Our group management protocol works by propagating leader heartbeats a specified number of hops from the leader, which determines the awareness horizon. Increasing the hop count allows us to track faster events since it extends the area in which nodes know about the oncoming event and requires a faster event to migrate faster than its corresponding logical entity. However as previously mentioned, the awareness horizon restricts the maximum leader heartbeat period, another important parameter of the algorithm. In the following experiment, we study the coupling between these parameters to analyze their affect on the maximum trackable event speed. Specifically, we vary the leader heartbeat period over a range above the pre-determined saturation points, and compute for each period the maximum event speed at which tracking always succeeds in maintaining a single entity for the moving target. A different curve is plotted for different awareness horizons.
Figure 7 shows the results of the above experiment. Following the curves from right to left, we can see that up to a threshold, reducing the leader heartbeat period results in the ability to track faster events. However, at this threshold, network collisions, congestion, and message loss become dominant. Hence, the maximum trackable speed deteriorates. This is apparent from the sudden drop in the maximum trackable speed seen on the far left side of the graph (about 100 ms). We also note that increasing the awareness horizon increases the trackable speed for slower heartbeats, but also congests the channel faster resulting in an inability to track faster targets. In the graph we notice that the single hop awareness horizon remains below the 2 and 3 hop settings up until about 400 ms, the point at which all but the 1 hop settings begin to break down.
A designer's decision to set the heartbeat period and the awareness horizon should be guided by the limitations on trackable speed shown in Figure 7. The trends seen in this figure illustrate the fundamental trade-offs involved in parameter selection in our algorithm. While the axes can be scaled depending on other platform settings such as node spacing, the figure provides interesting insights into the choice of protocol settings. For example, the figure shows that for speeds lower than 120 m/s (i.e., slightly more than half our communication radius per second) a designer has a choice of heartbeat period and awareness horizon settings that jointly allow a given speed to be tracked. The candidate settings are those that result from intersecting a horizontal line (drawn at the desired speed) with each of the three plots representing the different awareness horizons. Each intersection point gives the heartbeat period needed for the corresponding awareness horizon. In general, choosing a larger awareness horizon implies a more relaxed (i.e., larger) heartbeat period. For example, to track a target of speed 50 m/s, one can use a heartbeat period of 1600, 2900, and 4200 ms for a horizon of 1, 2, and 3 hops respectively. Interestingly, observe from Figure 6 that at those periods the network is fairly underloaded. When the target speed is higher than 120 m/s, however, larger values of awareness horizon fail, since they present a higher percentage of message loss and larger delays which allow spurious entities to be created. At those speeds a smaller awareness horizon is necessary.
If the designer has multiple choices, an important factor in choosing a particular combination of parameters is power consumption. The effect of parameter settings on power consumption is explored next.
