Keywords

1 Intersection Scenarios

In this section, selected intersection scenarios are discussed to exemplify the application of some of the methods described in Chap. 7.

1.1 Green Time Extension

Green time extension is a strategy for the platoon to cross the intersection without being split by the traffic light phasing. Conceptually, the intersection’s infrastructure receives information about the incoming platoon and extends the corresponding green phase within predefined limits. This reduces the lost time of the platoon, because the red phase is potentially avoided, as well as the platoon splitting. There is an additional advantage, namely the overall energy saving, because stopping a truck is more energetically expensive than stopping a car. Nevertheless, there is a negative effect for the traffic flow for some of the other streets in the intersection because their corresponding green time is reduced. Micro-simulation models and scenario variations allow to quantify this conflict numerically.

Micro-simulation Model

In order to quantify all these effects, it is necessary to develop a detailed micro-simulation model, as introduced in Sect. 7.1.3, containing the intersection geometry, traffic signs and traffic lights.

In order for the results to be representative, it is also necessary to quantify the initial and boundary conditions in the form of inflows, traffic composition or routing decisions. This can be achieved using the methods described in Sect. 7.1.1.

Systematic Scenario Simulations

Once a validated model is available, it can be used for systematic scenario simulations as described in Sect. 7.1.4. A high number of variants are generated by varying initial conditions, signal plans and control-specific parameters, such as the maximal green time extension. The specific intersection to be modelled is also subject to variation. These variants are then simulated, and the resulting key performance indicators are evaluated (as described in Sect. 7.1.5). As part of the evaluation, the benefits for platoons in terms of reduced lost time as well as the negative effects on other streets can then be analysed.

1.2 Coordinated Drive-Away

A further intersection scenario is the coordinated drive-away when the traffic light is initially red and turns to green during the scenario. The coordinated drive-away has been assessed as a strategy to minimise the accumulated reaction time. Trajectory optimisation methods can be used to calculate the optimal trajectories of the platooning trucks that comply with the given restrictions, such as minimal distance and acceleration limits (see Chap. 8). This assumes that the signal plan is known to the platoon, that is, it is known how many seconds are left until the green phase starts. In the resulting scenario catalogue, several parameters are varied, such as acceleration limits, initial spacing between the vehicles and others.

In this scenario, the focus lies on the evaluation of the minimised lost time in comparison with the lost times that result from the human driving behaviour, specifically the reaction times. It is thus necessary to quantify reaction times at intersections by using naturalistic driving studies, as outlined in Sect. 7.1.2.

1.3 Optimisation of Speeds and Distances Inside the Platoon

Another intersection scenario consists of the optimisation of the speeds and distances inside the platoon by making use of phase plan information. That is, the platoon can drive faster or with less distance between its vehicles in order to reach the green phase, assuming a fixed signal plan.

This strategy reduces the lost time of the platoon, since the red phase can be avoided. The traffic flow is also improved, making a better use of the fixed signal plan. Since platoon stopping or splitting is avoided, the strategy also generates advantages from an energetic point of view.

Assumptions

This scenario assumes that accurate information on the signal plan is known to the platoon, in order to be able to optimise the trajectories accordingly. This information could be sent to the platoon by means of I2V communication.

Systematic Scenario Simulations

In the scenario catalogue, the initial platoon positions and distances are systematically varied, as well as signal plans, vehicle lengths, vehicle characteristics such as acceleration ranges, and control parameters such as speed limits or minimal distances between the vehicles. Another aspect which is subject to variation is the minimal distance to the traffic light at which the trajectories optimisation can begin. It is important to vary this factor, since this is equivalent in evaluating the strategy with different communication ranges, and it allows to quantify the efficacy of different communication ranges in the context of this strategy.

2 Application of Analytic Approaches: Highway Throughput Based on Platooning Headway

This section proposes an example for a scenario in which analytic approaches can be taken. The influence of reduced platooning headway on traffic efficiency is assessed in two stages. First, a theoretical upper limit for the compression of the traffic under simplified assumptions is determined. Second, relevant parameters are sampled from broad ranges, and stochastic results are generated. These can be evaluated either in a very general way or specifically and a posteriori for a set of parameters whose values are unknown at the time of writing but will gradually become available as technology advances.

2.1 Analytical Models for the Traffic Throughput

The theoretical upper limit can be calculated based on mixed platooning (i.e. between all vehicle types) and full penetration with platooning capability. There is a functional relation between speed v, platooning distance \(h_{\text {p}}\) and traffic throughput \(\phi _0\),

$$\begin{aligned} \phi _0 = \frac{v_0}{(L_{\text {veh}} + h_p)} \end{aligned}$$
(9.1)

where \(L_{\text {veh}}\) is the mean length of the vehicles. By using such analytical relation, it is possible to assess the theoretical upper bound on traffic efficiency that we can achieve with a penetration rate of 100% and mixed platooning. Both assumptions are not realistic in the foreseeable future, so the results explicitly serve as a theoretical upper limit. Figure 9.1 shows the theoretical traffic flow that can be achieved for three levels of truck share.

Fig. 9.1
figure 1

Traffic flow as a result of specific combinations of driving speed and intra-platoon distance for three levels of truck share

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Using real-world data allows to use realistic truck shares in the traffic, as well as vehicle length distributions by vehicle type. It is then possible to calculate yet more realistic upper limits if arbitrary platooning vehicles penetrations are allowed. The following relation can be formulated:

$$\begin{aligned} \rho = \frac{1000}{\alpha \beta (L_{\text {truck}}+h_{\text {p}}) + \alpha (1-\beta ) (L_{\text {truck}}+h) + (1-\alpha )(L_{\text {car}}+h) } \end{aligned}$$
(9.2)

where

  • \(\rho \) is the density (vehicles/km).

  • \(L_{\text {truck}}\) is the length of the trucks.

  • \(L_{\text {car}}\) is the length of the cars.

  • \(\alpha \) is the proportion of trucks.

  • \(\beta \) is the proportion of platooning trucks over the total number of trucks.

  • \(h_{\text {p}}\) is the distance between the platooning vehicles.

  • h is the distance between the non-platooning vehicles.

The resulting traffic flow is then defined as \(\phi = \rho v\).

2.2 Stochastic Variations

By using an analytical model as above, it is possible to generate a large number of scene variants that include systematic variations of platooning share, traffic composition and vehicle lengths based on real-world data, as well as normal and platooning distances. It is possible to generate scenarios where all of the vehicles or only the trucks can be part of a platoon.

3 Theoretical Lower Limits on Intra-platoon Distance

A further example of the application of the methods of Chap. 7 is the study of the minimal intra-platoon distances for collision avoidance. In this scenario, non-platoon traffic participants are not considered. A stable moving platoon is assumed (constant, suitable speed, stable driving condition of all vehicles). More specifically, in this scenario there is a leading truck and a follower truck.

The leading truck brakes, and the reason of braking (obstacle, other vehicle, etc.) is not of interest here. This is communicated to the follower vehicle in the form of V2V messages. After a given communication delay, the follower truck starts to brake in order to try to avoid the collision. Safe braking distance considerations are illustrated in Fig. 9.2.

Fig. 9.2
figure 2

Safe braking within a platoon. Starting from an initial distance d and initial speeds \(v_1\) and \(v_2\) at time \(t_B\), each truck decelerates according to its deceleration capacity. A positive residual distance \(d_R\) at time \(t_S\) indicates that a collision can be avoided

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3.1 Scenario Definition

Several use cases can be defined, depending on the braking profile of the leading truck:

  • Normal braking.

  • Full braking.

  • Emergency braking.

Following the methodology proposed in Chap. 7, the basic scenarios for the analysis have to be defined. A basic scenario for any of these subcases comprises a combination of:

  • Street geometry, curvature profile.

  • Initial speed.

  • Initial positions.

  • Vehicle characteristics, including braking limits and mass.

  • Friction between street and tyre.

3.2 Evaluation of KPIs

The evaluation parameters that we use to evaluate the results (see Sect. 7.1.5) are the collision probability. In order to be able to quantify these probabilities, several simulations of the scenes are carried out varying the time delay with which the follower truck begins the braking manoeuvre (relative to the leading truck), as well as the braking profile of the follower truck (including acceleration limits and the braking duration). In each of the simulations, a crash can occur. The collision probability is thus the ratio between collisions observed and number simulations for each base scene.