## 5 Comparison of Different Topologies
### Topology Comparison Based on Reliability  
Reliability analysis is an important task for the successful operation of WSNs. IEEE P1451.5 web survey [56] identified data reliability as one of the most important parameters in the design of WSNs. Reliability is generally defined as the probability that the system will perform its intended function under stated conditions for a specified period of time [79].  
The WSN reliability can be studied for three different scopes of data delivery [80], collectively known as the infrastructure communication: (a) users send their interest to a single sensor node, (b) users send their interest to a subset of nodes in a sub-area and the message needs to be delivered to all sensors in the particular group, and (c) users send their interest to the entire sensor network and the message needs to be delivered to all sensors in the network. There exists another scope of message delivery, known as application communication, in which it is sufficient that the message from sink is reliably delivered to only a group of sensor nodes that together cover the entire sensor field or the intended area of observation [78]. This is different from the delivery to all sensors in the infrastructure communication, due to the typical redundant deployment of sensors.  
Given a single node failure, the flat topology reduces the chance of the entire network failure, because the failure of any node results only in the localized failure, leaving the rest of the system unaffected. However, when a node becomes obstructed, there is no alternate path from the associated node to the base station. A flat topology is highly fault-tolerant as it offers multiple redundant paths throughout the network. If a routing node fails or the link between nodes becomes unavailable, the network can automatically reconfigure itself around the failed component. In a WSN, the degree of redundancy, and in general the reliability of the network, is essentially a function of node density. In addition, a WSN with flat topology can be deliberately over-provisioned for reliability simply by adding extra nodes. The addition of redundant nodes also improves the reachability of WSN by providing multi-hop routes to inaccessible or hidden nodes. Besides, if certain environmental or architectural conditions results in poor reliability, it is difficult or impossible to adapt a point-to-point network like the network with a cluster topology to increase reliability. In contrast, the WSN reliability can be improved by redeploying redundant nodes in the affected area.  
The tree topology has the lowest reliability due to the use of only a single direct link between nodes at successive levels in the hierarchy. Chain-oriented topology offers better reliability than tree-based topologies as in the same hierarchy level it uses multi-hop communication from source to sink. Clustered hierarchical topology is a compromise between the two extremes. It is better than tree/chain-oriented topology, as it maintains multi-hop paths, while it has lower reliability than flat topology because each communication between nodes at different clusters must route through affiliated cluster heads. Thisis to note that, in WSNs, the residual energy of a node affects the reliability in an indirect way. For example, if the energy of the cluster head goes down, then the reliability decreases in an exponential manner. Moreover, energy simultaneously affects the number of normal and critical faults. As the energy decreases, the number of faults increases [81]. As energy efficiency of chain-based topology is higher than that of any other topology, it is possible that energy efficiency of chain-oriented topology compensates the relatively weak reliabilities.