Models of driving behavior (e.g., car following and lane changing) describe the longitudinal and lateral movements of vehicles in the traffic stream. Calibration and validation of these models require detailed vehicle trajectory data. Trajectory data about traffic in cities in the developing world are not publicly available. These cities are characterized by a heterogeneous mix of vehicle types and by a lack of lane discipline. This paper reports on an effort to create a data set of vehicle trajectory data in mixed traffic and on the first results of analysis of these data. The data were collected through video photography in an urban midblock road section in Chennai, India. The trajectory data were extracted from the video sequences with specialized software, and the locally weighted regression method was used to process the data to reduce measurement errors and obtain continuous position, speed, and acceleration functions. The collected data were freely available at http://toledo.net.technion.ac.il/downloads . The traffic flow characteristics of these trajectories, such as speed, acceleration and deceleration, and longitudinal spacing, were investigated. The results show statistically significant differences between the various vehicle types in travel speeds, accelerations, distance keeping, and selection of lateral positions on the roadway. The results further indicate that vehicles, particularly motorcycles, move substantially in the lateral direction and that in a substantial fraction of the observations, drivers are not strictly following their leaders. The results suggest directions for development of a driving behavior model for mixed traffic streams.

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h i g h l i g h t s• We propose novel performance metrics for numerical integration schemes. • For car-following models, the ballistic scheme is always superior to Euler's scheme.• The standard RK4 scheme is only efficient for unperturbed single-lane traffic.• Heun's scheme is generally the best for simple situations. • The ballistic scheme prevails for complex situations with stops and lane changes. a b s t r a c tWhen simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the fourth-order Runge-Kutta method (RK4) are rarely used while the simple Euler method is popular among researchers. We compare four explicit methods both analytically and numerically: Euler's method, ballistic update, Heun's method (trapezoidal rule), and the standard RK4. As performance metrics, we plot the global discretization error as a function of the numerical complexity. We tested the methods on several time-continuous car-following models in several multi-vehicle simulation scenarios with and without discontinuities such as stops or a discontinuous behavior of an external leader. We find that the theoretical advantage of RK4 (consistency order 4) only plays a role if both the acceleration function of the model and the trajectory of the leader are sufficiently often differentiable. Otherwise, we obtain lower (and often fractional) consistency orders. Although, to our knowledge, Heun's method has never been used for integrating car-following models, it turns out to be the best scheme for many practical situations. The ballistic update always prevails over Euler's method although both are of first order.

Most published microscopic driving behavior models, such as car following and lane changing, were developed for homogeneous and lane-based settings. In the emerging and developing world, traffic is characterized by a wide mix of vehicle types (e.g., motorized and non-motorized, two, three and four wheelers) that differ substantially in their dimensions, performance capabilities and driver behavior and by a lack of lane discipline. This paper presents a review of current driving behavior models in the context of mixed traffic, discusses their limitations and the data and modeling challenges that need to be met in order to extend and improve their fidelity. The models discussed include those for longitudinal and lateral movements and gap acceptance. The review points out some of the limitations of current models. A main limitation of current models is that they have not explicitly considered the wider range of situations that drivers in mixed traffic may face compared to drivers in homogeneous lane-based traffic, and the strategies that they may choose in order to tackle these situations. In longitudinal movement, for example, such strategies include not only strict following, but also staggered following, following between two vehicles and squeezing. Furthermore, due to limited availability of trajectory data in mixed traffic, most of the models are not estimated rigorously. The outline of modeling framework for integrated driver behavior was discussed finally.

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