Collision-free nonuniform dynamics within continuous optimal velocity models

Abstract

Optimal velocity (OV) car-following models give with few parameters stable stop-and -go waves propagating like in empirical data. Unfortunately, classical OV models locally oscillate with vehicles colliding and moving backward. In order to solve this problem, the models have to be completed with additional parameters. This leads to an increase of the complexity. In this paper, a new OV model with no additional parameters is defined. For any value of the inputs, the model is intrinsically asymmetric and collision-free. This is achieved by using a first-order ordinary model with two predecessors in interaction, instead of the usual inertial delayed first-order or second-order models coupled with the predecessor. The model has stable uniform solutions as well as various stable stop-and -go patterns with bimodal distribution of the speed. As observable in real data, the modal speed values in congested states are not restricted to the free flow speed and zero. They depend on the form of the OV function. Properties of linear, concave, convex, or sigmoid speed functions are explored with no limitation due to collisions.

Stop-and-go waves induced by correlated noise in pedestrian models without inertia

“…Simulations have been performed for the model defined by Eq. (4) and, for comparison, the unstable deterministic optimal velocity model with two predecessors in interaction introduced in [44] x…”

“…Top panels: Stochastic model defined by (4). Bottom panels: Unstable deterministic model from [44]. Parameter values are T = 1 s and = 0.3 m for the affine optimal velocity of both models, α = 0.1 ms −3/2 and β = 5 s for the noise of the stochastic model and T r = 0.7 s for the reaction time parameter of the deterministic model.…”

Vadere: An Open-Source Simulation Framework to Promote Interdisciplinary Understanding

“…ODE-based modeling turned from second order equations present in the SFM to first order equations, thus eliminating several artifacts known in the SFM [15]. The results are so-called velocity-based models [14,73]. At the same time several more model types emerged: velocityobstacle-based models [22,4,13] for collision avoidance inspired by robotics, rule-based models such as [65,84] and models which combine different approaches like the optimal steps model (OSM) [68].…”

“…Several approaches for modeling microscopic pedestrian dynamics have been developed in the last decades [88]. Among these are models based on cellular automata (CA) [25,5,45,79,18,87], models based on ordinary differential equations (ODE) [34,9,8,14,73], models based on cognitive heuristics [65,84] and models based on optimizing a utility, such as the quasicontinuous optimal steps model [68,75,76,77].…”

The Superposition Principle: A Conceptual Perspective on Pedestrian Stream Simulations

“…Although the underlying locomotion is based on the social force model, the actual decision-making process is not based on the superposition of scalar fields in the sense we define below. Finally, a concept that is currently being studied for pedestrian dynamics is represented by optimal velocity models, which stem from traffic simulations [31,32].…”