# Automated Methodology for Dependability Evaluation of Wireless Visual Sensor Networks
## 3 Problem Formulation and Background
### Link Modeling  
The link model consists of a description of the communication behavior between two nodes. Due to its wireless nature, we consider that link failures are transient. In addition, as a link is an abstract concept, we cannot materialize its repair. Thus, this repair action can be understood as the natural reestablishment of normal communication conditions after a failure, without a deliberate intervention. We assume that link failures also occur according to a Poisson process, leading to a constant failure rate \(\lambda_{lk}\). Repairs are modeled analogously to the hardware case, assuming a constant repair rate, \(\mu_{lk}\). That way, the link behavior with respect to availability is described as a binary relationship, which can be operable (UP) or failed (DOWN). In the former case, the link is operational, and in the latter it is failed. This behavior can be represented by a CTMC with two states (\(UP_{lk}\) and \(DOWN_{lk}\)). Transitions between these two states are described by the failure and repair rates, \(\lambda_{lk}\) and \(\mu_{lk}\)  
Figure 5: Battery discharging model. Figure 6: Battery model. respectively, as presented in Figure 7. Under the stated assumptions, the link availability, \(lk=A_{lk}(t)\), can be computed as the probability of being on state \(UP_{lk}\). Link dependability is also related to the routing protocol. A link failure can change the network topological arrangement, excluding a path to the sink node, disallowing or delaying the delivery of part of the network visual information. Searching a new path to the sink depends directly on the used routing strategy. In order to consider this behavior in the dependability evaluation, routing protocols are an important issue, which needs to be properly evaluated. Since there are too many routing protocols, it is very difficult to model all of them or even to find a general pattern. On the other hand, it would be very restrictive to model a specific protocol. Instead, some authors discuss and describe routing strategies that are common to several protocols. The most used strategies that can be found are DIRECT, FLOODING and HIERARCHICAL [40; 41; 62]. In this paper, we address DIRECT and FLOODING strategies, and consider HIERARCHICAL as a future work. The DIRECT strategy guarantees direct connection between each node and the sink node through one single hop. Although ideal for small networks, it may lead to high energy consumption, since it requires that radios to be set with high transmission power on nodes that are far away from the sink [40; 63]. This routing strategy will be used for comparison purposes. In this paper, we consider the radio connectivity modeled by disk graphs, where each pair of nodes within a given distance threshold \(\rho\) are connected and can communicate directly with each other by a link [62]. The FLOODING strategy is a multi-hop strategy to discover multiple paths to the sink. Each node broadcasts a message to all of its neighbors, who repeat this procedure until the message is delivered to the sink or it is dropped out due to a maximum number of hops. This routing strategy is easy to implement but has some problems: duplicate messages and network overheads [62; 63]. A good advantage of FLOODING is that it can deal with the loss of an intermediate node in a path, searching for new paths to the sink. This multiple path feature naturally provides a higher reliability, since the probability of a successful delivery of messages to the sink is higher with a high number of possible paths. In addition, as the nodes primarily communicate with their closest neighbors instead of communicating directly to the sink (which is probably more distant), each node can decrease the radio power to reach just the nodes in their vicinity, i.e., with a smaller distance threshold \(\rho\). This implies a smaller power consumption, a slower battery discharging and therefore a higher reliability. Figure 8 illustrates the network topology of the same arrangement of nodes, managed by different routing strategies.