The different m and k values found at different study sites gave an indication Wortmannin of the heterogeneity of vehicle-following behavior across locations. Among other vehicle-following models that have been studied extensively are the Helly model [9], Gipps model [10], and Intelligent Driver model [11]. Although these models take different functional forms, they share the same characteristics

of having the follower’s acceleration x¨ft+Δt as the response, and follower’s velocity x˙ft, relative velocity x˙lt-x˙ft, and space headway xl(t) − xf(t) among the stimulus terms. Earlier vehicle-following studies have assumed that the model form and constants, once calibrated, applied to all the driver-vehicles or at least all passenger cars observed

at the same site. Most of the available traffic simulation models, such as CORSIM [12] and VISSIM [13], assume one model form for all the driver-vehicles but account for variation between driver-vehicles by assigning different parameter values. In CORSIM, there are 10 types of drivers; each represents a different degree of aggressiveness in vehicle-following. Each vehicle generated in a CORSIM model is randomly assigned one type of driver. In VISSIM, users are able to define the probability distributions of desired speed, maximum acceleration, and other vehicle performance parameters. Recently, researchers have begun to study the different responses between drivers (interdriver heterogeneity) and for the same driver (intradriver heterogeneity, part of it is also known as asymmetric behavior) when presented with similar stimuli. Brockfeld et al. [14] and Ranjitkar et al. used trajectory data collected from nine vehicles driven in a test track in Hokkaido, Japan, using Global Positioning System receivers to calibrate many vehicle-following models [15]. They found that different vehicle-following

models produced different error magnitudes after parameter calibration. They noted that the variation of errors between drivers were larger than the variations between different vehicle-following models. Ossen and Hoogendoorn fitted the parameters λf, m, and k of the GHR model to a vehicle trajectory data set collected at the A2 Motorway in Utrecht, the Netherlands [16]. They found that different drivers had different calibrated λf, m, and k values. Punzo and Simonelli fitted four vehicle-following models to vehicle trajectory Entinostat data collected in Naples, Italy [17]. They found a high degree of variability of the calibrated parameter values among drivers and also for the same drivers under different driving conditions. This is perhaps the first report on the observation of intradriver heterogeneity. Ossen et al. again attributed the difference in the observed vehicle-following behavior between drivers to (i) different vehicle-following equations and (ii) different parameter values of the equations [18].