dorsal/arxiv
View SchemaSynchronized flow and wide moving jams from balanced vehicular traffic
| Authors | Florian Siebel, Wolfram Mauser |
|---|---|
| Categories | |
| ArXiv ID | physics/0509124 |
| URL | https://arxiv.org/abs/physics/0509124 |
| DOI | 10.1103/PhysRevE.73.066108 |
| Journal | Phys. Rev. E 73, 066108 (2006) |
Abstract
Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental diagram of traffic flow. In the current work we analyze the steady state solutions of the new model and their stability properties. In addition to the equilibrium flow curve the trivial steady state solutions form two additional branches in the flow-density diagram. We show that the characteristic structure excludes parts of these branches resulting in the reverse $\lambda$ shape of the flow-density relation. The upper branch is metastable against the formation of synchronized flow for intermediate densities and unstable for high densities, whereas the lower branch is unstable for intermediate densities and metastable for high densities. Moreover, the model can reproduce the typical speed of the downstream front of wide moving jams. It further reproduces a constant outflow from wide moving jams, which is far below the maximum free flow. Applying the model to simulate traffic flow at a bottleneck we observe a general pattern with wide moving jams traveling through the bottleneck.
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"abstract": "Recently we proposed an extension to the traffic model of Aw, Rascle and\nGreenberg. The extended traffic model can be written as a hyperbolic system of\nbalance laws and numerically reproduces the reverse $\\lambda$ shape of the\nfundamental diagram of traffic flow. In the current work we analyze the steady\nstate solutions of the new model and their stability properties. In addition to\nthe equilibrium flow curve the trivial steady state solutions form two\nadditional branches in the flow-density diagram. We show that the\ncharacteristic structure excludes parts of these branches resulting in the\nreverse $\\lambda$ shape of the flow-density relation. The upper branch is\nmetastable against the formation of synchronized flow for intermediate\ndensities and unstable for high densities, whereas the lower branch is unstable\nfor intermediate densities and metastable for high densities. Moreover, the\nmodel can reproduce the typical speed of the downstream front of wide moving\njams. It further reproduces a constant outflow from wide moving jams, which is\nfar below the maximum free flow. Applying the model to simulate traffic flow at\na bottleneck we observe a general pattern with wide moving jams traveling\nthrough the bottleneck.",
"arxiv_id": "physics/0509124",
"authors": [
"Florian Siebel",
"Wolfram Mauser"
],
"categories": [
"physics.soc-ph"
],
"doi": "10.1103/PhysRevE.73.066108",
"journal_ref": "Phys. Rev. E 73, 066108 (2006)",
"title": "Synchronized flow and wide moving jams from balanced vehicular traffic",
"url": "https://arxiv.org/abs/physics/0509124"
},
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