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Bin Jia

Publications and source records attributed to Bin Jia.

53 records · Page 3Linked to original sources
arXiv2016

Empirical analysis and simulation of the evolution concavity of traffic oscillations

This paper has investigated the growth pattern of traffic oscillations in the NGSIM vehicle trajectories data, via measuring the standard deviation of vehicle velocity involved in oscillations. We found that the standard deviation of the velocity increases in a concave way along vehicles in the oscillations. Moreover, all datasets collapse into a single concave curve, which indicates a universal evolution law of oscillations. A comparison with traffic experiment shows that the empirical and the experimental results are highly compatible and can be fitted by a single concave curve, which demonstrates that qualitatively the growth pattern of oscillations is not affected by type of bottleneck and lane changing behavior. We have shown theoretically that small disturbances increase in a convex way in the initial stage in the traditional models presuming a unique relationship between speed and density, which obviously deviates from our findings. Simulations show that stochastic models in which the traffic state dynamically spans a 2D region in the speed-spacing plane can qualitatively or even quantitatively reproduce the concave growth pattern of traffic oscillations.

nlin.CG↗
arXiv2016

Spurious symmetry-broken phase in a bidirectional two-lane ASEP with narrow entrances: A perspective from mean field analysis and current minimization principle

As one of the paradigmatic models of non-equilibrium systems, the asymmetric simple exclusion process (ASEP) has been widely used to study many physical, chemical, and biological systems. The ASEP shows a range of nontrivial macroscopic phenomena, among which, the spontaneous symmetry breaking has gained much attention. Nevertheless, as a basic problem, it has been controversial that whether there exist one or two symmetry-broken phases in the ASEP. Based on mean field analysis and current minimization principle, this paper demonstrates that one of the broken-symmetry phases does not exist in a bidirectional two-lane ASEP with narrow entrances. Moreover, an exponential decay feature is observed, which has been used to predict phase boundary in the thermodynamic limit. Our findings might be generalized to other ASEP models and thus deepen the understanding of the spontaneous symmetry breaking in non-equilibrium systems.

cond-mat.stat-mech↗
arXiv2016

Improved 2D Intelligent Driver Model simulating synchronized flow and evolution concavity in traffic flow

This paper firstly show that 2 Dimensional Intelligent Driver Model (Jiang et al., PloS one, 9(4), e94351, 2014) is not able to replicate the synchronized traffic flow. Then we propose an improved model by considering the difference between the driving behaviors at high speeds and that at low speeds. Simulations show that the improved model can reproduce the phase transition from synchronized flow to wide moving jams, the spatiotemporal patterns of traffic flow induced by traffic bottleneck, and the evolution concavity of traffic oscillations (i.e. the standard deviation of the velocities of vehicles increases in a concave/linear way along the platoon). Validating results show that the empirical time series of traffic speed obtained from Floating Car Data can be well simulated as well.

nlin.PS↗
arXiv2016

Hadwiger's conjecture for $\ell$-link graphs

In this paper we define and study a new family of graphs that generalises the notions of line graphs and path graphs. Let $G$ be a graph with no loops but possibly with parallel edges. An \emph{$\ell$-link} of $G$ is a walk of $G$ of length $\ell \geqslant 0$ in which consecutive edges are different. We identify an $\ell$-link with its reverse sequence. The \emph{$\ell$-link graph $\mathbb{L}_\ell(G)$} of $G$ is the graph with vertices the $\ell$-links of $G$, such that two vertices are joined by $μ\geqslant 0$ edges in $\mathbb{L}_\ell(G)$ if they correspond to two subsequences of each of $μ$ $(\ell + 1)$-links of $G$. By revealing a recursive structure, we bound from above the chromatic number of $\ell$-link graphs. As a corollary, for a given graph $G$ and large enough $\ell$, $\mathbb{L}_\ell(G)$ is $3$-colourable. By investigating the shunting of $\ell$-links in $G$, we show that the Hadwiger number of a nonempty $\mathbb{L}_\ell(G)$ is greater or equal to that of $G$. Hadwiger's conjecture states that the Hadwiger number of a graph is at least the chromatic number of that graph. The conjecture has been proved by Reed and Seymour (2004) for line graphs, and hence $1$-link graphs. We prove the conjecture for a wide class of $\ell$-link graphs.

math.CO↗
arXiv2016

Common feature of concave growth pattern of oscillations in terms of speed, acceleration, fuel consumption and emission in car following: experiment and modeling

This paper has investigated the growth pattern of traffic oscillations by using vehicle trajectory data in a car following experiment. We measured the standard deviation of acceleration, emission and fuel consumption of each vehicle in the car-following platoon. We found that: (1) Similar to the standard deviation of speed, these indices exhibit a common feature of concave growth pattern along vehicles in the platoon; (2) The emission and fuel consumption of each vehicle decrease remarkably when the average speed of the platoon increases from low value; However, when reaches 30km/h, the change of emission and fuel consumption with is not so significant; (3), the correlations of emission and fuel consumption with both the standard deviation of acceleration and the speed oscillation are strong. Simulations show that with the memory effect of drivers taken into account, the improved two-dimensional intelligent driver model is able to reproduce the common feature of traffic oscillation evolution quite well.

physics.soc-ph↗
arXiv2016

Analytical investigation on the minimum traffic delay at a two-phase intersection considering the dynamical evolution process of queues

This paper has studied the minimum traffic delay at a two-phase intersection, taking into account the dynamical evolution process of queues. The feature of delay function has been studied, which indicates that the minimum traffic delay must be achieved when equality holds in at least one of the two constraints. We have derived the minimum delay as well as the corresponding traffic signal period, which shows that two situations are classified. Under certain circumstance, extra green time is needed for one phase while otherwise no extra green time should be assigned in both phases. Our work indicates that although the clearing policies were shown in many experiments to be optimal at isolated intersections, it is sometimes not the case.

physics.soc-ph↗
arXiv2015

Impact of holding umbrella on uni- and bi-directional pedestrian flow: Experiments and modeling

In this paper, the impact of holding umbrella on the uni- and bi-directional flow has been investigated via experiment and modeling. In the experiments, pedestrians are required to walk clockwise/anti-clockwise in a ring-shaped corridor under normal situation and holding umbrella situation. No matter in uni- or bi-directional flow, the flow rate under holding umbrella situation decreases comparing with that in normal situation. In bidirectional flow, pedestrians segregate into two opposite moving streams very quickly under normal situation, and clockwise/anti-clockwise walking pedestrians are always in the inner/outer lane due to right-walking preference. Under holding umbrella situation, spontaneous lane formation has also occurred. However, when holding umbrella, pedestrians may separate into more than two lanes. Moreover, the merge of lanes have been observed, and clockwise/anti-clockwise pedestrians are not always in the inner/outer lane. To model the flow dynamics, an improved force-based model has been proposed. The contact force between umbrellas has been taken into account. Simulation results are in agreement with the experimental ones.

physics.soc-ph↗
arXiv2015

Original graphs of link graphs

Let $\ell \geqslant 0$ be an integer, and $G$ be a graph without loops. An $\ell$-link of $G$ is a walk of length $\ell$ in which consecutive edges are different. We identify an $\ell$-link with its reverse sequence. The $\ell$-link graph $\mathbb{L}_\ell(G)$ of $G$ is defined to have vertices the $\ell$-links of $G$, such that two vertices of $\mathbb{L}_\ell(G)$ are adjacent if their corresponding $\ell$-links are the initial and final subsequences of an $(\ell + 1)$-link of $G$. A graph $G$ is called an $\ell$-root of a graph $H$ if $\mathbb{L}_\ell(G) \cong H$. For example, $\mathbb{L}_0(G) \cong G$. And the $1$-link graph of a simple graph is the line graph of that graph. Moreover, let $H$ be a finite connected simple graph. Whitney's isomorphism theorem (1932) states if $H$ has two connected nonnull simple $1$-roots, then $H \cong K_3$, and the two $1$-roots are isomorphic to $K_3$ and $K_{1, 3}$ respectively. This paper investigates the $\ell$-roots of finite graphs. We show that every $\ell$-root is a certain combination of a finite minimal $\ell$-root and trees of bounded diameter. This transfers the study of $\ell$-roots into that of finite minimal $\ell$-roots. As a qualitative generalisation of Whitney's isomorphism theorem, we bound from above the number, size, order and maximum degree of minimal $\ell$-roots of a finite graph. This work forms the basis for solving the recognition and determination problems for $\ell$-link graphs in our future papers. As a byproduct, we characterise the $\ell$-roots of some special graphs including cycles. Similar results are obtained for path graphs introduced by Broersma and Hoede (1989). $G$ is an $\ell$-path root of a graph $H$ if $H$ is isomorphic to the $\ell$-path graph of $G$. We bound from above the number, size and order of minimal $\ell$-path roots of a finite graph.

math.CO↗
arXiv2015

On some experimental features of car-following behavior and how to model them

We have carried out car-following experiments with a 25-car-platoon on an open road section to study the relation between a car's speed and its spacing under various traffic conditions, in the hope to resolve a controversy surrounding this fundamental relation of vehicular traffic. In this paper we extend our previous analysis of these experiments, and report new experimental findings. In particular, we reveal that the platoon length (hence the average spacing within a platoon) might be significantly different even if the average velocity of the platoon is essentially the same. The findings further demonstrate that the traffic states span a 2D region in the speed-spacing (or density) plane. The common practice of using a single speed-spacing curve to model vehicular traffic ignores the variability and imprecision of human driving and is therefore inadequate. We have proposed a car-following model based on a mechanism that in certain ranges of speed and spacing, drivers are insensitive to the changes in spacing when the velocity differences between cars are small. It was shown that the model can reproduce the experimental results well.

nlin.AO↗
arXiv2015

Excluding long paths

Ding (1992) proved that for each integer ${m} \geqslant 0$, and every infinite sequence of finite simple graphs $G_1, G_2, \ldots$, if none of these graphs contains a path of length ${m}$ as a subgraph, then there are indices $i < j$ such that $G_i$ is isomorphic to an induced subgraph of $G_j$. We generalise this result to infinite graphs, possibly with parallel edges and loops.

math.CO↗
arXiv2015

Cellular automaton model with dynamical 2D speed-gap relation reproduces empirical and experimental features of traffic flow

This paper proposes an improved cellular automaton traffic flow model based on the brake light model, which takes into account that the desired time gap of vehicles is remarkably larger than one second. Although the hypothetical steady state of vehicles in the deterministic limit corresponds to a unique relationship between speeds and gaps in the proposed model, the traffic states of vehicles dynamically span a two-dimensional region in the plane of speed versus gap, due to the various randomizations. It is shown that the model is able to well reproduce (i) the free flow, synchronized flow, jam as well as the transitions among the three phases; (ii) the evolution features of disturbances and the spatiotemporal patterns in a car-following platoon; (iii) the empirical time series of traffic speed obtained from NGSIM data. Therefore, we argue that a model can potentially reproduce the empirical and experimental features of traffic flow, provided that the traffic states are able to dynamically span a 2D speed-gap region.

nlin.CG↗
arXiv2014

Microscopic driving theory with oscillatory congested states: model and empirical verification

The essential distinction between the Fundamental Diagram Approach (FDA) and Kerner's Three- Phase Theory (KTPT) is the existence of a unique gap-speed (or flow-density) relationship in the former class. In order to verify this relationship, empirical data are analyzed with the following findings: (1) linear relationship between the actual space gap and speed can be identified when the speed difference between vehicles approximates zero; (2) vehicles accelerate or decelerate around the desired space gap most of the time. To explain these phenomena, we propose that, in congested traffic flow, the space gap between two vehicles will oscillate around the desired space gap in the deterministic limit. This assumption is formulated in terms of a cellular automaton. In contrast to FDA and KTPT, the new model does not have any congested steady-state solution. Simulations under periodic and open boundary conditions reproduce the empirical findings of KTPT. Calibrating and validating the model to detector data produces results that are better than that of previous studies.

physics.soc-ph↗
arXiv2014

A study of link graphs

Graph theory is a branch of mathematics in which pair-wise relations between objects are studied. My PhD thesis, supervised by David R. Wood, introduces and investigates a new family of graphs, called link graphs, that generalises the notions of line graphs and path graphs. An s-link is a walk of length s such that consecutive edges are different. The s-link graph of a given graph G is the graph with vertices the s-links of G, and two vertices are adjacent if their corresponding s-links form an (s + 1)-link; Or equivalently, one corresponding s-link can be shunted to the other in one step. For example, the 1-link graph of G is the line graph of G. We give a characterisation for link graphs, which leads to algorithmic solutions to their recognition and determination problems, and implies that the recognition problem belongs to NP. Moreover, based on a recursive structure of linkgraphs, we obtain results about the chromatic number, Hadwiger number and isomorphism group of link graphs. We also obtain results about the uniqueness, tree-decomposition and better-quasi-ordering of the original graphs of a given link graph.

math.CO↗
arXiv2014

Microscopic driving theory with non-hypothetical congested steady state: Model and Empirical verification

The essential distinction between the fundamental diagram approach and three-phase theory is the existence of the unique space-gap-speed relationship. In order to verify this relationship, empirical data are analyzed with the following findings: (1) linear relationship between the actual space gap and speed can be identified when the speed difference between vehicles approximates zero; (2) vehicles accelerate or decelerate around the desired space gap most of the time. To explain these phenomena, we propose that, in homogeneous congested traffic flow, the space gap between two vehicles will oscillate around the desired space gap in the noiseless limit. This assumption is formulated in terms of a cellular automaton. Simulations under periodic and open boundary conditions reproduce the empirical findings of three-phase theory. Finally, the model is calibrated and validated. All verification results are acceptable and better than that of previous studies.

nlin.CG↗
arXiv2014

Traffic experiment reveals the nature of car-following

As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation pattern of disturbances. However, the traffic theories have been controversial due to a lack of precise traffic data. We have studied traffic flow from a new perspective by carrying out large-scale car-following experiment on an open road section, which overcomes the intrinsic deficiency of empirical observations. The experiment has shown clearly the nature of car-following, which runs against the traditional traffic flow theory. Simulations show that by removing the fundamental notion in the traditional car-following models and allowing the traffic state to span a two-dimensional region in velocity-spacing plane, the growth pattern of disturbances has changed qualitatively and becomes qualitatively or even quantitatively in consistent with that observed in the experiment.

nlin.AO↗
arXiv2009

A class of symmetric graphs with 2-arc-transitive quotients

Let $Γ$ be a finite X-symmetric graph with a nontrivial X-invariant partition $\mathcal {B}$ on $V(Γ)$ such that $Γ_{\mathcal {B}}$ is a connected (X,2)-arc-transitive graph and $Γ$ is not a multicover of $Γ_{\mathcal {B}}$. This article aims to give a characterization of $(Γ, X, \mathcal {B})$ for the case where $|Γ(C) \cap B| = 3$ for $B\in \mathcal {B}$ and $C \in Γ_{\mathcal {B}}(B)$. This investigation requires a study on (X,2)-arc-transitive graphs of valency 4 or 7. We give a characterization of tetravalent (X,2)-arc-transitive graphs at first; and as a byproduct, we prove that every tetravalent (X,2)-transitive graph is either the complete graph on 5 vertices or a near n-gonal graph for some $n\ge 4$. Then we show that a heptavalent $(X,2)$-arc-transitive graph $Σ$ can occur as $Γ_{\mathcal {B}}$ if and only if $X_τ^{Σ(τ)}\cong PSL(3,2)$ for $τ\in V(Σ)$.

math.CO↗