Abstract
The wide scattering nature of the fundamental diagram (FD) with observed flow-density data may be associated with the dynamical traffic flow process, especially on signalized intersection. To describe the uncertainty of FD, in this work we established stochastic fundamental diagram (SFD) which is defined by the distributions of shockwave speed. Our approach is based on a two-level stochastic process of the traffic flow system in terms of the dynamics of traffic density and state mode associated with signal phases which is named switching linear dynamical systems (SLDS). Then, variational Bayesian learning method is adopted to compute the distributions of SFD parameter to approximate the experimental distributions of shockwave calculated by the observed flow-density data. Given traffic flow data from the NGSIM program, the verification result demonstrated that the SFD can be more helpful to capture the main features of the observed widely scattering of the flow-density data compared with FD. With the shockwave speed sampled from the SFD, the SLDS could describe the dynamic characteristics of traffic flow and be applied to the maximum likelihood estimation of traffic density or flow rate. Because it is simple and automatically calculated, the SFD provides an alternative description for fundamental diagram and its uncertainty in the traffic flow.
Highlights
The model-based traffic simulation and traffic state estimation require stochastic models to describe the dynamical phenomena of traffic flow system when the traffic flow management is applied on the freeways and signalized arterials
The scattered fundamental diagram (FD) with observed flow-density data may be associated with the dynamical traffic flow system and the uncertainty of FD can be mostly expressed in terms of the variance of FD parameters [2, 4, 5]
The problem is how to numerically determine the variance of FD parameters which can be derived from macroscopic simulation model [4, 5] or stochastic differential equation [2]
Summary
The model-based traffic simulation and traffic state estimation require stochastic models to describe the dynamical phenomena of traffic flow system when the traffic flow management is applied on the freeways and signalized arterials. The scattered FD with observed flow-density data may be associated with the dynamical traffic flow system and the uncertainty of FD can be mostly expressed in terms of the variance of FD parameters [2, 4, 5]. Complex traffic flow evolution process can be regarded as jump Markov linear systems in which the traffic state transitions between different modes with constant FD [9, 10]. We developed a dynamical model to determine the dynamic changing process of traffic flow on signalized intersection by switching linear dynamical systems (SLDS). Each HMM mode can be associated with the patterns of traffic flow transition such as on freeway [3] or signalized intersection condition [13]. Appendix A is the derivation process of the posterior distribution of SFD which is proved to be the approximation distribution in Appendix B
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