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.

‘Power-as-a-Service’ – A Hierarchical On-Demand Charging Model for Recharging the Mobile Nodes of MANETs

Battery energy is a crucial issue that limits battery-powered mobile devices’ operational efficiency in Mobile Ad hoc Networks (MANETs). Failure of a node affects both the lifetime and connectivity of a MANET, which has to initiate finding a new route from source to destination. This initiation causes more energy consumption in nodes. Failure of a node also causes network partitions, thereby resulting in sparse networks being formed. Existing energy-efficient strategies only defer the end of a node’s battery lifetime; they could not guarantee the MANET’s nonstop functioning. To address the issues caused by battery depletion, this paper proposes a “Cloud” oriented approach called Power-as-a-Service (PaaS), a hierarchical on-demand charging model for recharging the mobile nodes of the MANET. In PaaS, the MANET is alienated into non-overlapping disjoint zones, and for each zone, one Zone Charging Cloud Node (ZccN) is deployed to recharge the mobile nodes of that particular zone wirelessly. A High-power Charging Cloud Node (HccN) is deployed to wirelessly recharge the ZccNs in the MANET for the entire network. In PaaS, the ZccN recharges both the selected node for recharge and other nodes around the selected node that requested recharge and has higher power transfer efficiency. This strategy of PaaS improves the charging efficiency of cloud chargers by minimizing the urgent charging requests in the future, and thus the operational efficiency of the MANET improves. Extensive simulations indicate that the proposed PaaS model with a hierarchy of cloud chargers improves the operational efficiency of MANETs in terms of reducing the death rate of mobile nodes, thereby improving the lifetime and connectivity probability of MANETs.

Capillary Water Absorption and Micro Pore Connectivity of Concrete with Fractal Analysis

This study focuses on the relationship between the complexity of pore structure and capillary water absorption of concrete, as well as the connection behavior of concrete in specific directions. In this paper, the water absorption of concrete with different binders was tested during the curing process, and the pore structure of concrete was investigated by mercury intrusion porosimetry (MIP). The results show that the water absorption of concrete with mineral admixtures is lower, mainly due to the existence of reasonable pore structure. The effect of slag on concrete modification is more remarkable comparing with fly ash. In addition, the analysis shows that the pore with different diameters has different fractal characteristics. The connectivity probability and water absorption of unidirectional chaotic pore are linearly correlated with the pore diameter of 50–550 nm, and the correlation coefficient reaches a very significant level, and detailed analysis was undertaken to interpret these results based on fractal theory.

Connectivity on Underwater MI-Assisted Acoustic Cooperative MIMO Networks

In traditional underwater wireless sensor networks (UWSNs), it is difficult to establish reliable communication links as the acoustic wave experiences severe multipath effect, channel fading, and ambient noise. Recently, with the assistance of magnetic induction (MI) technique, cooperative multi-input-multi-output (MIMO) is utilized in UWSNs to enable the reliable long range underwater communication. Compared with the acoustic-based UWSNs, the UWSNs adopting MI-assisted acoustic cooperative MIMO are referred to as heterogeneous UWSNs, which are able to significantly improve the effective cover space and network throughput. Due to the complex channel characteristics and the heterogeneous architecture, the connectivity of underwater MI-assisted acoustic cooperative MIMO networks is much more complicated than that of acoustic-based UWSNs. In this paper, a mathematical model is proposed to analyze the connectivity of the networks, which considers the effects of channel characteristics, system parameters, and synchronization errors. The lower and upper bounds of the connectivity probability are also derived, which provide guidelines for the design and deployment of underwater MI-assisted acoustic cooperative MIMO networks. Monte Carlo simulations were performed, and the results validate the accuracy of the proposed model.