# Low Power Multi-Hop Networking Analysis in Intelligent Environments
## 5 Discussion of the Results
### Multi-Hop Communications with Bluetooth Park Low Power Mode  
As a result of the tests with nodes in park mode, several figures are available to analyze the latency in Bluetooth multi-hop networks. In all cases, latency is expressed in seconds in the ordinates axis. Figure 4a summarizes the 95% percentile of the results of the latency tests vs. amount of hops for the master-to-slave communication when links in the network are always in the park mode. The results when the communication is from slave to master are compiled in Figure 4b. In these two figures the four cases of inactivity intervals (T) were considered. The percentile of the measured latencies depicted in Figure 4 shows a monotonically increase when the amount of hops is increased. Figure 4: Latency (vertical, seconds) vs. amount of hops (horizontal). Links always in _park_ mode. Inactivity intervals (from left to the right): 100, 500, 1000 and 2000 ms. (**a**) _master-to-slave_ communication; (**b**) _slave-to-master_ communication. The latency results when operating in park mode show higher values for the case of data packets going from master to slave (Figure 4a) when compared to data packets going from slave to master (Figure 4b). The reason behind such unexpected results can be found in the methodology of the tests. The slave-to-master data packets (i.e., _pingback_ data packets) for the DS flow along the network as soon as they are received in the ANE, and therefore, the pingback data packets find some slave nodes active, i.e., there is no need to unpark those links and hence the latency is not increased. On the other hand, Figure 5a shows the dependence of the latency with the inactivity interval in the same case, i.e., master-to-slave communication when links are in park mode. Furthermore, the dependence of the latency with the inactivity interval for the slave-to-master communication when links are in the park mode can be seen in Figure 5b. In these two figures five cases are depicted depending on the amount of hops considered, i.e., from two to six hops. Figure 5 confirms what Figure 4 points out, i.e., the latency from end-to-end in Bluetooth multi-hop wireless communications when links are always in the park mode exhibits linear dependence with the inactivity period of the nodes. The latency also depends on the amount of hops in the communication. This phenomenon happens not only in the master-to-slave communication but also in the slave-to-master communication. Figure 4 also indicates that the latency from end-to-end in Bluetooth multi-hop wireless communications when links are always in the park mode exhibits slight quadratic dependence with the amount of hops. This phenomenon is related to the probability of errors in the communication and the subsequent retransmissions, which increases as the communication includes more hops. It happens not only in the master-to-slave communication but also in the slave-to-master communication. These results are the basis to propose a model for the latency in asynchronous communications along Bluetooth multi-hop networks when master-slave gateway nodes are in park low power mode. The model describes and anticipates the upper limit of the latency in Bluetooth networks with linear topology. It embraces the four inactivity periods considered in the tests, i.e., 100, 500, 1000 and 2000 ms. The communication from master to slave is defined with the same model that defines the communication from slave to master, but the coefficients change, as shown next. The achievement of the models followed these steps. First, the results of the test were analyzed, and the dependencies of the latency with the amount of hops of the communication and the period of inactivity were extracted. Then, the coefficients of the master equation for the cases under study were defined. Next, linear regression was performed to calculate the coefficients of the equations that define the models. Then, the models were defined.