5.1. Simulation Setup
The experiments were carried out with the aid of three different simulators, namely OMNeT++ 5.0 [31
] (event-based network simulator), SUMO 0.29.0 [32
] (road traffic simulator) and Veins 4.5 [33
] (vehicular network simulator, which integrates both aforementioned simulators). The physical (PHY) and medium access control (MAC) layers were implemented based on the WAVE (Wireless Access in Vehicular Environment) standard, also known as IEEE 802.11p.
As for simulation parameters, each vehicle had a transmission rate of 6 Mbps, a transmission power of 0.98 mW, a receiver sensitivity of −82 dBm and a transmission range of 200 m. Channel 178 (control channel (CCH)) was used to exchange beacon packets, thereby excluding the effects caused by channel switching between the CCH and the SCH (service channel).
In order to evaluate the applicability of the egocentric betweenness approach in vehicular networks, a real map clipping of the Erlangen area (Germany), obtained from OpenStreetMap (www.openstreetmap.org
), was used (Figure 6
). Meanwhile, a set of feasible vehicle routes was synthetically generated with the aid of SUMO. Vehicle mobility used the Krauss car following model [34
]. Five different sets of vehicles traffic densities were generated to validate our approach (40, 60, 80, 100 and 150 vehicles/km
Finally, all experimental results of this work were executed thirty-three times on different vehicle traffic densities with a confidence interval of 95%. Table 3
summarizes the simulation parameter settings.
In order to evaluate the performance of the proposed approach, eight metrics were used and are described in detail below.
Overhead: shows the number of beacon packets transmitted in the network by all vehicles during the simulation run;
Beacon transmitted per vehicle: gives the number of beacon packets transmitted per each vehicle during the simulation run;
Beacon received: displays the number of beacon packets received per vehicle during the simulation run;
Total of lost packets: is the sum of both RxTx (receive/transmit) and SNIR (signal to noise plus interference ratio) lost packets; the first one occurs due to the busy communication channel, whereas the second one occurs due to bit errors in received packets;
Channel busy ratio: indicates the fraction of the time in which the channel is identified as busy;
Regression analysis: is a set of statistical processes to estimate the linear relationships between two datasets;
Pearson correlation coefficient: expresses the strength of a linear association between two datasets;
Window time: points out the smallest window time under which there are no changes in the egocentric betweenness.
In order to provide a better understanding of our approach, results are compared to the ones obtained from the sociocentric betweenness approach. For this purpose, a dynamic graph was generated, with the aid of the Dynamic Graph Library [35
], to perform the sociocentric betweenness calculation [30
]. This library requires floating car data (FCD) as the input parameter. FCD is a method applied to gather traffic knowledge. In the sociocentric approach, all the vehicle network topology knowledge was used as input.
5.2. Simulation Results
The first set of experiments investigated how accurately egocentric betweenness scores correlated with the sociocentric betweenness scores in a VANET scenario; in other words, how accurate the results were when using only the local knowledge of the network topology to compute the betweenness score in highly dynamic networks, instead of using global knowledge of the topology. The results of this approach are shown in the scatter diagram set in Figure 7
, which compares the two approaches for each vehicle traffic density.
A scatter plot revealed the relationships between two variables (in our case, such variables were the sociocentric and the egocentric score). The relationship between two variables is known as correlation. The higher the correlation between the two variables, the closer the sample observations will be to a straight line. If the sample observations go along a straight line (or regression line) from the origin to high x- and y-values, then the variables are assumed to have a positive correlation. Thus, it is possible to observe in Figure 7
that the egocentric and the sociocentric betweenness scores have a positive correlation.
a–e show the scatterplots for densities of 40, 60, 80, 100 and 150 vehicles/km
, respectively. As can be seen in these figures, these two measures do not provide the same betweenness scores, as expected. The egocentric betweenness scores (y-axis) were smaller than the sociocentric betweenness scores (x-axis). This can be explained by the fact that in the ego-network topology, the maximal geodesic distance between nodes was two, and this limitation did not apply to the sociocentric betweenness. On the other hand, through the analysis of the figures, the egocentric and the sociocentric betweenness scores have demonstrated a high degree of similarity regarding the ranking of nodes. This similarity can be confirmed in Table 4
. The table depicts the Pearson correlation coefficient (PCC) between the egocentric and the sociocentric betweenness approaches. The presented values ranged from 0.953–0.983 (where 1.0 represents a perfect linear relationship between the two datasets analysed), in all traffic densities.
Lastly, it is possible to notice that some scores lie relatively away from the regression line (red line). Even so, there is a clear positive relationship between the two betweenness measures in VANETs.
and Figure 9
depict the cumulative distribution function (CDF), in each vehicle traffic density, of the egocentric betweenness scores and the number of one-hop neighbours, respectively. The CDF measure is an interesting way of observing the behaviour of analysed variables. As can be observed in Figure 8
, the egocentric betweenness scores fluctuate in the same range as in Figure 7
, according to the vehicle traffic density. Another important information is to analyse the distribution of these scores. It is possible to observe that 90% of the samples, for densities of 40, 60, 80, 100 and 150 vehicles/km
, were lower than 7, 11, 16, 18 and 30, respectively. In other words, these scores were close to the regression line (red line of Figure 7
), i.e., 90% of the samples of the two variables had a high correlation. The same distribution analysis was performed for the number of one-hop neighbours, as shown in Figure 9
. In this example, it is possible to notice that 90% of the samples, for densities of 40, 60, 80, 100 and 150 vehicles/km
, were lower than 7, 9, 12, 14 and 21 neighbours, respectively.
The relationship between the egocentric betweenness scores and the number of one-hop neighbours is depicted in Figure 10
. This figure shows the average egocentric betweenness score (red line) and the average number of one-hop neighbours (blue line) for all vehicle traffic densities. Therefore, it summarizes all the information presented in the two sets of Figure 8
and Figure 9
. The observed behaviour of both measures is in agreement: as the traffic density increased, the number of vehicles in the vicinity and the egocentric betweenness scores also increased. For instance, in a low traffic density (40 vehicles/km
), the egocentric betweenness score was around 2.5, and the number of one-hop neighbours was around 3.9, on average. On the other hand, in a high traffic density (150 vehicles/km
), the egocentric betweenness score and the number of one-hop neighbours were around 12.2 and 9.8 on average, respectively.
Another important analysis that can be performed in the egocentric betweenness measure is the calculation of the smallest time window duration in which there were no changes to the egocentric betweenness scores in relation to the vehicle traffic densities. The CDF of the time window duration in each traffic density is shown in the Figure 11
set. In this case, it is possible to notice that 90% of the samples, for densities of 40, 60, 80, 100 and 150 vehicles/km
, have time window durations that were lower than 9, 8, 7, 6 and 5 s, respectively.
shows the average time window duration in each traffic density. This metric is important in vehicular networks because many applications rely on a stable period of connectivity between nodes [36
]. The figure shows that as the traffic increased, the average time window duration decreased, until reaching a stable plateau. For example, when the density was 40 vehicles/km
, the average time window was around 3.55 s. When the density increased, the average time window rapidly decreased until reaching the plateau at 2.95 s, for the cases of 100 vehicles/km
and 150 vehicles/km
. For many distributed applications, the real-time content distribution within the area of interest was less than 2 s [37
]. Therefore, the average time window reached into all densities of the simulations was sufficient to meet the requirements of such applications. The behaviour depicted in the picture confirmed our expectation: as traffic increased, the trend was that the list of one-hop neighbours fluctuated rapidly over time. One point worth highlighting is that the time can vary according to the scenario used, as well as the mobility model and the vehicle traffic densities applied.
The second set of experiments consisted of performing the analysis of the network traffic. This analysis is needed to demonstrate the scalability of our proposed approach, since the periodic exchange of beacon packets, to stay aware of the one-hop neighbour topology, was carried out by means of vehicle-to-vehicle communications. The experiment results of the metrics such as overhead, beacon transmitted per vehicle, beacon received and total lost packets are depicted in Figure 13
. The detailed results of each one of these metrics are given below.
a provides a macroscopic view of the total number of the beacon packets transmitted in each traffic density. For instance, in densities of 40, 60, 80, 100 and 150 vehicles/km
, we had on average 49,000, 70,000, 90,000, 120,000 and 180,000 transmitted beacon packets, respectively. As can be seen, the beacon overhead increased linearly as a function of the traffic density, as expected. This expectation was well founded since as the density of vehicles increased, the higher the transmission rate of beacon packets into the network would be.
The microscopic view is depicted in Figure 13
b, which shows the average number of beacon packets transmitted by each vehicle in each traffic density. When the experimental scenario had a density of 40 vehicles/km
, each vehicle, on average, transmitted around 148 beacons during the simulation time; while, in the scenarios with 60 and 80 vehicles/km
, on average, 134 and 138 beacons were transmitted, respectively. For 100 and 150 vehicles/km
, there were, on average, 144 and 150 beacons transmitted by each vehicle, respectively. It is easy to see that the number of beacon packets transmitted, for each vehicle, is directly related to its trip time during the simulation time. With that in mind, Figure 14
depicts the average trip time of the vehicles during the simulation. It is possible to observe that in both of the aforementioned figures, the same behaviour appears in all the vehicle traffic densities. For example, in Figure 14
, for the scenarios with 40 and 150 vehicles/km
, the average trip times are higher than all other evaluated scenarios, reaching 2.8 and 2.55 min, respectively. On the other hand, the scenario with 60 vehicles/km
presented the lowest average (2.0 min). These behaviours are following the same pattern as in Figure 13
b, as well as the confidence interval.
c depicts the total number of beacon packets lost either by the fact that the communication channel was busy, or by errors in the received packets. As can be observed, the low densities (40 and 60 vehicles/km
) presented a minimum packet loss rate. As the vehicle traffic density increased up to 150 vehicles/km
, the total number of packets lost also increased. The observed behaviour was directly related to the channel busy ratio. Taking this into account, Figure 15
shows the average channel busy ratio for each vehicle traffic density. As the simulation time was set to 100 s, the calculation of the total busy time was nothing more than the channel busy ratio multiplied by the simulation time. In our case, for densities of 40 and 60 vehicles/km
, the channel was busy for the shortest time, and as the density increased, the average time also increased. Even in the density of 150 vehicles/km
, a maximum of 35% of channel availability was consumed. These results show that the beacon transmission frequency of 1 Hz was suitable, for this scenario, together with the mobility model applied, due to low channel utilization.
The number of beacon packets received per vehicle is depicted in Figure 13
d. This metric, combined with the channel busy ratio (Figure 15
), can indicate if the beacon transmission frequency is adequate or not. In the same way as the total number of beacon packets transmitted, the number of beacon packets received also increased linearly as a function of the vehicle traffic density. For instance, for densities of 40, 60, 80, 100 and 150 vehicles/km
, there were, on average, 480, 1300, 1700, 2000 and 3450 beacon packets received per vehicle, respectively. As mentioned before, the channel utilization in our approach was low; this confirmed, once again, that the beacon transmission frequency of 1 Hz was proper.