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each driver decides whether or not to increase the distance to the next car. there are many such decisions that result in the total distance to the next car: i think it's a constant adjustment rather than just one decision.

another view might be that an exponential distribution on distances would lend (a lot of) support to zero distance: hopefully that's pretty rare.

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Interesting... makes some sense.

another view might be that an exponential distribution on distances would lend (a lot of) support to zero distance

Well, I think that would be a case of sticking a bit too closely to the model. Its likely that, even if the distribution is generally exponential, at very short distances the decision process changes.

In fact, one would probably argue that the distribution would always change based on how dense the traffic is.

the gamma distribution is often used (for example, in neuroscience for spiking rates for the refactory period) to capture the case where you do not wish to give support to zero plus some short period after zero.

the exponential distribution is a kind of gamma distribution: Gamma(1,lambda) = Exp(lambda)

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