Advertisement

Interactions between Multiple Junctions

  • Takahiro Tannai
  • Katsuhiro Nishinari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8751)

Abstract

We consider a simple TASEP (Totally Asymmetric Simple Exclusion Process) network model with an aggregation point and a branching point. Generally speaking, the aggregation point behaves as a bottleneck and the branching point enables particles to encourage their velocity. However, the correlation among multiple junctions in TASEP network is not known so much. In order to investigate the correlation, we consider a simple TASEP network which including two junctions and discuss the network with an aggregation point and a branching point. From our theoretical analysis and numerical results, it is shown that aggregations become bottlenecks in TASEP networks and that branches enable flow of particles to be larger in many cases.

Keywords

TASEP network interactions among multiple junctions effects of junctions in TASEP network 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Conway, R.W., Maxwell, W.L., Miller, L.W.: Theory of Scheduling. Dover Publications, Inc., MinesotaGoogle Scholar
  2. 2.
    Ghrist, R.: Configuration Spaces and Braid Groups on Graphs in Robotics. In: Braids, Links, and Mapping Class Groups: the Proceedings of Joan Birman’s 70th Birthday. AMS/IP Studies in Mathematics, vol. 24, pp. 29–40 (2001)Google Scholar
  3. 3.
    Rajewsky, N., Santen, L., Schadschneider, A., Schreckenberg, M.: The Asymmetric Exclusion Process: Comparison of Update Procedures. Journal of Physics 92(1/2), 151–194 (1998)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Huang, D.-W.: Ramp-induced transitions in traffic dynamics. Physical Review E 73, 016123 (2006)Google Scholar
  5. 5.
    Huang, D.-W.: Analytical results of asymmetric exclusion processes with ramps. Physical Review E 72, 016102 (2005)Google Scholar
  6. 6.
    MacDonald, C.T., Gibbs, J.H.: Kinetics of Biopolymerization on Nucleic Acid Templates. Biopolymers 6, 1–25 (1968)CrossRefGoogle Scholar
  7. 7.
    Spitzer, F.: Interaction of Markov Process. Advances in Mathematics 5, 246–290 (1970)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Pronina, E., Kolomeisky, A.B.: Theoretical investigation of totally asymmetric exclusion processes with on lattices with junctions. J. Stat. Mech., P07010 (2005)Google Scholar
  9. 9.
    Wang, X., Jiang, R., Hu, M.-B., Nishinari, K., Wu, Q.-S.: Totally Asymmetric Exclusion Process on Lattices with a Branching Point. International Journal of Modern Physics C 20(12), 1999–2012 (2009)CrossRefzbMATHGoogle Scholar
  10. 10.
    Derrida, B., Evans, M.R., Hakim, V., Pasquier, V.: Exact solution of a ID asymmetric exclusion model using a matrix formulation. J. Phys. A: Math. Gen. 26, 1493–1517 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Wang, X., Jiang, R., Nishinari, K., Hu, M.-B., Wu, Q.-S.: Asymmetric Exclusion Processes on Lattices with a Junction: The Effect of Unequal Injection Rates. International Journal of Modern Physics C 20(6), 967–978 (2009)CrossRefzbMATHGoogle Scholar
  12. 12.
    Parmeggiani, A., Franosch, T., Frey, E.: The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics. Physical Review E 70, 046101 (2004)Google Scholar
  13. 13.
    Kolomeisky, A.B., Schütz, G.M., Kolomeisky, E.B., Straley, J.P.: Phase diagram of one-dimensional driven lattice gases with open boundaries. J. Phys. A: Math. Gen. 31, 6911–6919 (1998)Google Scholar
  14. 14.
    Embley, B., Parmeggiani, A., Kern, N.: Understanding Totally Asymmetric Simple-exclusion-process Transport on Networks: Generic Analysis via Effective Rates and Explicit Vertices. Physical Review E 80, 041128 (2009)Google Scholar
  15. 15.
    Raguin, A., Parmeggiani, A., Kern, N.: Role of Network Junctions for the Totally Asymmetric Simple Exclusion Process. Physical Review E 88, 042104 (2013)Google Scholar
  16. 16.
    Lebacque, J.-P.: First-order Macroscopic Traffic Flow Models: Intersection Modeling, Network Modeling. In: Mahmassani, H.S. (ed.) Transportation and Traffic Theory Flow, Dynamics, and Human Interaction, Proceeding of 16th International Symposium on Transportation and Traffic Theory, pp. 365–386 (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Takahiro Tannai
    • 1
  • Katsuhiro Nishinari
    • 2
  1. 1.Department of Advanced Interdisciplinary Studies, School of EngineeringThe University of TokyoMeguro-kuJapan
  2. 2.Research Center for Advanced Science and TechnologyThe University of TokyoMeguro-kuJapan

Personalised recommendations