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Rényi's Parking Constants comes up when one puts down unit length cars on a interval, such that the probability of covering any two interval is the same.

Are there any published results when the distribution is non-uniform?

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Here is one: Jean-François Marckert, Parking with density, Random Structures and Algorithms 18 (4), 364-380 (2001). A preprint version is available on this page.

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