In the deterministic limit, p = 0, the velocity is constant at the maximum velocity (here 5) up to a density ρ = 1/(maximum velocity 1) = 1 / 6 = 0.167, at which point there is a discontinuity in the slope due to the sudden appearance of traffic jams.
Then as the density increases further, the average velocity decreases until it reaches zero when the road is 100% occupied.
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It is essentially a simple cellular automaton model for road traffic flow that can reproduce traffic jams, i.e., show a slow down in average car speed when the road is crowded (high density of cars).
The model shows how traffic jams can be thought of as an emergent or collective phenomenon due to interactions between cars on the road, when the density of cars is high and so cars are close to each other on average.
This feature of one car braking at random and causing a jam is absent in a deterministic model.
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Black pixels are cells with cars in them, white pixels are empty cells.
From the top to the bottom successive lines of pixels are the road at successive times, i.e., the top line is the road at t = 1, the line below it is the road at t = 2, etc.A road with jams of cars, in the Nagel–Schreckenberg model.Each line of pixels represents the road (of 100 cells) at one time.Without the randomization step (third action), the model is a deterministic algorithm, i.e., the cars always move in a set pattern once the original state of the road is set.With randomization this is not the case, as it is on a real road with human drivers.One can think of a cell as being a few car lengths long and the maximum velocity as being the speed limit on the road.