Two-way traffic flow: Exactly solvable model of traffic jam

@article{Lee1997TwowayTF,
  title={Two-way traffic flow: Exactly solvable model of traffic jam},
  author={H.-W. Lee and V. Popkov and D. Kim},
  journal={Journal of Physics A},
  year={1997},
  volume={30},
  pages={8497-8513}
}
We study completely asymmetric two-channel exclusion processes in one dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars in the other lane. Particularly, we consider in detail the system with a finite density of cars on one lane and a single car on the other. When the interchannel interaction reaches a critical value, a traffic jam occurs, which turns out to be of first… 

Figures from this paper

Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic
Firstly, we consider a unidirectional flux of vehicles, each of which is characterized by its 'natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of
Studying on the Bidirection Two-lane Mixed Cars Traffic Flow Model
TLDR
A new bidirectional two-lane mixed cars traffic flow model is proposed, which considers canceling the restrictions on the queue of low-speed car, combine with FI model, and thinks when the car is changing lane, the behind vehicles from its adjacent lane have effects on it.
Exactly solvable statistical model for two-way traffic
We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included
A Cellular Automata (CA) Model for Two-Way Vehicle Flows on Low-Grade Roads Without Hard Separation
  • Qun Chen, Y. Wang
  • Computer Science
    IEEE Intelligent Transportation Systems Magazine
  • 2016
TLDR
This paper analyzes the behavior rules of drivers when oppositely directed vehicles meet and proposes a cellular automata (CA) model for interacting two-way vehicle flows.
Phase Separation in a Bidirectional Two-Lane Asymmetric Exclusion Process
This paper studies a bidirectional two-lane asymmetric exclusion process, in which particles move in opposite direction on the two lanes. Interaction between the two lanes is implemented as follows:
The Study on T-intersection Mixing Vehicles Flow in the Open Boundary
  • Changsheng Zhu, Qi Shao
  • Computer Science
    2013 International Conference on Computational and Information Sciences
  • 2013
TLDR
Under the condition of open boundary, it proposes a new model which is based on the improved two-way two-lane cellular automaton traffic flow model which consists of two independent running main roads and two cross by-roads which allow overtaking.
Modelling Traffic Flow At Multi-Lane Urban Roundabouts
TLDR
This paper proposes Multi-stream Minimum Acceptable Space (MMAS) Cellular Automata (CA) models to study unsignalised multi-lane (two- or three-lane) urban roundabouts to study heterogeneity and inconsistency of driver behavior and interactions in cross traffic at entrances of roundabouts.
Traffic and related self-driven many-particle systems
Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why
Weakly coupled, antiparallel, totally asymmetric simple exclusion processes.
  • R. Juhasz
  • Mathematics, Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
TLDR
A system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely proportional to the length of the system, undergoes a discontinuous phase transition.
Simon-Gutowitz bidirectional traffic model revisited
The Simon-Gutowitz bidirectional traffic model (Phys. Rev. E 57, 2441 (1998)) is revisited in this letter. We found that passing cars get stuck with oncoming cars before returning to their home
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 21 REFERENCES
Particle hopping models and traffic flow theory.
  • Nagel
  • Computer Science, Medicine
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
TLDR
This paper shows connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equation, and particle hopping models, and starts building a foundation of a comprehensive dynamic traffic theory, where strengths and weaknesses of different models can be compared, and thus allowing to systematically choose the appropriate model for a given question.
Exact results for the asymmetric simple exclusion process with a blockage
We present new results for the current as a function of transmission rate in the one-dimensional totally asymmetric simple exclusion process (TASEP) with a blockage that lowers the jump rate at one
Exact diffusion constant for one-dimensional asymmetric exclusion models
The one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, is considered on a ring of size N. The steady
Generalized Bethe ansatz solution of a one-dimensional asymmetric exclusion process on a ring with blockage
We present a model for a one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring of lengthL with a single defect, across which they move with probability
Exact solution of a 1d asymmetric exclusion model using a matrix formulation
Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be
Exact solution of the totally asymmetric simple exclusion process: Shock profiles
The microscopic structure of macroscopic shocks in the one-dimensional, totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model
Finite-size effects and shock fluctuations in the asymmetric simple-exclusion process.
  • Janowsky, Lebowitz
  • Physics, Medicine
    Physical review. A, Atomic, molecular, and optical physics
  • 1992
TLDR
This work considers a system of particles on a lattice of L sites, evolving according to the asymmetric simple-exclusion process, and finds that fluctuations of the shock position about its average value grow like ${\mathit{L}}^{1/2}$ or £1/3$ depending upon whether particle-hole symmetry exists.
Microscopic-Shock Profiles: Exact Solution of a Non-equilibrium System.
The full microscopic structure of macroscopic shocks is obtained exactly in the onedimensional totally asymmetric simple exclusion process from the complete solution of the uniform stationary
Statistical mechanics of driven diffusive systems
Publisher Summary This chapter discusses the systems coupled to two reservoirs of energy in such a way that there is a steady energy flow through the system. An example is a resistor in steady state,
Proceedings of STATPHYS 19
  • Proceedings of STATPHYS 19
  • 1996
...
1
2
3
...