In order to investigate the impact of packet loss ratio and beacon sending frequency on ACC and CACC string stability performance, a simulation study was performed. By observing the speed and acceleration of following vehicles it can be investigated whether the disturbance of the leading vehicle is amplified upstream through the platoon, as was described in Section 2.2. Therefore, the vehicle speed as well as its undershoot or overshoot in situations of traffic disturbances, can be used as string stability performance measures. Vehicle speed undershoot (or overshoot) can be defined as the absolute difference between the lowest (or highest) vehicle speed of the last following vehicle and the (target) speed of the leading vehicle.
4.1 Experiment setup
The topology that is used in all our experiments is illustrated in Figure 3. A platoon of ten vehicles is placed on a straight single lane road 5,000 m long. We use a pre-defined time headway of 0.7 s. The distance at standstill is set to 7.7 m and vehicle length is 4.46 m. Varying Dstandstill is not of interest to the dynamic platoon behavior because it has no effect on the dynamic behavior, Dstandstill could be seen as a "virtual extension" of the vehicle. It is a margin a vehicle uses around its preceding vehicle. The distance between vehicles will change with different Dstandstill setting, which may impact communication. However, variations in the range [5, 10] m are not of that much influence.
The upper limit of the vehicle's acceleration is specified to be 2 m/s2 and the minimal acceleration is specified to be -9 m/s2, i.e., the deceleration does not go below -9 m/s2. These parameters apply to all experiments in our study except for those where we investigate the influence of different time headway values. In order to guarantee a high statistical accuracy of the obtained results, multiple runs have been performed and 90% confidence intervals have been calculated. For all performed experiments, the largest calculated confidence interval is ± 3.1052% of the shown calculated mean values.
In order to validate the controller model and traffic model, we simulate the performance of ACC (without communication), and CACC with perfect communication, where for CACC each vehicle can always get its preceding vehicle's acceleration within SUMO without loss and delay. The results (not shown here) are very similar to the results obtained in [9] and it is concluded in [23] that the original Simulink model and the combined SUMO-Simulink model are satisfactorily equivalent. In these baseline experiments, CACC outperforms ACC on string stability. Details of this experiment and its corresponding results and analysis can be found in [23]. This article covers a comparison between the string stability of an ACC system and of a CACC system which uses a non-perfect communication medium.
4.1.1 Simulation scenarios
The leading vehicle starts with an initial speed of 20 m/s that is kept constant until t = 80 s (i.e., up to the 8,000th simulation time step, where one time step = 10 ms). During this period each following vehicle has a stable speed (no fluctuations) of 20 m/s and distance between any two neighboring vehicles is also stable.
The leading vehicle performs a pre-set mobility pattern depending on the scenario--it either accelerates or decelerates, enabling study of these events in isolation. The metrics of interest depend heavily on the behavior of the leading vehicle and are calculated relative to the behavior of veh0 (e.g., under/overshoot of velocity). Using a step change of the lead vehicle acceleration heavily excites the system, such that the important dynamics become clearly visible.
For the first scenario, at time step 8,000, we let the leading vehicle decelerate with an acceleration of -9 m/s2, until the leading vehicle reaches the speed of 15 m/s. For the second scenario, at time step 8,000, we let the leading vehicle accelerate with acceleration 2 m/s2 until the speed of the leading vehicle reaches the value of 25 m/s. For experiments in this section, the packet loss ratio (PLR) and beacon sending frequency (BSF) are varied. The chosen values of packet loss ratio are 0%, 10%, 20%, 30%, 40%, 50% and that of beacon sending frequency are 25 Hz, 20 Hz, 15 Hz, 10 Hz, 5 Hz. We also simulate the case with a default beacon sending frequency and packet loss ratio of 15 Hz and 20%, and different time headway (TH) values: 2 s, 1.5 s, 1.0 s, 0.9 s, 0.8 s, 0.7 s, 0.6 s, and 0.5 s. Note that in all these experiments packet loss is artificially accomplished in a random fashion according to a uniform distribution, see [23]. Moreover, the dropping of a packet is independent from that of other packets.
In these experiments, we are only observing the velocity response of the last following vehicle, because when the platoon is not string stable it is this vehicle that will experience the strongest disturbances.
4.2 Simulation results and analysis
For the first scenario, due to space limitations, we only show a subset of the results obtained during this research activity. The other simulation results of vehicles with respect to both velocity and acceleration, and two-sided 90% confidence intervals for all the simulation results can be found in [23].
4.2.1 Deceleration
The curves from bottom up at the 9,000th time step of Figure 6 indicate packet loss ratio in descending order. It can be seen from Figure 6 that for a constant value of beacon sending frequency (10 Hz) and time headway (0.7 s), as the packet loss ratio increases, the velocity fluctuations of veh9 are increasing, which means that the disturbance of the leading vehicle is amplified more through the platoon upstream. In other words, the platoon is more string unstable. Moreover, the undershoot of the velocity is also getting larger as the packet loss ratio increases according to Figure 6. Figure 7 shows the acceleration corresponding to Figure 6; higher PLR results in delayed but larger response.
The undershoot of velocity for the last vehicle is shown in Figure 8. The undershoot is shown for different combinations of selected beacon sending frequencies and packet loss ratios.
From Figure 8 it follows that, with a selected value of beacon sending frequency and time headway (0.7 s), the undershoot of velocity for the last vehicle increases as the packet loss ratio increases, which means that the platoon becomes more string unstable. It can also be observed that for a selected value of packet loss ratio, the string stability becomes worse as the beacon sending frequency decreases. A vehicle always uses the acceleration value which is most recently received from its preceding vehicle as the input of the CACC controller. Therefore, a higher beacon sending frequency for the preceding vehicle results in a higher possibility of receiving fresh information under a constant packet loss ratio. Besides, lower packet loss ratio can also result in a higher possibility of receiving fresh information under a constant beacon sending frequency. For a BSF of 25 Hz packet loss has little effect because vehicles can still easily receive sufficiently fresh information. It should be noted, however, that at 25 Hz the wireless channel capacity will become a limiting factor when considering larger numbers of vehicles [10], so a low PLR is not always achievable.
4.2.2 Varying time headway
Figure 9 shows the velocity of the last vehicle for varied time headway settings for the BSF of 15 Hz and 20% PLR. Note that the curves from left to right at a velocity of 18 m/s of Figure 9 show the headway in ascending order. It can be seen from Figure 9 that with our selected beacon sending frequency and packet loss ratio, as time headway increases, the platoon becomes more string stable, i.e., the velocity of the last vehicle decreases with less fluctuations, findings also reported in [9, 18]. Figure 10 shows the acceleration of veh9 in response to the sudden deceleration of the lead vehicle. It clearly shows that, with shorter time headway, reaction of veh9 is sooner but more aggressive than with larger time headways, even to such a degree that deceleration resembles an emergency stop.
Furthermore, with larger time headways, the relative distance between vehicles is larger. when a disturbance occurs on a leading vehicle, the following vehicles do not react as aggressively as when small time headways are used. Though large time headways may be beneficial for string stability, they are detrimental to road throughput and capacity. Therefore, it is important though challenging to find the smallest time headway to guarantee string stability, while maximizing the road capacity, especially in the face of traffic and network dynamics.
4.2.3 Acceleration
For the second scenario, we again observe the velocity of the last vehicle. The results of the simulation are plotted in similar fashion as the first scenario.
Note that the curves from top down at the 9,100th time step of Figure 11 indicate packet loss ratio in descending order. For PLR = 0%, there is hardly any overshoot. The associated acceleration is shown in Figure 12 and shows that higher PLR results in larger acceleration.
Different from Figures 8 and 13 depicts the overshoot of the velocity associated with the last vehicle. From Figures 11 and 13 it can be seen that for a given value of beacon sending frequency and time headway, the CACC controller's performance on string stability is decreasing with a higher packet loss ratio. Accordingly, for a given value of packet loss ratio and time headway, the string stability gets worse with a lower beacon sending frequency. The acceleration of veh9, plotted in Figure 12, shows that with a higher PLR reaction is later and more aggressive.
4.2.4 Varying time headway
Note that the curves from left to right at a velocity of 22 m/s of Figure 14 indicate time headway in ascending order for a BSF of 15 Hz and 20% PLR. From Figure 14, the same conclusions can be derived as the ones derived from Figure 9 in the deceleration scenario. In particular, it can be observed that string stability is improving when the time headway is increased. Figure 15 shows the corresponding acceleration curves. It becomes clear that, even in an acceleration scenario, string instability may result in sudden deceleration of vehicles, clearly visible for TH = 0.5 s
4.3 ACC versus CACC
The third and fourth experiment scenarios are used to compare the ACC and CACC string stability performance. In particular, the third experiment scenario is similar to the first experiment scenario, where the lead vehicle suddenly decelerates. The undershoot of velocity for the last vehicle is shown for different combinations of selected beacon sending frequencies and packet loss ratios, see Figure 16. The fourth experiment is similar to the second scenario, where the lead vehicle suddenly accelerates. The overshoot of velocity for the last vehicle is shown for different combinations of selected beacon sending frequencies and packet loss ratios, see Figure 17. Note that in both experiments the string stability performance of the ACC system is not affected by the beacon sending frequencies and packet loss ratios, since ACC does not use beaconing, but radar measurements for the calculation of, e.g., time headway and acceleration, as modeled in the "Radar" block in Figure 2.
In both Figures 16 and 17, it can be observed that from the point of string stability performance, CACC strongly outperforms ACC. In particular, for a beaconing packet loss ratio of 0% the CACC string stability overshoot and undershoot are more than 10 times smaller than those measured on the ACC system. Even for a beaconing packet loss ratio of 50% the CACC string stability overshoot and undershoot are more than 5 times smaller than those measured on the ACC system.
High packet loss ratio or low beacon sending frequency can result in a low refresh rate of inputs at the controller. Though differences between, e.g., 0 and 50% PLR are large, the resulting CACC still outperforms ACC, reinforcing the conclusion of [9] that the CACC feed forward controller enables smaller time headways than the ACC feedback controller, while still maintaining string stability.
This research evaluated PLR and BSF. The delay of the communicated information is minimal, as 10 vehicles do not load the wireless channel to such an extent that contention delay increases significantly. It should be noted that in an 802.11p system high PLR is usually accompanied by increased delay due to its carrier sense multiple access with collision avoidance (CSMA/CA) medium access mechanism [24].