Abstract
The broad objective of this thesis is to explore the potential for the use of Cellular Automata (CA) models to provide a testbed for comparison of different kinetic models of vehicular traffic. We intend to develop a quantitative technique for comparing various kinetic equations that model a given CA-based microscopic model of vehicular traffic. We also plan to apply this technique to two instances of kinetic models, which are differentiated only by their assumptions regarding inter-vehicular correlation and are intended to statistically predict the behavior of ensembles of instances of the underlying CA. We apply different versions of the L₁ norm as a metric to compare two kinetic models within two scenarios that are representative of typical vehicular traffic problems. The kinetic models are both derived from the same simple CA traffic model, known as CA-184-CC, but they are based on different models of vehicle correlation: the modified vehicular chaos model; and the Nelson and Raney model, an ad-hoc model developed in an earlier paper by P. Nelson and the author. The traffic scenarios are "near-jam," in which a large traffic jam has a high probability of occurring in a particular location; and "pseudo-free-flow," in which vehicles have a high probability of being spaced out from one another enough to allow driving at the maximum desired speed. Results show that the L[distribution][superscript]₁₃̦[w][subscript] norm produces slightly smaller values for the near-jam scenario and significantly smaller values for the pseudo-free-flow scenario. Also, the L[distribution][superscript]₁₃̦[w][subscript] norm comparing the CA model to the modified vehicular chaos correlation model is smaller than that of the CA to the Nelson and Raney ad-hoc correlation model, indicating that the modified vehicular chaos model is a better fit to the ensembled CA model.
Raney, Bryan Keith (2000). The use of a simple cellular automata model as a testbed for kinetic theories of vehicular traffic flow. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -2000 -THESIS -R365.