DEVELOPING A NEW HYBRID SAFETY CAR-FOLLOWING MODEL

For more than five decades, car-following models have been developed based on different theoretical backgrounds and conditions. The importance of these models belongs to their representation of longitudinal movement for any simulation model. Therefore, the accuracy of the car-following model is still the core of strength of any simulation model. For the purpose of this study, a hybrid car-following model has been developed to represent “go and stop” conditions. These conditions mostly occur in a weaving section. This model has been developed as a corner stone for a microscopic simulation model of representation of driver behaviour at a weaving section. A new condition that improves a driver behaviour in a situation at which the driver should not accelerate under specific condition as approaching from decelerated leading vehicle. Some assumptions of this model have been adopted from the CARSIM model. After developing this model using Visual Compact Fortran (version 6.5), the developed model has been calibrated with a set of field data from Germany. The results show that this model is more reasonable than other models such as Paramics, VISSIM, AIMSUN and CARSIM using the same set of data. This model show significantly improvement in representing the reality than the others.


Introduction
The selection of the suitable car-following model is a crucial task in developing a simulation model. Therefore, different car-following models have been developed and tested. These models are GHR, CARSIM, AIMSUN, WEAVSIM and Paramics (Gazis et al., 1960; Beneckohal, 1986; Zarean, 1987; and Panwai and Dia, 2005). The assumptions of GHR, CARSIM and WEAVSIM have developed using Visual Compact Fortran as test bed. Then, they have been tested under different sets of data including different traffic conditions. The results of these tests showed that CARSIM is the more reasonable in replicating the reality among the others in representing different traffic conditions (AL-Jameel, 2009 and 2010). Therefore, some of the CARSIM assumptions have been adopted to develop this carfollowing model. Accordingly, a new car-following model has been developed. This model was developed to represent the weaving section. High interactions and stop and go conditions need considerable attentions to be correctly represented. So, this was down by selecting the suitable limits of reaction time, buffer spacing, start-up delay and other characteristics as discussed in the following sub-sections. This model has been developed based on the assumptions adopted from CARSIM model as mentioned in the above paragraph. Each assumption governs the behaviour of the following vehicle in terms of the amount of acceleration/deceleration that would be produced.

Methodology
The methodology for this study is summarised by showing the main assumptions of the acceleration that have been adopted by this model and then explaining the calibration of the model with field data.

Acceleration Procedure
The acceleration procedure represents the main parts of the car-following model because it governs the nature of response of the following vehicle as shown in Figure1.

Vehicle Mechanical Ability Condition
As the vehicle is generated in the system, the type of each vehicle is assigned as either a passenger car or a heavy good vehicle. A passenger car has more mobility in the movement and manoeuvre because of its short length and light mass. These differences in these characteristics have been translated in the amount of acceleration/ deceleration that can be achieved by each type of vehicles (ACC B ) as shown in Table 1. Max deceleration (m/s 2 ) 4.9

Slow Moving Conditions
When a vehicle moves slowly due to platoon conditions, the spacing between this vehicle and its leader is governed by the length of the leading vehicle and the buffer space between the two vehicles. This buffer space has different values ranging from 1.8m to 3m and its value depends on the type of a vehicle (Benekohal, 1986 and Yousif, 1993). The smaller value is used for a passenger car and is higher than a HGV. However, different studies reported the opposite, i.e., passenger car following HGV with smaller headway than passenger car following passenger car Where; POSL=position of leading vehicle (m). POSF=position of following vehicle (m). SPF= speed of follower (m/s). ACCc= acceleration of following vehicle due to slow conditions (m/s 2 ). Dt= scanning time (sec).

Stopping Distance Conditions
To satisfy the safety conditions for a vehicle within the developed model, a sufficient space must be provided at every time of scanning to stop safely even the leading vehicle stops suddenly. The acceleration or deceleration that satisfies this condition can be determined from the following equations (Benekohal, 1986):-
G is the gradient of the roadway segment (%).

Moving From Stationary Condition
When a vehicle stops under platoon conditions and then it tries to move due to the movement of the leading vehicle, its acceleration (ACC E ) in this case depends mainly on the type of this vehicle. Therefore, the amount of start-up delay, in this study, was taken as 1 second which is suitable for driver with shorter reaction time and 2 second which is suitable for the rest of drivers (Benekohal,1986).

Approaching from a Deceleration Vehicle Condition
In this condition, when a vehicle approaching from another vehicle but there is a spacing less or equal to 76m and the difference in speed between the leader and follower is relatively high and the leader decelerates but according to the preceding conditions the vehicle needs to accelerate for a certain point and then decelerate. This is a high challenge for the existing safety car-following models and according to these models the driver behaviour at this

Kufa Journal of Engineering (K.J.E) ISSN 2207-5528 Vol. 5, Issue 2, June, 2014 Printed in Iraq
situation is unreasonable. Therefore, this condition has been adopted. In this condition, when a driver approaches from a decelerating vehicle and the separating distance is less or equal to 76m and the speed is increased, the speed of the vehicle in this case will be constant when the difference in speed is greater than 2m/sec. This is because that in reality, the driver seeing that his/her leader decelerates so he will not accelerate but try to maintain his speed for a certain distance and then take the appropriate action. The ACC F represents the symbol of this acceleration.

Calibration of the Developed Car-Following Model
The calibration of car-following model has been implemented with sets of field data using statistical tests. The specifications of the statistical tests and field data will be explained in details in the following sections.
There are several tests: Firstly, the Root Mean Square Error (RMSE) which is considered from a good test to make a comparison between empirical and simulated data The EM is used by Panwai and Dia (2005) as a measure of precision between the simulated and field data. This measure is affected by the number of points which are considered in the comparison of simulated and field data.
The field data was collected by the Robert Bosch GmbH Research Group. It was gathered by using an instrumented vehicle to record the relative speed and space headway (Panwia and Dia, 2005).This data consists of two vehicles: the leader and follower.This set of data provides a comparison of the distance between the leader and follower as shown in Figure 2. This set of data is characterised by:A range of speed between 0 and 60 kph.  Three stop situations.  The duration of this test is 300 seconds.
The selection of calibration parameters could be a serious issue. Basically, the developed car-following model can be classified as a safety model or non-collision model. Therefore, the reaction time is a critical factor that affects the spacing between the follower and leader and this parameter is taken from the accumulative curve according to Johansson and Rumer (1971). Several iterations have been implemented to select the suitable reaction time and then it is considered as a constant.
In brief, all characteristics of vehicles and drivers are considered constants and other factors have been changed. At this case, another condition has been used. In this condition,

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when a vehicle at distance less or equal to 76 m from its leader and the latter decelerates. At this situation, the following vehicle will accelerate and then decelerate hardly and this behaviour is not realistic behaviour because the driver in reality can see the objects ahead according to his/her sight distance. This limit (76 m) has been selected according to two conditions. Firstly, it was reported that a following vehicle does not affect by its leader when the spacing between the following and its leading vehicle is greater than 76 m vehicles (Edie  et al., 1963 and Aycin, 2001). Secondly, different iterations have been carried out as shown in Figures 2 from case 1 to 6.However, this limit does not affect at case 1 to 3 because the following driver under the influence of its leader according to the assumption of the developed model and there is no chance for free following. Whereas, the 4 th case (70) has the influence on the behaviour in the first part, free following case. This influence reduces from the difference between simulated and field data as shown in Figure 2-D and Table 2.
The 5 th case of the iterations (76 m) shows how this condition improves the behaviour graphically and mathematically as shown in Figure 2-E and Table 1-case 5. However, the sixth case is still as the same as the fifth case without any change. This is because the limited distance, just few minutes, at which 80 m lasted so the effect of this case could not be considered. Moreover, the effect of length more than 90 m has been not considered because this set of data is within the limited spacing as shown in Figure 2. Figure 2 shows the difference of the spacing between the leading and current (following) vehicle and the time of test extending up to 300 seconds. The first part of this graph, up to 25 seconds, there is a difference from the observed data. This means that the behaviour in the free following case needs a correction. Moreover, there are other situations at which there are other differences between the simulated and observed data such as following at low speeds and at stop conditions.  Furthermore, Figure 3 also shows the consistency between the simulated and the observed speed of following vehicle for the second case. On the other hand, another comparison has been implemented by using the same set of the data to calibrate other simulation models as indicated in Table 2 with the developed model. Table 2 shows each simulator with calculated values for each EM and RMSE.The minimum values of these measurements are corresponding with the AIMSUN. Whereas,the maximum values are for the paramics. Therefore, the AIMSUN is the best model among these models which mimics the reality. However, its value for the EM (2.55) is higher than the corresponding value obtained by the developed model (2.01). Moreover, the RMSE for AIMSUN (4.99) is higher than the value obtained by the developed model (3.49). Consequently, the developed model is the best among all these models in representing the car-following model.

Conclusions and Recommendations
The main conclusions that can be summarised from this study are:  The graphical representation and mathematical tests (EM and RMSE) show that the developed model is closer to the observed data than other models such as the AIMSUN (4.15), VISSIM (v3.70) and Paramics (v4.1).  The new condition adopted in this study has improved the developed model by reducing amount of error between the model and observed data ( reducing the value of RMSE from 4.99 to 3.49).  The developed car-following model could be the fundamental step to represent different sections such as merging, diverging and weaving.