Modelling the gap size distribution of parked cars

We have measured the distribution of distances between parked cars in a number of roads in central London. We compare the results with models of random sequential adsorption, or random car parking models, as they are often called. Our empirical results do not agree with these models, and hence we introduce alternative models for the parking process. The first model we propose is one where cars can only park if the space is greater than or equal to a chosen minimum size; where the extra space can be used for manoeuvering. The results of this model suggest that in addition to a deposition process, a re-positioning process is required to explain our empirical results. Hence, we introduce a further model where at each time step, with probability p, a car is randomly placed on a line if the space is empty and with probabilty 1-p, is placed in a space but then rolls to the nearest parked car so that it is y distance from the nearest car with probability f(y). We concentrate on two specific probabilities f(y) and find that for one case, the gap size distribution agrees with the empirical results.