Analysis of the probability of connectivity of a telecommunications network based on the reduction of several non-connectivity events to a union of independent events

Introduction: For large and structurally complex telecommunication networks, calculating the connectivity probability turns out to be a very cumbersome and time-consuming process due to the huge number of elements in the resulting expression. The most expedient way out of this situation is a method based on the representation of a network connectivity event in the form of sums of products of incompatible events. However, this method also requires performing additional operations on sets in some cases. Purpose: To eliminate the main disadvantages of the method using multi-variable inversion. Results: It is shown that the connectivity event of a graph should be interpreted as a union of connectivity events of all its subgraphs, which leads to the validity of the expression for the connectivity event of the network in the form of a union of connectivity events of typical subgraphs (path, backbone, and in general, a multi-pole tree) of the original random graph. An iterative procedure is proposed for bringing a given number of connectivity events to the union of independent events by sequentially adding subgraph disjoint events. The possibility of eliminating repetitive routine procedures inherent in methods using multi-variable inversion is proved by considering not the union of connectivity events (incoherence) degenerating into the sum of incompatible products, but the intersection of opposite events, which also leads to a similar sum. However, to obtain this sum, there is no need to perform a multi-variable inversion for each of the terms over all those previously analyzed. Practical relevance: The obtained analytical relations can be applied in the analysis of reliability, survivability or stability of complex telecommunications networks.

Connectivity Analysis of Underwater Optical Wireless Sensor Networks

<pre>In this paper, we analyze the connectivity in the underwater optical wireless networks in which similar nodes with a certain range and coverage angle, and random surface distribution are used. In our analysis, we first classify the nodes into two categories of nodes located in the inner area and nodes located in the border strip by defining the width of the border strip as the node range. Then, we conduct their connectivity analyses separately. Finally, by combining the mentioned analyses, we obtain closed form formulas to calculate the probability of connectivity (from orders 1 and 2). Moreover, by numerical evaluation, we will compare the results of the analyses with the results of computer simulation.</pre>

Connectivity Analysis of Underwater Optical Wireless Sensor Networks

<pre>In this paper, we analyze the connectivity in the underwater optical wireless networks in which similar nodes with a certain range and coverage angle, and random surface distribution are used. In our analysis, we first classify the nodes into two categories of nodes located in the inner area and nodes located in the border strip by defining the width of the border strip as the node range. Then, we conduct their connectivity analyses separately. Finally, by combining the mentioned analyses, we obtain closed form formulas to calculate the probability of connectivity (from orders 1 and 2). Moreover, by numerical evaluation, we will compare the results of the analyses with the results of computer simulation.</pre>

The Review of Ecological Network Indicators in Graph Theory Context: 2014-2019

Ecological Network Analysis (ENA) capability has led to develop a set of indicators. Ecological Network Indicators (ENIs) investigates a range of subject in different context “e.g. Graph theory”, which is the origin of variety of questions such as following: What is the geographical distribution of studies and their relationship with each other? On what fields these studies are focused? What graph-based index or indexes have been used in the studies of ecological networks? What are the most widely used indexes in ecological studies? Accordingly, this study is to investigate the related literature between 2014 and 2019 in the framework of graph theory. To answer the mentioned question, we conducted systematic literature review. To find as many potentially eligible articles as possible, the search was performed multiple times using diverse related keywords. We identified 456 related records. After the screening process, 114 articles were left as the basis of further analysis. The results indicate that ENA applied mainly in China, USA, France. ENIs is studied more frequently among plants and mammals. We identified about 58 ENIs. But the Probability of Connectivity (PC), Integral index of connectivity (IIC) have been consistently used in most studies. Also, these two indices are used in combination with others ENIs. The outcomes show researchers introduce new indexes every year. The increasing trend of introducing new indicators shows the usability and applicability ENIs. But so far, PC, IIC, and LCP seem to be the most credible graph-based indexes for use in ecological network research. The overall results imply that graph theory as base of ecological network is developing, presents new indicators and opening new dimensions in the study and analysis of connections and communications in ecological networks. It has adequate flexibility to answer questions that may arise in the future in the field of ecological network analysis.

PROBABILITY OF THE UTILITY NETWORKS DOUBLE-RING STRUCTURES’ CONNECTIVITY FOR SITES WITH VARIOUS RELIABILITY

The analytical description study results on probability of connectivity for the structures used to model the reliability of various complicated systems are presented. Expressions are formed to calculate the connectivity probability of systems that have structural redundancy. The characteristic components of the formulas are distinguished and they are systematized according to their increasing complexity and the number of elements. The features of the equations’ structure permitting to conveniently formulate the probability of the structures connectivity in the process of their construction and transformations are determined. The examples show the formation of formulas and their structural parts at various levels of complexity. The use of the ratio value of the network structure element’s unreliability and its reliability is justified, thus reducing the awkwardness of exact expressions for the connectivity probability of network structures and substantially improves the compactness and convenience of using the equations.

SACA: Self-Aware Communication Architecture for IoT Using Mobile Fog Servers

Internet of things (IoT) aims at bringing together large business enterprise solutions and architectures for handling the huge amount of data generated by millions of devices. For this aim, IoT is necessary to connect various devices and provide a common platform for storage and retrieval of information without fail. However, the success of IoT depends on the novelty of network and its capability in sustaining the increasing demand by users. In this paper, a self-aware communication architecture (SACA) is proposed for sustainable networking over IoT devices. The proposed approach employs the concept of mobile fog servers which make relay using the train and unmanned aerial vehicle (UAV) networks. The problem is presented based on Wald’s maximum model, which is resolved by the application of a distributed node management (DNM) system and state dependency formulations. The proposed approach is capable of providing prolonged connectivity by increasing the network reliability and sustainability even in the case of failures. The effectiveness of the proposed approach is demonstrated through numerical and network simulations in terms of significant gains attained with lesser delay and fewer packet losses. The proposed approach is also evaluated against Sybil, wormhole, and DDoS attacks for analyzing its sustainability and probability of connectivity in unfavorable conditions.