## 3 System Model and Preliminaries  
### System Model  
We consider a deployment scenario, in which diverse types of _in-vivo_ nodes are placed in a human body forming a WBAN. A Body Coordinator(\(BC\)) is attached to the body surface, that serves as a central data sink for the WBAN as shown in Figure 1a. _In-vivo_ nodes in a WBAN are usually energy constrained and responsible for sensing and transmission functions, while the \(BC\) could be equipped with external power supply having some advanced functionalities (_i.e._, data aggregation, exchanging control and management packets _etc._). The \(BC\) aggregates the data received data from the nodes, processes it, and then sends it to a Base Station (BS) or server through other networks (_i.e._, cellular, WLAN or wired) as depicted in Figure 1a, and this communication paradigm is out of the scope of this paper.  
Figure 1: Network Model. (**a**) A Wireless Body Area Network (WBAN); (**b**) Communication Network Topology.  
The above deployment scenario can be modeled as a connectivity graph, \(\mathbf{G}=(N,E)\), where \(N\) is the set of vertices representing the nodes in the network including \(BC\), and \(E\) is the set of edges that represents the communication network topology as illustrated in Figure 1b. An edge, \((n_{i},n_{j})\in E,\)_iff_\(n_{i},n_{j}\) are within the communication range of each other. We assume every node \(n_{i}\) uses fixed transmission power for the communication with neighboring nodes. We define the neighbor set of \(n_{i}\), denoted as \(NB(n_{i})\), are the nodes with which \(n_{i}\) has direct edges. We consider all the communication links are symmetric, that is, if \(n_{i}\in NB(n_{j})\), then \(n_{j}\in NB(n_{i})\). To save energy and attain higher network connectivity, _in-vivo_ nodes are assumed to have limited transmission range, thus data will be delivered to the BC through multiple hops. We assume that all the _in-vivo_ nodes have forwarding capabilities (_i.e._, forward other node's data) along with their sensing and transmission functions.  
In this paper, we focus on designing a new localized and thermal-aware QoS routing protocol for a WBAN having _in-vivo_ nodes. The term \"localized routing\" can be formally defined as  
**Definition 1**.: _A routing protocol \(A\) is said to be a localized protocol, if given the information of a current node \(n_{i}\) and its neighbor set \(NB(n_{i})\), the current node \(n_{i}\) can decide which neighboring node \(n_{j}\), \(n_{j}\in NB(n_{i})\) is suitable to forward the data._  
To know the information of the neighboring nodes every node runs a HELLO protocol. For a localized routing to be effective, we assume that nodes are either stationary or having very low mobility, otherwise, nodes need to exchange HELLO packets more frequently which could be resource consuming. This assumption also agrees with the WBAN architecture with _in-vivo_ nodes, since nodes are implanted inside the biological tissue of the human body. We also assume that in the network, node density is sufficient enough to prevent any \"void\" situation, where the void situation is termed as the situation between two neighboring nodes when there is no node in the network closer to one of them than the other.