# Tracking Mobile Sinks via Analysis of Movement Angle Changes in WSNs
## 4 Performance Evaluation
### Effect of Footprint Appointment Interval  
The interval to appoint footprints directly affects the number of DAMST points and distance between two adjacent footprints, which further influences the energy consumption and overhead in DAMST. To provide a vivid evaluation about effect of the footprint appoint interval, DAMST with different footprint appointment intervals is performed. In the simulation, each mobile sink moves in the random pattern, the interval from designating a RA to sending a data query is 30 min, and the period of each simulation run is also 30 min. Simulation results for each footprint appointment interval are averaged after taking 20 simulation runs.  
Figure 11 shows the effect of footprint appointment interval on the length of the DAMST point list. The drop-down curves indicate the greater the footprint appointment interval, the smaller the average number of nodes in the DAMST point list. This trend does not change with the variance of number of mobile sinks.  
Figure 10: Length of the DAMST point list in the four trajectory patterns.  
Figure 9: Trajectory patterns.  
However, as the footprint appointment interval increases, the distance between two adjacent DAMST points becomes longer. If the distance between the two adjacent DAMST points is less than node communication radius, the energy consumption on communication is proportional to square of the distance. And if the distance is over the communication radius, Algorithm 2 needs to be executed, in which more energy is consumed on constructing a shortest path. Either way, the increasing of the footprint appointment interval directly leads to the increasing of the distance between two adjacent DAMST points, which indirectly incurs more average energy consumption in network. Figure 12 exactly confirms our analysis. The average energy consumption on communication bulges exponentially with the increasing number of mobile sinks.  
While determining an appropriate footprint appointment interval, its effect on both average energy consumption and average overhead should be considered. Figure 13 shows us how the footprint appointment interval affects the average overhead. As the footprint appointment interval gets longer, the average overhead decreases firstly then increases. On the decrease part, it can be clearly explained: Appropriately extending the footprint appointment interval results in fewer footprints and shorter DAMST point list, which further cause less overhead in Algorithm 1. And in this case, the distance between two adjacent DAMST points becomes longer but still within node communication radius, which is also beneficial for reducing overhead in Algorithm 2.  
We can also make an inference on the increase part: excessively extending footprint appointment interval may produce more unconnected adjacent DAMST points, which further causes more overhead in Algorithm 2. Simulation results on the ratio of unconnected adjacent DAMST points in the DAMST  
Figure 11: Average length of the DAMST point list with different footprint appointment intervals.  
Figure 12: Average energy consumption with different footprint appointment intervals.  
point list are displayed in Figure 14. As expected, the ratio of unconnected adjacent DAMST points becomes greater as the footprint appointment interval is prolonged, which incurs more overhead in finding a shortest path between any two unconnected adjacent DAMST points. Besides, in Figure 13, it is obviously that more mobile sinks brings heavier overhead in network.