# A Reliable Handoff Mechanism for Mobile Industrial Wireless Sensor Networks
## 4 Trigger Condition
### Window of Historical Information  
Nodes proactively realizing the state of mobility is key for advanced handoff mechanisms. To be aware of mobility in time, the number of valid measurements and the time ranges limitation for the valid measurements should be carefully considered. We call the time ranges limitation for the valid measurements as the window of historical information, which is denoted by \(W\). A wide window causes slow discovery and deficient statistics give insufficient evidence of the varied state. The difference between mobility awareness and the link estimation during network formation is the coherence time for measurements collection. The link estimation need to decide a more reliable link for each node, which is estimated by a lots of consecutive transmissions. However, the mobility awareness only depends on the periodical data packets to make a fast trigger decision. According to [32], the quality of channel is not constant in time, especially in industrial environments. Thus, the setting of \(W\) correlates with the speed of node movement and the period of packet transmission.  
Figure 2: The structure of a superframe.  
We assume that the maximum speed of node movement is \(\mathbb{V}\) and \(10\times L\) is the period of packet transmission. In our triggering approach, two types of range are defined to differentiate the quality of communication. We assume that the circles with radius of \(l_{p}\) and \(l_{t}\) represent two boundaries of the transmission quality during node communication. The circle with \(l_{p}\) represents the good-quality boundary and another one represents the limited boundary of the communication quality. Nodes can have high packet delivery with their parent within the good-quality range, but the basic performance of such delivery cannot be guaranteed when the \(M\)N exceeds the limited boundary. Thus the radius is also expressed as the communication quality though it is not a circle in practice. \(M\)N needs to realize mobility and trigger the handoff process before exceeding its parent's limited communication boundary. As shown in Figure 3a, \(M\)N is currently \(l_{1}\) away from its parent, and \(l_{d}\) is the dynamic length of \(M\)N's movement until it reaches the limited boundary. In Figure 3b, the worst case is that \(M\)N is very close to the good-quality boundary and it moves away from its parent along the radius. Thus we have \(l_{d}\geq l_{t}-l_{1}\geq l_{t}-l_{p}\). We define \(t\) as the time interval from the beginning of the movement to the handoff triggering. It has to meet \(t\leq t_{worst}\). The \(t_{worst}\) is the minimum interval to discover the mobile state and is expressed as  
\[t_{worst}=\frac{\lambda(l_{t}-l_{p})}{\mathbb{V}} \tag{1}\]  
where \(\lambda\) is the factor of interference. Therefore, the length of window \(W\) can be calculated by  
\[W=\max\left\{\left[\frac{t_{worst}}{10\times L}\right],W_{min}\right\} \tag{2}\]  
where \(\left\lceil\cdot\right\rceil\) represents that the result must be fixed to the given time unit such as superframe in this paper and \(W_{min}\) refers to the minimum window able to observe the variation.