**3. Proposed model**

The network model we consider here is composed of a base station, a sink node, and a set of distributed wireless sensor nodes. The base station can be inserted in any suitable place whether in the field or somewhere else. It is directly connected to the sink node through a wire or wireless link. The sink node is a wireless sensor with high capability in memory, processing, power, and wireless coverage. It works as an intermediate node between the base station and the other sensors. It receives commands from the base station and then conveys them to the deployed sensors. In addition, it collects data from the sensors and sends it to the base station. The other sensor nodes are categorized into mission-critical (MC) sensor nodes and regular sensor nodes. A mission-critical sensor node is a node that is responsible for sensing or reading mission-critical information such as a sensor node in the battle field. while the regular sensor node is any other node. These sensors which have limited capabilities in their battery-powers, memory, and processing are distributed all over the area of interest in such a way that any deployed node has at least one path to the sink node.

In the rest of this section we present the problem formulation of our proposed model in section 3.1. Then, in section 3.2 we introduce the routing process based on the above mentioned network model. Finally, we demonstrate the region failure analysis under single and dual region-failures in section 3.3.
