Tuesday, February 17, 2015

Three Dimensional (3D) Trajectories

Interested to learn more about 3D trajectories? See the following two papers recently published in Transportation Research Record.

Estimating Network Fundamental Diagram Using Three-Dimensional Vehicle Trajectories: Extending Edie’s Definitions of Traffic Flow Variables to Networks
ABSTRACT. This paper evaluates measurement methods for traffic flow variables taken at the network level. Generalized Edie’s definitions of fundamental traffic flow variables along highways are extended for considering vehicles traveling in networks. These definitions are used to characterize traffic flow in networks and form the basis for estimating relationships among network density, flow, and speed in the form of a network fundamental diagram. The method relies on three-dimensional vehicle trajectories to provide estimates of network flow, density, and speed. Such trajectories may be routinely obtained from particle-based microscopic and mesoscopic simulation models and are increasingly available from tracking devices on vehicles. Numerical results from the simulation of two networks, in Chicago, Illinois, and Salt Lake City, Utah, are presented to illustrate and validate the estimation methodology. As part of the verification process, the study confirms that the traffic flow fundamental identity (Q = K • V) holds at the network level only when networkwide traffic flow variables are defined consistently with Edie’s definitions.
How to cite this paper?
Saberi, M., Mahmassani, H., Hou, T., Zockaie, A. (2014) Estimating Network Fundamental Diagram using Three-Dimensional Vehicle Trajectories: Extending Edie's Definitions of Traffic Flow Variables to Networks. Transportation Research Record: Journal of the Transportation Research Board. No. 2422, 12-20.

Exploring Areawide Dynamics of Pedestrian Crowds: Three-Dimensional Approach
ABSTRACT. The main objectives of this paper are to evaluate existing measurement methods of pedestrian traffic flow and to propose a three-dimensional approach that extends Edie’s definitions of fundamental traffic variables to multidirectional walking areas by using three-dimensional pedestrian trajectories. Pedestrian crowds have an areawide fundamental diagram that is similar to a network fundamental diagram of vehicular traffic. Pedestrian traffic in a multidirectional area exhibits hysteretic behavior similar to that of some other many-particle physical systems. Some of the underlying dynamics of bidirectional pedestrian streams are explored with empirical data. Pedestrian streams behave somewhat differently from ordinary fluids with regard to the viscosity concept in the models based on fluid dynamics. The velocity profile for both unidirectional and bidirectional pedestrian streams is hyperbolic (with higher values on the boundaries and lower values in the middle), opposite that of fluids. The formation and dissipation of self-organized pedestrian lanes also are explored. A modification to Helbing’s social force model is proposed with regard to the attractive force between pedestrians.

How to cite this paper?
Saberi, M., and Mahmassani, H. (2014) Exploring Areawide Dynamics of Pedestrian Crowds: Three-Dimensional Approach. Transportation Research Record: Journal of the Transportation Research Board. No. 2421, 31-40.

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