## 4 Adaptive Fault-Tolerant Communication Scheme
### Fault-Tolerant Priority Queue  
In order to guarantee the priorities of critical sensors, the control node maintains a fault-tolerant priority queue to manage the current reliability requirements of each sensor. The fault-tolerant priority of a sensor can be statically configured by the clinician through the user interface. It can also be dynamically adjusted according to the perceived fault-related information. An example of the fault-tolerant priority queue containing 5 sensors is shown in Figure 3, where a smaller value indicates a higher priority. Figure 3: A fault-tolerant priority queue. Each sensor has a fault-tolerant priority set. For example, the priority set of sensor \(S_{1}\) is {1, 3}, _i.e._, the control node can only choose 1 or 3 as the current fault-tolerant priority for \(S_{1}\). When two sensors have the same fault-tolerant priority, the one requiring less bandwidth reservation (_i.e._, \(BW_{SCdata}\), see Section 4.3) is served first. For example, for \(S_{4}\) and \(S_{5}\) in Figure 3, though their current fault-tolerant priorities are identical, the sensor \(S_{4}\) will be served first because it requires less bandwidth reservation than \(S_{5}\). After the system deployment, each sensor in the system has a default fault-tolerant priority. During the system operation, according to the perceived information, the control node dynamically selects a new fault-tolerant priority as the current priority for the sensor from its fault-tolerant priority set. If the control node perceives channel impairments, it will first provide reliability assurance for the sensors with higher priorities in the queue. We will give detailed illustration of how to adjust the fault-priority based on some parameters in the following section. (1). Activation threshold  
The parameter \(\theta\) is defined as the activation threshold for triggering the adjustment of the fault-tolerant priority of the sensor. For the sake of simplicity, we use one activation threshold for the whole system. As illustrated in Figure 4, the activation threshold is \(\theta\)= 0.4. (2). Priority tuner  
Priority tuner is used to adjust the current fault-tolerant priority of the sensor. For any fault-tolerant priority \(p\) of the sensor \(S_{i}\) in the fault-tolerant priority set, the priority tuner is represented by \(m_{ip}\). If \(m_{ip}\) exceeds the activation threshold, then the priority \(p\) may be activated as the new current priority. All priority tuners of fault-tolerant priorities for the sensor \(S_{i}\) will be set to 0 when its current fault-tolerant priority is reset. (3). Adjustment factor  
\(\delta_{ip}(t)\) is defined as the adjustment factor of the fault-tolerant priority \(p\) for the sensor \(S_{i}\) at time \(t\). If the fault-related information is favorable for the priority \(p\), \(\delta_{ip}(t)\) will increase. Otherwise, \(\delta_{ip}(t)\) will decrease. For example, for the body temperature biosensor \(S_{temperature}\), its fault-tolerant priority set is {\(p_{1}\), \(p_{2}\), \(p_{3}\)}, where \(p_{1}\)\(>\)\(p_{2}\)\(>\)\(p_{3}\). According to Table 2, at time \(t\), if the body temperature is low without fluctuation, then \(\delta_{ip_{1}}(t)\)\(\leq\)\(\delta_{ip_{3}}(t)\)\(\leq\)\(\delta_{ip_{2}}(t)\). If the body temperature is high and sharply fluctuating, then \(\delta_{ip_{1}}(t)\)\(\leq\)\(\delta_{ip_{2}}(t)\)\(\leq\)\(\delta_{ip_{3}}(t)\) and \(\delta_{ip_{1}}(t)\) may be negative. \begin{table}
\begin{tabular}{l c c c} \hline
**Sensor readings** & \(p_{1}\) & \(p_{2}\) & \(p_{3}\) \\ \hline Low temperature & unfavorable & favorable & favorable \\ Normal temperature & favorable & unfavorable & unfavorable \\ High temperature & unfavorable & favorable & favorable \\ Large fluctuations in temperature & unfavorable & unfavorable & favorable \\ \hline \end{tabular}
\end{table} 
Table 2: Impact of body temperature on fault-tolerant priority. (4). Priority acquiescence  
The priority acquiescence parameter \(\lambda_{ip}(t)\) is used to prevent frequent changes in priority.