Analysis of Testing Node 00/02

Meanwhile, it is necessary to understand that there are many factors contributing to the rate of hidden node collisions, including transmission coverage, length of vehicle fleet, packet generation frequency and vehicle location in group. For instance, we can predict that such a two-peak phenomenon dwindles when a vehicle is located further from the middle line of the group, thus indicating that there is only one peak at two edges of group 01, which is proved in Figure 7-16.

Figure 7-16 Throughput peaks of AC 3 at Testing Nodes 00 and 02

Analysis: From the above chart, we notice that, unlike Figure 7-13, there is only one highest peak and one lowest bottom for testing nodes at two edges of the vehicle group. The performance of throughput for each one turns out to be asymmetrical. For instance, throughput of 00 reaches its lowest value at a time point of around 3m17s, and experiences its second lowest bottom at 1m10s, as circled in orange on the chart. Meanwhile, there are symmetrical peaks and dips of testing nodes 00 and 02, which also show similarities at other

points.

In order to explain and prove these statements and assumptions, it is necessary to further illustrate all eleven stages of vehicle group mergence in Figure 7-17.

Figure 7-17 Eleven Stages of Vehicle Group Mergence

Parts 01 and 02 here are effective communication coverage for testing nodes 00 and 02, respectively. As we mentioned in previous analysis, due to the two types of collision existing in VANET, the packet receiving rate not only depends on how many vehicles are in coverage but also their locations. In our scenario, using testing node 02 as an example, part 02 can be sub-divided into left and right parts. Then, we define the vehicle number ration between left and right part as ɏ_{୪ୣ୤୲Ȁ୰୧୥୦୲}. Before the vehicle number changes in part 02, ɏ is always 20/0 {Stage 01}, followed by 20/ (1-20) {Stage 01-02}, (21-40)/20 {Stage 02-04}, 40/(20-0) {Stage 04-06} and (40-20)/0 {Stage 06-08}. Thus, we can see that within these eight stages mostly affecting the performance of testing node 02, no pair can be considered symmetric. For instance, if ɏ‹•36/20 at Stage 03, we can never find 20/36 throughout all stages, due to the initial ɏ being 20/0 in an asymmetric manner. That explains why

one lowest bottom happening at Stages 05 and 01, respectively.

Next, we study two less fluctuated trend lines of testing node 02, namely 2 and 3 marked by a dashed arrow line in Figure 7-16. Concerning the first trend, it happens when two vehicles get close to each other until a little portion of vehicles in group 02 enters into effective coverage of testing node 02 (Stage 01). Meanwhile, trend line 3 comes under an opposite situation when vehicles of group 02 are further away from the coverage (Stage 09). Most of the time, there are no vehicle number changes within part 02 throughout these two trend lines, which indicates that such a phenomenon is mainly due to the impact of vehicles outside of the testing node 02 effective coverage. According to the conclusion of scenario-2, packets transmitted by vehicles located more than 1 Km, even if they can be harder decoded or sensed along with distance, will arouse a higher probability of a sensed busy period, thus reducing the throughput of testing node 02. A similar mechanism causes trend line 03, where out of coverage vehicles, to gradually have a lower negative impact on part 02. However, the reason that the lowest bottom is found on trend line 2 rather than 3 is because there are still hidden node collisions on time periods of trend lines 2 and 3. Also, the former instance turned out to represent a much more balanced pattern on two sides of part 02, namely lower

ɏ. Thus, hidden node collisions in trend line 02 will be higher than their counterparts of 03. By reviewing Figure 7-17 again, we notice that there are symmetric patterns in this chart, which are based on middle Stage 06. For instance, Stage 02/10 can be considered as a ͳͺͲ଴

rotated pair. However, it requests us to change the view from testing node 02 to 00; otherwise, it cannot be considered as equal. Combining what we studied previously, we can conclude that every stage experience by testing node 02 will not repeat itself but will still be a counterpart of 00 in a reversed sequence, due to the location and relative movement of these two vehicle groups. Therefore, we predict that their throughput patterns need to be both rotated and shifted based on a time axle, which is proved in Figure 7-18.

Figure 7-18 Rotation and Shift of Testing Node 02 Throughput Diagram

From what is stated above, it reveals that throughout the procedure of an approaching vehicle group at any given time point, every vehicle in the group will contribute a different performance. Their delays will all be presented in a bell-shaped curve but will have space between one another due to location difference. On the other side, the performance of throughput turns out to be more complex, whereby every node evolves based on the counterpart in the middle of the vehicle group. Figures 7-19 and 7-20 demonstrate the evolution.

Figure 7-20 Reception Throughput of Vehicle 01/10/15/20

From Figure 7-20, we see how this two peak phenomenon evolves from edge to middle of the vehicle group. It seems that when the distance between node and group middle line becomes shorter, the side containing the lowest bottom will gradually ramp up, which will push the existing peak (green arrow indicated) backwards and will make itself approach the middle line of the time axle (red arrow indicated) until the two peaks equally locate at each side of it.