Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata

Abstract

In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research.

Short Term Traffic State Prediction via Hyperparameter Optimization Based Classifiers

“…Many researchers, therefore, consider it as the most commonly implemented network topology [44][45][46]. Recently, in the study by Chen et al, they adapted a novel approach using dynamic graph hybrid automata for the modeling and estimation of density on an urban freeway in the city of Beijing, China [47]. The authors validated the feasibility of their modeling approach on Beijing's Third Ring Road.…”

Development and investigation of methods of graphic-functional modeling of distributed systems

“…The use of dynamic graphs for modeling and researching traffic flows is considered in the paper [12]. The process is based on a combination of dynamic graphs and hybrid automata in a single geometric model.…”

Decentralized State-Observer-Based Traffic Density Estimation of Large-Scale Urban Freeway Network by Dynamic Model

“…The macroscopic traffic flow model of an urban freeway network has been proposed by combining the dynamic graph hybrid automata (DGHA) with the cell transmission model (CTM), and as a result, the traffic flow network can be deduced a centralized piecewise affine linear system (PWALS) in our previous work [9]. The detailed modeling process can be seen in reference [9].…”

“…In the model, the triangular fundamental diagram ( Figure 1) is used to approximately describe the relationship between traffic flow and density of road segment (cell), where ρ i is the traffic density (vpkm), q i is the traffic flow (vph), C i is the traffic capacity (vph), V i is the free flow speed (kmph), W i is the traffic wave speed (kmph), ρ 0 i is the critical density (vpkm), and ρ m i is the maximum/jam density (vpkm). In reference [9], based on model (1), the following centralized state observer was designed to estimate the traffic densities:…”

“…Canudas-de-Wit et al [6] proposed the graph constrained-CTM observer and applied it to reconstruct the densities of the Grenoble south ring, and in [7] they further introduced a robust mode selector for the uncertain graph constrained switching mode model and applied it to highway traffic densities estimation via a switched state observer. Chen and Guo et al [8,9] deduced a piecewise affine linear system (PWALS) by combining the cell transmission model (CTM) with the dynamic graph hybrid automata (DGHA), and then based on the model designed switched state observer to estimate traffic densities. In addition, Wang and Papageorgiou [10] proposed a general stochastic macroscopic traffic flow model of freeway stretches, and based on this model the extended Kalman filter was designed to estimate traffic state in freeway stretches.…”