2.5 Simulation
2.5.2 Evaluation II: a two-lane freeway
The objective of the second evaluation was to test the controller performance when applied to a two-lane freeway with driving behavior differences between vehicles. This case study was selected to test the performance of the algorithm in a more realistic set-up. An important difference with the single lane case study is that vehicles can change lanes, and that the traffic flow characteristics, e.g. the location of the jam-head can differ per lane. In this implementation the algorithm is not adjusted to include these effects. Thus, when applying the COSCAL v1 algorithm it assumes that all the vehicles drive in the same lane, and that the traffic flow characteristics are identical per lane. In Section 2.6 the extensions of the algorithm that have to be investigated when dealing with multi-lane freeways are discussed.
A 2 lane freeway of 7.5 km long was implemented in Vissim and speed differences between vehicles were allowed. A constant demand of 3550 veh/h was applied to the freeway and a simulation time of 1800 seconds was considered. A jam wave was created by slowing down vehicles between location 6.9 km and 7.4 km to 0 km/h from time 250 s to 350 s. The evaluation was repeated ten times for different random seeds, namely random seeds 1 to 10.
The Wiedemann 99 model which is implemented in VISSIM was used to model the driving behavior with the following settings: the number of vehicles observed ahead:
3, standstill distance: 3.5 m, headway time: 0.7 s, ‘following’ variation: 6.0 m, thresh-old for entering ‘following’: -8.0 m, negative ‘following’ threshthresh-old: -0.10, positive
‘following’ threshold: 0.10, speed dependency of oscillation: 6.00, oscillation accel-eration: 0.25 m/s2, standstill acceleration: 0.5 m/s2, and acceleration at 80 km/h:1.50 m/s2
Figure 2.8: The vehicle trajectories per lane for the uncontrolled – A, B, E, and F – and controlled – C, D, G, and H – scenario II. The trajectories are colored according to: (A, B) detection mode with green detection mode F, and red detection mode J, (C, D) driving mode with A: green, R: blue, and S: orange, and (E, F, G, H) speed.
Uncontrolled case
The uncontrolled situation is shown in Figure 2.8 for random seed 2. The detection mode (top) and speed (bottom) in the left and right lane are shown in this figure. The queue discharge rate is measured as 3550 veh/h implying a capacity drop of approxi-mately 5.3%, since, the freeway capacity was approximated as 3750 veh/h. The TTS for all the different random seeds from time 400s to time 800 s is 130.7 veh·h with a standard deviation of 9.5 veh·h.
Controlled case
The control was started after 400 seconds when the jam wave was fully formed. The tuning variables are shown in Table 2.1. Some small changes to the tuning variables used for the first evaluation set were made, namely, the flow over the jam head was set to 4200 veh/h, the speed of the jam head was set to -16.5 km/h, and the target following distance was set to 1/55 veh/km, the deceleration was set to -2m/s2, and the S-head line speed was set to -100 km/h.
Figure 2.8 shows the trajectories plots for the controlled situation for random seed 2.
From this figure it can be observed that the jam wave is successfully resolved. Also, a clear difference can be observed in the jam resolution (blue) area between the left and right lane, clearly vehicles move to the right lane because of the lower flow and speed in this area and in the jam wave the vehicles move back to the left lane. Also, in the stabilization are (orange area) less vehicles seem to be present in the left lane.
Figure 2.9 shows the density in the stabilization area in the left (top) and right (middle)
400 450 500 550 600 650
400 450 500 550 600 650 Time (s)
400 450 500 550 600 650 Time (s)
Figure 2.9: The density of vehicles in mode S over time in situation II in the different lanes. The dashed dotted line indicates the target density.
400 450 500 550 600 650 700 750 800
Time (s)
Figure 2.10: Comparison of the freeway outflow in the controlled and uncontrolled situation II.
lane over time. From these plots it can be observed that the density in the left lane is lower than the target density and in the right lane lower. The bottom plot in Figure 2.9 shows that these effects compensate each other resulting in a density in the stabilization area that is near the target density.
Figure 2.10 compares the freeway outflow for the controlled and uncontrolled situa-tion with random seed 2. Similar as in Figure 2.10, the outflow increases after some time. This time – around 600 s – corresponds with the time when the flow out of the stabilization area reaches the downstream end of the freeway.
The following quantitative results were found. The TTS for all the different random seeds from time 400 s to time 800 s was 108.0 veh·h with a standard deviation of 6.1 veh· h indicating an average TTS gain of 17.3%. The average density in the stabi-lization area on both lanes for the different random seeds was 53.5 veh/km/lane with a standard deviation of 1.4 veh/km. The average density on the right lane was 27.8 veh/km/lane with a standard deviation of 1.3 veh/km/lane and on the left lane it was 24.3 veh/km/lane with a standard deviation of 0.4 veh/km/lane. This indicates that the speed-limited vehicles prefer to drive on the right lane causing a density difference on both lanes which on the average results in a density slightly lower than the target density of 27.5 veh/km/lane.