Interactions between Multiple Junctions
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.
KeywordsTASEP network interactions among multiple junctions effects of junctions in TASEP network
Unable to display preview. Download preview PDF.
- 1.Conway, R.W., Maxwell, W.L., Miller, L.W.: Theory of Scheduling. Dover Publications, Inc., MinesotaGoogle Scholar
- 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
- 4.Huang, D.-W.: Ramp-induced transitions in traffic dynamics. Physical Review E 73, 016123 (2006)Google Scholar
- 5.Huang, D.-W.: Analytical results of asymmetric exclusion processes with ramps. Physical Review E 72, 016102 (2005)Google Scholar
- 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
- 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.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.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.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.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