Evaluation I: a single lane freeway

The first case study consisted of a single lane freeway network and no driving behav-ior differences between vehicles. This simplified case study was selected in order to obtain full control over the experiment. Also, it prevents undesirable effects, such as, a moving bottleneck that is caused by a slow driving vehicle that cannot be overtaken. A one lane freeway of 5 km long was implemented in Vissim. A demand was created by generating an identical vehicle every 1.4 s while skipping occasionally a vehicle, for testing the homogenizing effect of the stabilization mode. This resulted in an inflow of 2323 veh/h. The vehicles had a uniform desired speed of 120 km/h in mode A, and of 80 km/h in modes R and S (assuming that 60 km/h is displayed). It is assumed that the penetration rate is 100% and thus all vehicles receive the instructions and comply with the instructions (in the sense that they all drive 80 km/h if 60 km/h follows from the instructed mode).

A period of 650 seconds was simulated for a jam wave scenario. The jam wave was created by artificially lowering the first vehicle’s desired speed to 20 km/h between the 80th and 115th second. The sampling time of the in-vehicle algorithm was set to the simulation time step (0.2s), and the sampling time step of the roadside controller was set to 5 seconds.

The Wiedemann 99 model which is implemented in VISSIM was used to model the driving behavior. For the reproducibility of the experiments but without going in too much detail, the parameters that were changed from the default settings are reported here: the number of vehicles observed ahead: 3, standstill distance: 1.5 m, head-way time: 0.9 s, ‘following’ variation: 4.0 m, threshold for entering ‘following’: -8.0 m, negative ‘following’ threshold: -0.35, positive ‘following’ threshold: 0.35, speed dependency of oscillation: 11.44, oscillation acceleration: 0.25 m/s², standstill accel-eration: 1.0 m/s², and acceleration at 80 km/h:1.50 m/s².

Figure 2.6: The vehicle trajectories per lane for the uncontrolled – A, B, E, and F – and controlled – C, D, G, and H – scenario I. The trajectories are colored according to speed, density and flow in the corresponding sub-figures. In plot F, the figures are colored green when they are in detection mode F, and red when they are in detection mode J. In plot H the trajectories are colored according the driving mode with A: green, R: blue, and S: orange.

Uncontrolled case

The resulting jam can be seen in Figure 2.6. The figure shows the speed, density, flow and the detection modes along each vehicle trajectory. Due to the jam wave scenario, the jam grows when the first vehicle’s desired speed is limited to 20 km/h, needs some time to set to a steady state, and finally it propagates upstream with a speed of approximately -18.5 km/h. The queue discharge rate is measured as 2350 veh/h, implying a capacity drop of 23%, since, the freeway capacity was measured as 3000 veh/h. The gaps that are created due to the skipping of some vehicles during the vehicle generation are clearly visible.

Controlled case

For the controlled case, the algorithm was roughly tuned, but even the initial tuning led to acceptable behavior. The parameter settings of the algorithm can be found in Table 2.1.

The control was started after 175 seconds when the jam was fully formed. The vehicle trajectories for the controlled case are shown in Figures 2.6. Several observations can be made from these plots. First of all, it can be observed that the jam wave is resolved around t = 220 s, indicating that the algorithm is capable of resolving a jam wave. Secondly, the structure of the algorithm is similar to the SPECIALIST algorithm. Initially, speed-limits are imposed over a stretch of approximately 1 km resulting in a low flow that resolves the jam wave. Upstream of these vehicles the

Table 2.1: The parameter settings used in the evaluations.

Variable Value I Value II

v^th 50 km/h 50 km/h

z^jam, z^ff 0.0417, -0.0417 km 0.0417, -0.0417 km

q^head 2800 veh/h 4200 veh/h

v^head -18.5 km/h -16.5 km/h

v^eff 80 km/h 60 km/h

d^headway 1/25 veh/km/lane 1/27.5 veh/km/lane

γ 0.5 0.5

a^T -3 m/s² -2 m/s²

v^max 130 km/h 130 km/h

v^S−head -180 km/h -100 km/h

ǫ^veff 5 km/h 5 km/h

speed-limited area is gradually increased in order to stabilize traffic. When the jam is resolved, speed-limits are released along a straight line causing a high outflow. An important difference is that the COSCAL v1 algorithm allows the speed-limited area to be adjusted over time due to the feedback structure.

The influence of the feedback can be observed at the tail of the blue area containing vehicles in mode R, and at the tail of the orange area containing vehicles in mode S.

Interestingly enough, it can be observed that initially – at time 175 s – the algorithm finds the jam resolving vehicle correctly. Later on, the algorithm moves the tail of the blue area upstream and downstream resulting in an overestimation of the required vehicles at the time instance when the jam resolves. The reason why this happens is that the speed with which the jam head propagates upstream decreases when the jam starts to resolve. This is due to the driving behavior created by VISSIM and it is uncertain whether it is realistic. It can also be observed that the speed with which the orange area is moved upstream changes in such a way that the gaps are closed. In this way the density is homogenized.

The following quantitative results were found. The total time spent (TTS) from time 165 s to 650 s of all the vehicles on the freeway in the uncontrolled situation was 14.33 veh·h and in the controlled situation this was 13.28 veh·h implying a gain of 7.3%. The reason why the TTS is improved is that the outflow of the freeway is increased after the jam is resolved as can be observed in Figure 2.7 A. The outflow is higher, since, the flow downstream of the stabilization area is higher than the flow downstream of the jam wave.

Figure 2.7 B shows the density in the stabilization area over time. It can be observed that from time 200 s to 240 s the density is close to the desired density of 25 veh/km.

However, when the stabilization area is just created or almost resolved, it is small so the density is not close to the desired density. On average the density is 24.4 veh/km with a standard deviation of 2.4 veh/km. The peaks that can be observed in the density

200 300 400 500 600

B: Density of vehicles in mode S

Density Target density

Figure 2.7: A: Comparison of the freeway outflow in the controlled and uncontrolled situation I. B:

Density of vehicles in mode S in situation I.

between time 200 s and 240 s are caused by the gaps that were created in the inflow.

It takes some time for the algorithm to fill these gaps but it can be observed that the algorithm is able to restore the density to the desired density.