# A mathematical model of a road block

##### Citations

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### Additional excerpts

...[4] [5] [6]....

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### Cites background from "A mathematical model of a road bloc..."

...1 Background Traffic flows in urban areas became in the last years a very active research field; see, for instance, [4, 5, 8] and references cited therein....

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##### References

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### "A mathematical model of a road bloc..." refers background in this paper

...More accurate quantitative predictions may require more sophisticated models in which the traffic velocity may depend on a power of the traffic density or on the density gradient [3, 4]....

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3,015 citations

### "A mathematical model of a road bloc..." refers background or methods in this paper

...A continuum model for traffic flow ([1] to [5]) is used which assumes that the traffic is travelling steadily along a long road with no side turnings before the road block is set up....

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...Using the theory of characteristic for first order quasi-linear partial differential equations ([1] to [5]) it can be verified that the characteristic projections on the (x, t) plane are the one-parameter family of straight lines t− 1 = x 1− 2f(σ) − σ 1− 2f(σ) , f(σ) 6= 1 2 (25) x = σ, f(σ) = 1 2 (26) and that on these lines ρ(s, σ) = f(σ) , (27) where σ is the parameter along the initial curve and s is the parameter along the characteristic curves....

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95 citations

73 citations

### "A mathematical model of a road bloc..." refers background or methods in this paper

...The velocity of the shock is determined from the Rankine-Hugoniot condition [1, 4]....

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...A continuum model for traffic flow ([1] to [5]) is used which assumes that the traffic is travelling steadily along a long road with no side turnings before the road block is set up....

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...It can be shown that if the density decreases across the shock then the shock is unstable while if it increases then the shock is stable [1]....

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...Using the theory of characteristic for first order quasi-linear partial differential equations ([1] to [5]) it can be verified that the characteristic projections on the (x, t) plane are the one-parameter family of straight lines t− 1 = x 1− 2f(σ) − σ 1− 2f(σ) , f(σ) 6= 1 2 (25) x = σ, f(σ) = 1 2 (26) and that on these lines ρ(s, σ) = f(σ) , (27) where σ is the parameter along the initial curve and s is the parameter along the characteristic curves....

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