Abstract
In this work, we propose an alternative stochastic model for the fundamental diagram of traffic flow with minimal number of parameters. Our approach is based on a mesoscopic viewpoint of the traffic system in terms of the dynamics of vehicle speed transitions. A key feature of the present approach lies in its stochastic nature which makes it possible to study not only the flow-concentration relation, namely, the fundamental diagram, but also its uncertainty, namely, the variance of the fundamental diagram—an important characteristic in the observed traffic flow data. It is shown that in the simplified versions of the model consisting of only a few speed states, analytic solutions for both quantities can be obtained, which facilitate the discussion of the corresponding physical content. We also show that the effect of vehicle size can be included into the model by introducing the maximal congestion density kmax. By making use of this parameter, the free flow region and congested flow region are naturally divided, and the transition is characterized by the capacity drop at the maximum of the flow-concentration relation. The model parameters are then adjusted to the observed traffic flow on the I-80 Freeway Dataset in the San Francisco area from the NGSIM program, where both the fundamental diagram and its variance are reasonably reproduced. Despite its simplicity, we argue that the current model provides an alternative description for the fundamental diagram and its uncertainty in the study of traffic flow.
Highlights
Aside from its complexity and nonlinearity, traffic flow modeling has long attracted the attention of physicists due to the connections to transport theory and hydrodynamics (For reviews, see for example (Hoogendoorn and Bovy, 2001; Kerner, 2009; Maerivoet and De Moor, 2005; Pedersen, 2011; Prigogine and Herman, 1971; Treiber and Kesting, 2012))
One sees that the model reproduces the main features observed in the fundamental diagram: flow increases from zero when the density of the vehicles increases, it hits the maximum starts to decrease; the flow variance increases from zero with increasing density while the traffic starts to build up, it attains its maximum at a bigger density value than that of the flow
An alternative stochastic transport model is proposed to calculate the fundamental diagram of traffic flow and its variance
Summary
Aside from its complexity and nonlinearity, traffic flow modeling has long attracted the attention of physicists due to the connections to transport theory and hydrodynamics (For reviews, see for example (Hoogendoorn and Bovy, 2001; Kerner, 2009; Maerivoet and De Moor, 2005; Pedersen, 2011; Prigogine and Herman, 1971; Treiber and Kesting, 2012)). Siqueira et al / Transportation Research Part B 87 (2016) 1–13 treated as a continuous fluid without distinguishing its individual constituent parts In this approach, the traffic stream is represented in terms of macroscopic quantities such as flow rate, density and speed. The last section is devoted to the conclusion remarks and perspectives
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