## 3 Preliminaries  
In this section, we describe the application scenario. The variables used in the AFTCS scheme will be defined. We consider a scenario where the BSN is formed by a collection of biosensors, control nodes and a base station, as shown in Figure 1. In general, the biosensors are wireless wearable or implanted vital sign sensors which consist of a processor, memory, transceiver, sensors and a power unit. Each biosensor node is typically capable of sensing, processing, storing and transmitting the data. The control node periodically sends the sampled data to the medical server in the hospital through the base station, where they are stored for further processing [20].  
Due to the size and energy consumption restrictions, biosensors (such as sweat, EKG, temperature) cannot afford heavy computation and communication. Compared with biosensors, the control node (such as a cell phone or PDA) and the base station have comparatively higher transmission rate and computation power. In other words, BSN is a typical asymmetric structure.  
We first give the definitions of some variables used in the AFTCS scheme, as listed in Table 1.  
**Definition 1:** Fault-tolerant priority \(p\). \(p\) indicates the level of reliability requirements of a sensor. It can be dynamically adjusted at runtime.  
**Definition 2:** Fault-tolerant priority set. Each sensor has a fault-tolerant priority set. Based on the fault-related information, the control node dynamically selects an appropriate priority for the sensor from its priority set.  
**Definition 3:** Fault-tolerant priority queue \(Q\). The \(Q\) is a priority queue managing the fault-tolerant priorities of all the sensors in the system. The sensors in \(Q\) are sorted by priority in descending order.  
\begin{table}
\begin{tabular}{l l} \hline
**Variable** & **Description** \\ \hline \(T_{interval}\) & Length of each interval divided in VMAC \\ \(N_{plt}\) & Maximum of packets handled within each interval \\ \(S_{plt}\) & Effective data payload size in bytes \\ \(T_{minPt}\) & Minimum response time for handling a packet request \\ \(T_{maxPt}\) & Maximum response time for handling a packet request \\ \(S_{i}\) & A sensor with a specific function \\ \(T_{i}\) & The time for MAC to send a packet for sensor \(S_{i}\) \\ \(D_{i}\) & Packet number should be sent within \(T_{i}\)\(\triangleright\)\(D_{i}\) for sensor \(S_{i}\) \\ \(T_{wait}\) & Actual wait time of the control node in a polling process \\ \(N_{received}\) & Number of packets received by the control node \\ \(Size_{plt}\) & Data payload of data packet size in bytes \\ \(Size_{pollingPt}\) & Data payload of polling packet size in bytes \\ \(BW_{effective}\) & Effective bandwidth \\ \(\theta\) & Activation threshold \\ \(p\) & Fault-tolerant priority \\ \(m_{ip}\) & Priority tuner for fault-tolerant priority \(p\) of sensor \(S_{i}\) \\ \(\delta_{ip}(t)\) & Adjustment factor of priority \(p\) for sensor \(S_{i}\) \\ \(\lambda_{ip}(t)\) & The time that \(S_{i}\) wants to maintain \(p\) at time \(t\) \\ \(BW_{ideal}\) & Ideal bandwidth \\ \hline \end{tabular}
\end{table}
Table 1: Variables and Notations.  
Figure 1: BSN application scenario.