Obtaining and Using Cumulative Bounds of Network Reliability

In this chapter, we study the task of obtaining and using the exact cumulative bounds of various network reliability indices. A network is modeled by a non-directed random graph with reliable nodes and unreliable edges that fail independently. The approach based on cumulative updating of the network reliability bounds was introduced by Won and Karray in 2010. Using this method, we can find out whether the network is reliable enough with respect to a given threshold. The cumulative updating continues until either the lower reliability bound becomes greater than the threshold or the threshold becomes greater than the upper reliability bound. In the first case, we decide that a network is reliable enough; in the second case, we decide that a network is unreliable. We show how to speed up cumulative bounds obtaining by using partial sums and how to update bounds when applying different methods of reduction and decomposition. Various reliability indices are considered: k-terminal probabilistic connectivity, diameter constrained reliability, average pairwise connectivity, and the expected size of a subnetwork that contains a special node. Expected values can be used for unambiguous decision-making about network reliability, development of evolutionary algorithms for network topology optimization, and obtaining approximate reliability values

On Pairwise Connectivity of Wireless Multihop Networks

This paper experimentally investigates the service availability of wireless multihop networks based on the following two metrics: average pairwise connectivity and pairwise connected ratio, where the former denotes the average number of node-disjoint paths per node pair in a network and the latter is the fraction of node pairs that are pairwise connected. Further, a theoretical upper-bound has been derived for the average pairwise connectivity, which can approximate the exact value very well. Since in wireless multihop networks nodes may fail either naturally or maliciously, the fault tolerance and attack resilience are important issues. In this paper we have also studied the fault tolerance and attack resilience of wireless multihop networks, and proposed a new resilience metric, α-p-resilience, where a network is α-p-resilient if at least α portion of nodes pairs remain connected as long as no more than p fraction of nodes are removed from the network. Three different node removal patterns have been studied: random removal, selective removal according to node degree, and partition, and the experimental studies show that wireless multihop networks are more sensitive to partition attacks than random removal and selective removal attacks, and selective removal attacks are a little bit more severe than random removal attacks