Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical Results For The Steady State Of Traffic Flow Models With
  Stochastic Delay   Exact mean field equations are derived analytically to give the fundamental
diagrams, i.e., the average speed - car density relations, for the
Fukui-Ishibashi one-dimensional traffic flow cellular automaton model of high
speed vehicles $(v_{max}=M>1) $ with stochastic delay. Starting with the basic
equation describing the time evolution of the number of empty sites in front of
each car, the concepts of inter-car spacings longer and shorter than $M$ are
introduced. The probabilities of having long and short spacings on the road are
calculated. For high car densities $(\rho \geq 1/M)$, it is shown that
inter-car spacings longer than $M$ will be shortened as the traffic flow
evolves in time, and any initial configurations approach a steady state in
which all the inter-car spacings are of the short type. Similarly for low car
densities $(\rho \leq 1/M)$, it can be shown that traffic flow approaches an
asymptotic steady state in which all the inter-car spacings are longer than
$M-2$. The average traffic speed is then obtained analytically as a function of
car density in the asymptotic steady state. The fundamental diagram so obtained
is in excellent agreement with simulation data.

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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin