# Link Quality Estimation from Burstiness Distribution Metric in Industrial Wireless Sensor Networks
## 3 Link Quality Measurement and the Metric for Evaluating  
### Measure Link Quality Principle  
To measure the link quality between two sensor nodes, probe packets are used in which the number of probes is predefined. Each node generates a probe packet, P(node_id, sequence), in which sequence is a sequence of probe packets generated, and it increases from 1 up to the number of probes. Upon receiving P(node_id, sequence), the receiver calculates the burstiness value by using the sequence number in P for the sender node and then saving it to the burstiness distribution list (BDL). If a burstiness value duplicates others in the BDL, the burstiness time count for this burstiness value increases by 1. For example, let us consider the measurement link quality for nodes 1 and 4 in Figure 1, where node 1 received a probe packet from node 4 with the sequence number 1, denoted by P(4, 1). The next received probe packet from node 4 is P(4, 4), which means probe packets P(4, 2) and P(4, 3) were lost due to burstiness, and thus the burstiness value is 2. At this time, the current received probe packet is P(4, 4), and the receiver will receive the next probe packet and will again calculate the burstiness value. Assume that the probe packet is P(4, 7) the next time, so the burstiness value is again 2, but the burstiness time count will increase by 1 to indicate that burstiness value 2 was duplicated. Let the result of a transmission per link at the ith sequence be \"S\" if it was successful and \"F\" if it failed. With the above example of node 1 and node 4, we have the result of the transmissions after seven probe packets as \"SFFSFFS\". After finishing the measure link quality (MLQ) period, we have the BDL of a link with 1000 probe packets transmitted, as shown in Table 1.  
Consider the relationship between burstiness value and burstiness time count in the BDL. The burstiness value is defined as the number of consecutive losses during probe packet transmission, and the burstiness time count is defined as the number of times the burstiness value appeared.  
Figure 1: An example of a network topology.  
For example, in Table 1, after transmitting 1000 probe packets, a burstiness value of 0 occurred 634 times, a burstiness value of 1 occurred 129 times, and so on. It means that in the 1000 probe packets transmitted, 634 times the result of transmission was \"SS\" and 129 times the result of transmission was \"SFS\", and so on. With a link of good quality, the burstiness value will be small, whereas the burstiness time count will be large for the minimum burstiness value. Conversely, a bad link has a higher burstiness value and a low burstiness time count for the minimum burstiness value.  
For example, Figure 2 shows the simulation result from one pair of nodes with the different configurations of the PRR value. In Figure 2, the distribution of the burstiness values is compared with a link PRR of 70%, 80%, and 90%, when the number of probes is 1000 packets. Figure 2 describes how with a good link (PRR 90%) we have a burstiness time count with a minimum burstiness value at 816 and a maximum burstiness value of 2. On the other hand, with bad link quality (PRR 70%), we have a burstiness time count with a minimum burstiness value of 480 and a maximum burstiness value of 4.