In this section the collection of metrics is discussed with diagrams and presentation of the results. All the simulations were run with varying settings, so that an appreciation of all the situations that may occur (that we can control in the simulator) can be established. It is important to note, as previously mentioned, that in the initial studies we assumed that all vehicles in the simulation are equipped with the technology for message propagation. In reality this market penetration will take many years to achieve, but many car manufacturers are working on supplying this technology soon [18].
In later studies, as shown in Section 6.5, we have explored different rates of equipped vehicles in the simulation. This requires that all parameters remain static whilst testing the equipped vehicle rates, such that we can rule out any influence from transmission range, vehicular density and vehicle velocity. For each run at different parameters we tested equipped vehicle rates from 0% to 100% in increments of 10% and performed 20 runs to average out the data and remove any transient or artifactual data.
6.1. Velocity Experiments
These experiments test the effectiveness of the algorithm as vehicle velocity changes, to see if the algorithms are suited to an urban (slow) or highway (fast) environment. When ignorant (no messages have been received), the cars will still attempt to change lane to avoid the obstacle, but only as part of the original lane-changing algorithm, and so congestion builds up in a short amount of time, for most simulations. Below a certain network load the road will never become congested, so the vehicular load of the experiment was varied for each experiment. The vehicular load on the road was also set low enough so that the algorithm could affect the flow of cars as, at high loads, this would not be possible. To this end there is, in any system, a critical value of vehicular load after which no action can prevent or reduce congestion.
Some early simulations with low vehicular loads showed that it is sometimes more efficient to be ignorant of the obstacle, and this must be taken into account, as in this case the best course of action is to drive normally, using the normal algorithm.
Figures 2 and 3 show results from a sample of the experiments we ran to test this theory. By varying all the parameters available we found that certain velocities, transmission ranges, and vehicular load had different levels of effectiveness to the overall congestion in the system. In the main the results showed that our algorithm always produced a positive effect. In order to produce valid data we ran several simulations with the same parameters and then averaged this data, to show results for a typical case.
Figures 2 and 3 show the number of cars exiting the field in a simulation run as an aggregate over time. Both show an advantage for infected cars using the advanced lane-changing algorithm, but the advantage is greater at higher velocities, where the vehicles have more distance between them for the same vehicular load, meaning they can more easily change lane.
We found, and Figures 2 and 3 corroborate this, that the advanced algorithm increased the time before congestion began to build up and then once congested, the infected cars still moved through the system more efficiently. By running the simulation for 15 minutes we can monitor the development of congestion in the system and how the flow is affected by the changed algorithm.
The results show interesting behaviour, beyond the reduction of congestion in the system. By analysing the first 5–7 minutes of simulation time, we can see that the development of congestion is also slower once vehicles do start to slow down. This is because of the algorithm moving vehicles into the opposite lane to the obstacle, reducing the load on the lane with the obstacle and therefore reducing the number of stopped vehicles behind the obstacle which, when changing lane, cause a dramatic slowdown in the new lane. This reduction in stop-and-go vehicular formation is also seen elsewhere in the field when the cars are infected with the warning message and switch to our adapted algorithm.
6.2. Position of Lane Change
A factor that affects the build-up of congestion in the system is related to the location of the lane change. The following results show where the lane change occurs with no communication and then using our enhanced lane change algorithm with communication active. The simulation settings were set at 2200 cars/hour load, speed limit of 120 km/h and a transmission range of 100 m.
During the simulation the message propagates backwards towards position 0 and, with the advanced algorithm, the location of the lane-change also reduces. When the system starts to slow and vehicular density increases, the lane-change moves right back, causing a slower build-up of congestion and a greater amount of free vehicular flow, as shown by Figure 4. This does place greater load on the opposite lane to the obstacle, but the reduction of stop-and-go behaviour negates this. In Figure 4 the rapid reduction in position of most lane changes between 395–405 seconds and again at 475–500 seconds represents a period when the propagation of the message is continuous, and the periods of little change (of lane change position) are due to reduced propagation of the warning message. The initial peak of lane change position between 0 and 35 seconds represents the initialisation of the system, that cars can change lane very close to the obstacle due to the road being less loaded. The data to produce this result came from a single typical simulation, with parameters set as per the previous paragraph.
6.3. Transmission Method Experiments
In this experiment the available transmission methods are tested with the new algorithm, to see how they affect the overall congestion in the system. Figure 5 shows a simulation run until congestion is present at the origin of the field (i.e., position = 0). The simulation is stopped when the congestion reaches the origin as after this point the algorithm is not affecting the vehicular flow. The values represent the proportion of cars leaving the field in relation to the cars entering
. This indicates how vehicles are flowing through the system, where an increase of the gradient represents free flow and a decrease represents congestion.
The models shown in Figure 5 are simple flooding, where the message is rebroadcast just once, edge detection which is explained in Section 3.1, and distance detection, which is a different probabilistic method and a mixture of edge and distance detection. These models are all running in the simulation, but the mixed (edge detection and distance detection) offers the best simulation of a real epidemic protocol.
As can be seen in Figure 5 the edge detection method alone offers little improvement over no propagation, and the simple flooding and distance detection methods offer a good initial advantage (0–200 seconds) but then suffer very fast congestion build-up. The mixture of edge and distance detection algorithm, with our changes to the lane change model offers excellent results keeping near free flow until ca. 420 seconds, when the network then slows and starts to congest, but this takes longer (ca. 250 seconds from the first slowdown) than the other algorithms.
The addition of this propagation method and the changed algorithm prevent several congestion-causing situations to occur. The main situation avoided is when vehicles are unable to change lane to avoid the obstacle and begin to slow down, but then do change lane causing the cars behind to slow. This cause has been seen to initiate the build-up of congestion by earlier warning of the obstacle so that the cars can change lane at a high velocity. Another behaviour of the system is that when the congestion is initiated, the cars will fill up behind the obstacle, unable to change lane. With the adapted algorithm the extra incentive to change lane means that the opposite lane fills first and so vehicles can still move, increasing the time before the whole system becomes congested.
6.4. System Velocity
The average velocity through a system is of great importance. If a higher average velocity can be achieved the number of vehicles passing through the area of congestion will be higher than if there is much slowing of vehicles. Figures 6 and 7 show the average velocity calculated for intervals of 10 metres on the
axis and an interval of 30 seconds across the
axis. Each point represents the average velocity at that time/position interval. In both figures there is a noticeable slowdown as the vehicles pass the obstacle. This can be accounted for by the IDM attempting to retain a minimum safe distance between vehicles.
Figure 6 shows that after an initial even velocity through the field, congestion begins to build up at the position of the obstacle between 100 and 200 seconds, which causes a slowdown further back to position 0. By time of 330 seconds the congestion has reached position 0, and the average velocity falls from 20–25 ms
to 0–5 ms
.
As can be seen in Figure 7, there is a uniform average velocity before and after the obstacle during the whole period of the simulation (10 minutes). This reinforces the results from the other simulations and proves that there is a better flow of vehicles through the network, as well as a reduction in the build-up of congestion, when effective transmission of the road condition occurs.
We note that for both figures there is a spike in velocities (between time 0–10 and position 1200–1400). This is the period when the first cars are leaving the field. As they have no cars in front they can accelerate up to the full speed limit unhindered. To remove this artefact future simulations will have a "warm-up" period, with low vehicular load, that initialises the field.
6.5. Varying Penetration Rate of Radio-Equipped Vehicles
In all of the simulation studies and results presented in Section 5, we have assumed that 100% of the vehicles in the simulated field are radio equipped and therefore able to receive and retransmit (where necessary) the data about the upcoming incident or congestion. This is a somewhat idealised view of how deep uptake of radio-equipped vehicles will be. More likely, as vehicle manufacturers and radio equipment providers begin releasing the products to operate and support a VANET, the ratio of equipped vehicles will increase. Due to the critical safety-of-life applications of VANET, it is important to study the efficiency and resilience of simulated applications, to study the point at which they become usable and reliable. This simulation study involved the same system as in previous experiments, but here the proportion of equipped vehicles is increased from 10% to 90%. The plots in Figure 8 show the flow trajectories of vehicles in the system.
We ran each simulation several times, to ensure no artifactual or erroneous data was included in our results, but the results shown here represent only one simulation. As can be seen at low penetration rates (10%–40%) the vehicles reach the obstruction and begin to congest, but between 60% and 70% there is a noticeable improvement, or smoothing, of the vehicles velocity through the field of study. The figures show that above 70%, where there is still some congestion build-up around the obstruction, the propagation of information to vehicles further away, and the change to the lane-changing algorithm this triggers, allows for more steady driving through the field of study, and less congestion.