it looks more like it's gamma distributed to me: you could imagine the generative process is something like a sum of exponentially distributed decisions times.
another view might be that an exponential distribution on distances would lend (a lot of) support to zero distance: hopefully that's pretty rare.
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 exponential distribution is a kind of gamma distribution: Gamma(1,lambda) = Exp(lambda)