dorsal/arxiv
View SchemaRelating the dynamics of road traffic in a stochastic cellular automaton to a macroscopic first-order model
| Authors | Sven Maerivoet, Steven Logghe, Ben Immers, Bart De Moor |
|---|---|
| Categories | |
| ArXiv ID | physics/0506206 |
| URL | https://arxiv.org/abs/physics/0506206 |
Abstract
In this paper, we describe a relation between a microscopic traffic cellular automaton (TCA) model (i.e., the stochastic TCA model of Nagel and Schreckenberg) and the macroscopic first-order hydrodynamic model of Lighthill, Whitham, and Richards (LWR). The innovative aspect of our approach, is that we explicitly derive the LWR's fundamental diagram directly from the STCA's rule set, by assuming a stationarity condition that converts the STCA's rules into a set of linear inequalities. In turn, these constraints define the shape of the fundamental diagram, which is then specified to the LWR model. Application of our methodology to a simulation case study, allows us to compare the tempo-spatial behavior of both models. Our results indicate that, in the presence of noise, the capacity flows in the derived fundamental diagram are overestimations of those of the STCA model. Directly specifying the STCA's capacity flows to the LWR fundamental diagram, effectively remedies most of the mismatches between both approaches. Our methodology sees the STCA complementary to the LWR model and vice versa, so the results can be of great assistance when interpreting the traffic dynamics in both models. Especially appealing, is the fact that the STCA can visualize the higher-order characteristics of traffic stream dynamics, e.g., the fans of rarefaction waves.
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"abstract": "In this paper, we describe a relation between a microscopic traffic cellular\nautomaton (TCA) model (i.e., the stochastic TCA model of Nagel and\nSchreckenberg) and the macroscopic first-order hydrodynamic model of Lighthill,\nWhitham, and Richards (LWR). The innovative aspect of our approach, is that we\nexplicitly derive the LWR\u0027s fundamental diagram directly from the STCA\u0027s rule\nset, by assuming a stationarity condition that converts the STCA\u0027s rules into a\nset of linear inequalities. In turn, these constraints define the shape of the\nfundamental diagram, which is then specified to the LWR model. Application of\nour methodology to a simulation case study, allows us to compare the\ntempo-spatial behavior of both models. Our results indicate that, in the\npresence of noise, the capacity flows in the derived fundamental diagram are\noverestimations of those of the STCA model. Directly specifying the STCA\u0027s\ncapacity flows to the LWR fundamental diagram, effectively remedies most of the\nmismatches between both approaches. Our methodology sees the STCA complementary\nto the LWR model and vice versa, so the results can be of great assistance when\ninterpreting the traffic dynamics in both models. Especially appealing, is the\nfact that the STCA can visualize the higher-order characteristics of traffic\nstream dynamics, e.g., the fans of rarefaction waves.",
"arxiv_id": "physics/0506206",
"authors": [
"Sven Maerivoet",
"Steven Logghe",
"Ben Immers",
"Bart De Moor"
],
"categories": [
"physics.soc-ph"
],
"title": "Relating the dynamics of road traffic in a stochastic cellular automaton to a macroscopic first-order model",
"url": "https://arxiv.org/abs/physics/0506206"
},
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