Modelling traffic flow fluctuations

Abstract

By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear stochastic process with multiplicative noise, ${\dot{T}}_i=\alpha (m_T-T_i)+D{T}_i\xi$. The resulting stationary distribution has a power-law tail, especially for densities where cars are interacting strongly. Analyzing additionally the headways for accelerating and decelerating cars, the slow-to-start effect proposed as a mechanism for traffic jam stability can be demonstrated explicitly. Finally, the standard deviation of the speed differences between following cars can be used to get a clear characterization of (at least) three different regimes of traffic flow that can be identified in the data. Using the empirical results to enhance a microscopic traffic flow model, it can be demonstrated that such a model describes the fluctuations of traffic flow quite satisfactorily.

11 pages, 12 figures

References in corpus (15)

• Congested Traffic States in Empirical Observations and Microscopic Simulations
• Emergent Traffic Jams
• Mechanical restriction versus human overreaction triggering congested traffic states
• Steady-state selection in driven diffusive systems with open boundaries
• Memory effects in microscopic traffic models and wide scattering in flow-density data
• Coherent Moving States in Highway Traffic (Originally: Moving Like a Solid Block)
• Single-vehicle data of highway traffic: microscopic description of traffic phases
• Traffic flow models with 'slow-to-start' rules
• Interpreting the Wide Scattering of Synchronized Traffic Data by Time Gap Statistics
• Exact results for one dimensional stochastic cellular automata for different types of updates
• Boundary induced phase transitions in driven lattice gases with meta-stable states
• Determination of Interaction Potentials in Freeway Traffic from Steady-State Statistics
• The nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions
• Stationary Velocity Distributions in Traffic Flows
• Empirical basis for car-following theory development