Car-following models

Micro-simulation models are commonly built up by using numbers of sub-models; one of the most important sub-models is car-following (Olstam and Tapania, 2004). The car-following model describes the interaction between a vehicle and its leader (the vehicle immediately in front) in the same lane by calculating the acceleration/deceleration rates used in updating the longitudinal position of the vehicle in correspondence to its leader. For any vehicle in traffic, when its acceleration/deceleration rates are known, the speed and position of this vehicle can be easily determined through the manipulation of the standard equations of motion.

In previous studies, several car-following models have been proposed to represent the longitudinal movement of vehicles. The following sub-sections discuss the main groups.

2.8.1.1 Gazis Herman Rothery (GHR) model

The Gazis Herman Rothery (GHR) model represents the earlier well-known car-following model and it was developed in the late fifties at General Motors’ Research Laboratories (Brackstone and McDonald, 1999). The GHR model is based on a stimulus- response type of function and its mathematical formulation states that the acceleration of the following vehicle (n) is related to the differences in speeds and spacing between the following vehicle (n) and its leading vehicle (n-1), as shown in Equation 2.2 (Brackstone and McDonald, 1999). Figure 2.3 shows the car-following notations.

𝑎𝑛(𝑡) = α𝑣𝑛𝛽(𝑡)

𝛥𝑣(𝑡 − 𝑅𝑡)

𝛥𝑥𝛾_{(𝑡 − 𝑅𝑡)} Equation 2.2

Where:

vn(t):the speed of vehicle n (m/sec) at time (t),

∆x(t-Rt): the relative distance (m) between vehicle n and n-1 assessed at earlier time (t-Rt),

∆v(t-Rt): the relative speed (m/sec) between vehicle n and n-1 assessed at earlier time (t-Rt),

Rt: the driver reaction time (sec), and

α, β, γ: the model parameters.

Figure 2.3: Car-following notations

Brackstone and McDonald (1999) provided detailed information about the GHR model parameters values (i.e. α, β and γ), and they also listed the researchers who tried to improve this model during the past five decades. However, the authors reported that due to the large number of contradictory findings of the values used to represent the model parameters, the GHR model is being used less frequently. Gipps (1981) reported that there is no obvious relationship between the parameters of the model and drivers’ or vehicles’ characteristics. In addition, Olstam and Tapania (2004) reported that the driver of the following vehicle reacts to its leader actions even when the spacing between them is too large. However, some traffic simulation models, such as MITSIM (Yang and Koutsopouls, 1996), used this type of car-following model (Al-Jameel, 2012 and Al-Obaedi, 2012).

2.8.1.2 Safety distance or collision avoidance (CA) models

The main idea of this group of car-following models is to avoid the colliding of vehicles by providing a safe separation distance between the following vehicle and its leader. According to Brackstone and McDonald (1999), Kometani and Sasaki in 1959 produced the first model of this group.

In 1981 Gipps presented a car-following model which depends on the idea of safe distance keeping. The model by Gipps (1981) is based on the assumption that the driver of the following vehicle can select a safe speed to ensure that he/she can bring his/her vehicle to a safe stop if the vehicle in front comes to a sudden stop. The Gipps model has been used in many micro- simulation models such as the DRACULA (Liu,2005) and AIMSUN (Barceló and Casas, 2005) models.

The CAR-following SIMulation model (CARSIM) (Benekohal, 1986) is another example of a CA model. According to the CARSIM model, the drivers are assumed to maintain a sufficient

n n-1 Traffic direction

distance from their leaders to react safely if any changes occur ahead. The CARSIM model can represent traffic in both normal and stop and go conditions (Benekohal and Treiterer, 1988), since the acceleration rate of the following vehicle is selected from five different situations (acceleration/deceleration). The CARSIM model has been used in many micro-simulation models (see for example Yousif, 1993; Purnawan, 2005; Al-Obaedi, 2012; Al-Jameel, 2012; and Alterawi, 2014).

2.8.1.3 Psychophysical or action point (AP) models

According to these models, the driver will perform an action (acceleration or deceleration) when a certain threshold is reached. This threshold can be expressed as a function of the difference between pairs of vehicles in speeds or spacing. According to Ahmed (1999), Leutzbach (in 1968) proposed the psycho-physical model which addresses two limitations of the GHR models. These two limitations are, first, the driver of the following vehicle reacts to its leader actions even when the spacing between them is too large, and second, the driver reacts to small changes in front relative speeds.

The AP models produced perceptual thresholds which represent the minimum value of the stimulus to which the driver will respond (Toledo, 2007). For example, at low space headways the relative speed threshold is small and gradually increases with the space headway. At certain high space headways, this threshold becomes infinity which means that the follower no longer follows its leader. PARAllel MICroscopic Simulation (PARAMICS) (Duncan, 1995) is a good example of this group of models. However, these models suffer from difficulties in calculating and calibrating the perceptual thresholds (Brackstone and McDonald, 1999; and Panwai and Dia, 2005).

2.8.1.4 Other car-following models

There are several other approaches which have been used by researchers to model car- following. The fuzzy logic-based model is one of these approaches. This model is based on the theory that some of the system sets are not crisp but fuzzy (Khodayari et al., 2011). The model divides variables into a number of overlapping sets combining each one with a specific term which describes how sufficiently a variable fits the description of a term (Brackstone and McDonald, 1999). The linear (Helly) model is another approach to the car-following modelling. This model is based on the GHR models and was improved by Helly in 1959 by introducing a desired following distance factor (Panwai and Dia, 2005).