De la Sattelzeit de Koselleck al contractualismo iusnaturalista de Duso

The ITS Modeller is a modelling environment in which intelligent cooperative vehicle- infrastructure systems can be modelled, tested and evaluated for their impacts on traffic efficiency, traffic safety and the environment (Versteegt et al., 2005). The environment has been build in the Java programming language and uses a modular set-up so that new models can be easily added. The ITS Modeller has to be connected to a commercially available traffic simulation tool for the road network and the generation of vehicles. Paramics was used in this study (Quadstone, 2005).

Each time step of 0.1 s, the ITS Modeller calculates new vehicle positions and states by a driver and a vehicle model. Next to these models, the ITS Modeller has an ITS model that describes the working of intelligent systems, such as a driver support system. The combined models produce the new vehicle acceleration and the decision to change lane or not. In each iteration, the driver model – and if applicable also the ITS model – produce driver actions, such as the desired acceleration and the new positions of the gas and brake pedals. Together with other input, such as vehicle characteristics and road geometry, these driver actions are then used by the vehicle model to generate the resulting vehicle acceleration and position of the vehicle. The different components of the ITS Modeller (see Figure 8.1) are discussed below. Most focus is put onto the longitudinal driver model, because this model forms the basis of the functional definition of the Congestion Assistant (see Section 8.2.3) and it has a large impact on the formation of traffic jams (see Section 8.3.4).

ITS Modeller Paramics - Road network Evaluation modules - Traffic efficiency Vehicle model ITS model Driver model

Figure 8.1: Components of the simulation environment ITS Modeller Longitudinal driver model

The longitudinal driver model describes the driver’s actions with respect to longitudinal vehicle control. This model distinguishes free driving and car-following behaviour. In each iteration, a desired acceleration is calculated for both situations. The most restricted one is used as the resulting desired acceleration. Several driver types can be modelled that differ in their longitudinal driving behaviour. In this study, drivers of a passenger car and a truck were taken into account.

Free driving

In the free driving situation, the driver attempts to reach or maintain his desired speed within certain boundaries. The desired speed indicates the speed that would be maintained in the absence of other traffic and is drawn from a normal distribution. The mean and standard deviation of the free driving speed have been determined from loop detector measurements (Van Arem et al., 1997). For passenger car drivers the mean desired speed is set at 121 km/h (SD = 12 km/h) and for truck drivers at 86 km/h (SD = 6 km/h). The desired acceleration for free driving is computed on the basis of the difference between the current speed and the desired speed:

(

v v

)

r a_{ref_v} = ⋅ _ref − (8.1) With v ref

a _{_} desired acceleration for free driving (m/s2₎

ref

v desired speed (m/s)

v current speed (m/s)

r relaxation factor (1/s) (default set at 0.4/s)

If the current speed deviates more than a given proportion (set at 3%) from the desired speed, the desired acceleration is made proportional to the speed error. The resulting desired acceleration is limited within the boundaries for comfortable acceleration and deceleration, which are set at 3 m/s2 and -5 m/s2 respectively.

Car-following

In the car-following situation, the driver has to adjust his speed and/or following distance with respect to traffic ahead. The model is based upon the assumption that drivers try to keep the relative speed to the predecessor zero and simultaneously attempt to keep the distance headway at a desired value. In addition to the original model, also the relative speed to the vehicle ahead of the predecessor is taken into account. The desired distance headway increases according to a quadratic function of the current speed:

2 3 2 1 c v c v c d_ref = + ⋅ + ⋅ (8.2) With ref

d desired distance headway (m)

v current speed (m/s)

3 2

1,c ,c

c constant factors (default set at 3, 0.25 and 0.02 respectively)

The desired acceleration for car-following is denoted by a linear combination of the relative speeds to the predecessor and the pre-predecessor and the deviation from the desired distance headway:

(

)

(

_{r ref}

)

_{v p rel p}

(

_r

)

_{v pp rel pp}

(

_r

)

d d ref c d t t d c v t t c v t t a _{_} = ⋅ − − + _{_} ⋅ _{_} − + _{_} ⋅ _{_} − (8.3) With d ref

a _{_} desired acceleration for car-following (m/s2₎

(

t tr

)

ref

d desired distance headway (m)

(

r

)

p

rel t t

v _{_} − relative speed to predecessor at current time t minus reaction time t_r (m/s)

(

r

)

pp

rel t t

v _{_} − relative speed to pre-predecessor at current time t minus reaction time t_r (m/s) d

c constant factor for distance deviation (default set at 0.3)

p v

c _{_} constant factor for speed deviation predecessor (default set at 1.5) pp

v

c _{_} constant factor for speed deviation pre-predecessor (default set at 0.2)

Equation 8.3 is based on the original Helly model (see Section 7.3.2). It is extended by including the speed difference with the pre-predecessor as an additional stimulus, so that the driver can better anticipate the downstream traffic situation (Klunder et al., 2006). As can be seen, the reaction time of the driver is taken into account when evaluating the distance headway and the relative speeds. Like the desired speed, the reaction time is drawn from a normal distribution. For car drivers a mean value of 0.3 s (SD = 0.05 s) is used and for truck drivers 1.0 s (SD = 0.3 s) (Van Arem et al., 1997). Note that these values are exclusive of aspects like delays for moving the foot between the gas and brake pedals and perception thresholds. These aspects are modelled separately.

Lateral driver model

The lateral driver model describes the driver’s actions with respect to lateral vehicle control. This model distinguishes free lane-changing and mandatory lane-changing and includes similar steps as the lateral models mentioned in Section 7.3.2. The free lane-change model represents overtaking when a slower predecessor is forcing the driver to reduce his speed below his desired speed. The mandatory lane-change model is applied if a driver is aware that the lane he is driving on does not lead to his destination, does not continue on the next link, or is not accessible to him. Generally, the free lane-change model is applied, unless a driver has to make a mandatory lane-change.

Free lane-changing

The first step of the free lane-change model is to determine whether the driver decides to execute a lane-change manoeuvre to the right or left lane. Secondly, when a lane-change decision has been taken, a simple procedure is used to simulate the actual lane-change execution. Rules are specified for ‘want to change’ and ‘perform the change’, both to the left and to the right. The rules for ‘want to change’ include a comparison of the current speed with the desired speed and with the speed of the predecessor in the current lane. Also the vehicle’s current acceleration with respect to the maximum comfortable acceleration and deceleration is evaluated. The rules for ‘perform the change’ refer to the safety of the intended manoeuvre, determined by a sufficiently large gap in the target lane. A time delay is used to simulate the actual lane-change execution. When a lane-change decision has been taken, it is executed not immediately, but only after this delay. For gaining speed advantage, the free lane-change model primarily considers lane-changes to the left. However, the model was adapted to introduce lane-changes to the right in congested traffic conditions to gain speed advantage (i.e. when the lane to the right moves faster than the current lane). This adaptation is applicable as soon as the current vehicle speed is below a threshold, set at 70 km/h. The safety of the manoeuvre is evaluated using the relative speed with respect to the new successor. Mandatory lane-changing

The mandatory lane-changing process consists of a number of steps. First, the driver has to perceive the forthcoming situation and choose a target lane. The simulated road network

might include discontinuity points. Such points imply that the current lane of the driver will not remain to be available for him. For each discontinuity point, there is a pre-warning distance. In this study, the pre-warning distance was set at 1150 m, which was based on the Dutch standard distance of 1000 m to announce a lane drop and a perception distance of 150 m. As soon as the driver passes the pre-warning distance, the target lane is determined. Next, the driver has to decide on the intention to change lane. There is a distance at which the driver will start to undertake action to change lane. If a mandatory lane-change is needed, the intention to change is drawn from a normal distribution cut off between the pre-warning distance and some distance before the discontinuity point. Then, the driver has to scan for an appropriate gap in the adjacent lane and control the relative speed and position. The driver controls his speed to the speed of the adjacent lane. If a gap is found, it is checked whether it is large enough. If that is the case, fine-tuning of the relative position takes place. When approaching the discontinuity point, the driver will gradually accept shorter distance headways. Also the minimum required gap decreases with decreasing distance to this point. At the same time, the fierceness with which the driver tries to control deviations from his intended relative distance or speed increases. Finally, the driver performs the lane-change if the gap is large enough, the relative position to the gap is right and the angular speed with respect to the new predecessor and successor are less than a certain threshold (default set at 0.021 rad/s).

ITS model

The ITS Modeller is particularly suitable for modelling the impacts of roadside and in-vehicle systems as well as cooperative systems. These systems can be implemented in the ITS Modeller as a new ITS model. The ITS model describes the behaviour of the system in question and the interaction between the driver and the system. The system may take over certain tasks from the driver. This can be represented by adapting the equations of the longitudinal and lateral driver models. If the driver is overruled by the system, the output of the ITS model is directly given to the vehicle model. Otherwise, the output is used by the driver model.

Vehicle model

The vehicle model describes the dynamic behaviour as a result of the interaction with the driver and the road, taking into account the ambient conditions. The input variables from the driver model are the positions of the gas and brake pedals. Together with these input variables, the vehicle model uses information about the characteristics of the vehicle, the road geometry, the condition of the road and the wind. The output of the model is an updated vehicle acceleration, which is used to calculate the new speed and position of the vehicle. Several vehicle types can be modelled that differ in their vehicle characteristics. In this study, passenger cars and trucks were taken into account.

Evaluation modules

The impacts of ITS systems, such as driver support systems, on the traffic flow can be evaluated by the evaluation modules of the ITS Modeller for throughput and safety. Both modules can provide a range of measurements. In this study, the following data on traffic efficiency and traffic safety were measured. For traffic efficiency: flow and speed, and for traffic safety: speed variation, Time-To-Collision (TTC) and acceleration behaviour (see also Section 8.3.5). The evaluation data can be retrieved per time interval (e.g. 1 minute) for cross- sections (i.e. detectors), links, routes and the whole network.

Paramics

The ITS Modeller functions as a shell for several commercially available traffic simulation tools. For this study, the ITS Modeller was connected to Paramics (Quadstone, 2005). This means that Paramics was used to build the road network, generate the vehicles and graphically represent the simulation. To release vehicles onto the network, Paramics calculates each time step the probability that a vehicle will be generated between pairs of origins and destinations. It then uses that probability against a randomly generated number from a so-called random seed to decide whether the vehicle will be released or not. The stochastic elements of the ITS Modeller (e.g. the desired speed) are connected to this random seed. To simulate the randomness of traffic behaviour, this study used a number of replications with different random seeds (see also Section 8.3.5). The behavioural models of Paramics are overruled by those of the ITS Modeller.

In document La hegemonía neoliberal. Historia de un simulacro (página 108-118)