictability. Then, utilizing defuzzification of fuzzy numbers, the associated WSN problem was transformed into a crisp one. The widely used signed distance approach has been applied for the defuzzification of fuzzy numbers in this case. To determine the best outcome and to illustrate the usefulness of the suggested technique, a numerical example has been solved using the modified Floyd–Warshall’s algorithm. Finally, concluding remarks on the proposed approach as well as future studies have been provided.

In this study, the multi-criteria decision-making (MCDM) technique is used in collaboration with K-medoids clustering to establish a novel algorithm for extending the lifetime of wireless sensor networks (WSNs) in the presence of uncertainty. One of the most important problems in WSNs is the energy consumption. Furthermore, extending the network lifetime in WSNs is highly dependent on selecting the appropriate cluster heads (CHs), and this can be a challenging task for the decision makers. In addition, parameters associated with WSNs are completely unexpected due to uncertainty. Therefore, after proposing K-medoids clustering and a MCDM technique, we have developed a novel algorithm for extending the lifetime of WSNs. As criteria, we have taken into account four important aspects of the proposed WSN: the distance from sink, average distance of cluster nodes, reliability of cluster and residual energy. To represent uncertain parameters in this work, we have considered triangular fuzzy numbers (TFNs). Finally, an experiment involving a WSN under uncertainty was investigated, and the findings have been graphically displayed. In this research, it has been observed that the proposed strategy with the novel algorithm exhibits 42% greater network lifetime as compared with a hybrid energy efficient distributed (HEED) algorithm and 11% and 18% with respect to optimal clustering artificial bee colony (OCABC) and particle swarm optimization (PSO) applied to a clustering optimization problem. We have also conducted statistical hypotheses for the purpose of confirming the presented outcomes.

This study compares websites that take live data into account using search engine optimization (SEO). A series of steps called search engine optimization can help a website rank highly in search engine results. Static websites and dynamic websites are two different types of websites. Static websites must have the necessary expertise in programming compatible with SEO. Whereas in dynamic websites, one can utilize readily available plugins/modules. The fundamental issue of all website holders is the lower level of page rank, congestion, utilization, and exposure of the website on the search engine. Here, the authors have studied the live data of four websites as the real-time data would indicate how the SEO strategy may be applied to website page rank, page difficulty removal, and brand query, etc. It is also necessary to choose relevant keywords on any website. The right keyword might assist to increase the brand query while also lowering the page difficulty both on and off the page. In order to calculate Off-page SEO, On-page SEO, and SEO Difficulty, the authors examined live data in this study and chose four well-known Indian university and institute websites for this study: www.caluniv.ac.in, www.jnu.ac.in, www.iima.ac.in, and www.iitb.ac.in. Using live data and SEO, the authors estimated the Off-page SEO, On-page SEO, and SEO Difficulty. It has been shown that the Off-page SEO of www.caluniv.ac.in is lower than that of www.jnu.ac.in, www.iima.ac.in, and www.iitb.ac.in by 9%, 7%, and 7%, respectively. On-page SEO is, in comparison, 4%, 1%, and 1% more. Every university has continued to keep up its own brand query. Additionally, www.caluniv.ac.in has slightly less SEO Difficulty compared to other websites. The final computed results have been displayed and compared.