**2. Problem investigation**

2 Will-be-set-by-IN-TECH

resulting in network holes, cuts (partitions) or even breakdown of the overall network connectivity as shown in Fig. 1. Therefore, it is essential to assess the vulnerabilities of mission

Some research has been conducted to understand the impact of region failures on wired backbone networks such as [11–18]. On the other hand, the cut detection problem has been

Recently, few studies have tackled the region-failure problem in wireless networks. The authors in [7–9] investigated the region- based connectivity issue in wireless networks and demonstrated the effect of the transmitting power on maintaining a region-based connectivity in the presence of single and multiple region failures. The authors in [10] proposed a more general Probabilistic Region Failure (PRF) Model to capture the key features of geographically correlated region failures. They also developed a framework to apply the PRF model for the

(b) Partitions due to dual

(d) Two holes due to dual

region-failure

region-failure

All of the aforementioned studies about regional-failures consider a worst-case cut as the cut which maximizes or minimizes certain performance metric (such as capacity) of the

critical networks to such region-failures.

reliability assessment of wireless mesh networks.

(a) Partitions due to single

(c) A hole due to a single

region-failure

region-failure

**Figure 1.** Example of Network Partitions and holes

investigated by [19] and [20].

Most of the available studies [21–23] in the literature consider that the failure probability of a node is independent of its location in the deployment area. Few studies [6–10] addressed the region failure problem of spatially correlated network nodes in the physical topology. Available studies focusing on region failures consider link-cuts due to a region-failure as the main criteria for identifying the worst-case region-failure and can be interpreted in terms of the network capacity and throughput. However, such fault scenario is inadequate to capture many realistic situations where the failure region may influence larger number of nodes rather than larger number of link-cuts as shown in Fig.2.

(a) Link-Based (b) Node-Based

**Figure 2.** Selection of the Worst-case region cut

For the network shown in Fig. 2, suppose that all links have the same capacity. Then, it can be easily seen that the region failure in Fig. 2a leads to 10 link-cuts while the region failure shown in Fig. 2b leads to only 6 link-cuts. Based on the current studies, the region with the

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maximum number of link-cuts is identified as the worst-case cut (i.e the region in Fig. 2a). On the other hand, the failure region depicted in Fig. 2b disconnects the dashed region (8 nodes) from the rest of the network which has a greater impact on the network than the case shown in Fig. 2a which has only 6 disconnected nodes.

Therefore, we first propose a new model for the worst-case region-cut considering disconnected nodes (Node-Based) due to a region-failure as the major criteria for identifying the worst-case region-cut. In our proposed model, we may select a region with less number of link-cuts as the worst-case cut if it isolates a larger number of nodes. Moreover, in our proposed model mission-critical nodes are given more weight during the worst-case analysis process to reflect the importance of its service continuity.
