Street parking spots for automobiles are a scarce commodity in most urban environments. The heterogeneity of car sizes makes it inefficient to rigidly define fixed-sized spots. Instead, unmarked streets in cities like New York leave placement decisions to individual drivers, who have no direct incentive to maximize street utilization. In this paper, we explore the effectiveness of two different behavioral interventions designed to encourage better parking, namely (1) educational campaigns to encourage parkers to "kiss the bumper" and reduce the distance between themselves and their neighbors, or (2) painting appropriately-spaced markings on the street and urging drivers to "hit the line". Through analysis and simulation, we establish that the greatest densities are achieved when lines are painted to create spots roughly twice the length of average-sized cars. Kiss-the-bumper campaigns are in principle more effective than hit-the-line for equal degrees of compliance, although we believe that the visual cues of painted lines induce better parking behavior.
The parking density is defined as @math , with the R ' e nyi parking constant giving the limit of density as @math . Numerical calculations show that [ l f(l) l 0.7476 ] For small integral values of @math , exact values of @math are known, including @math , @math , @math , and @math . The variance in this process has been determined @cite_1 @cite_11 . Recently, the expected number of gaps of certain size was analyzed for a discrete version of the parking problem @cite_10 .
@cite_10 @cite_1 @cite_11
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Renyi’s parking problem (or 1D sequential interval packing problem) dates back to 1958, when Renyi studied the following random process: Consider an interval I of length x, and sequentially and randomly pack disjoint unit intervals in I until the remaining space prevents placing any new segment. The expected value of the measure of the covered part of I is M(x), so that the ratio M(x) x is the expected filling density of the random process. Following recent work by [4], we studied the discretized version of the above process by considering the packing of the 1D discrete lattice interval 1, 2,…,n + 2k − 1 with disjoint blocks of (k + 1) integers but, as opposed to the mentioned [4] result, our exclusion process is symmetric, hence more natural. Furthermore, we were able to obtain useful recursion formulas for the expected number of r-gaps (0 ≤ r ≤ k) between neighboring blocks. We also provided very fast converging series and extensive computer simulations for these expected numbers, so that the limiting filling density of the long line segment (as n →∞) is Renyi’s famous parking constant, 0.7475979203…. 1. Introduction. Consider the following random process in which cars of length 1 are parked on a street [0, x] of length x ≧ 1. The first car is parked so that the position of its center is a random variable which is uniformly distributed on ( [ 1^. 2 ,x - 1 2 ] ) If there remains space to park another car then a second car is parked so that its center is a random variable which is uniformly distributed over the set of points ( [ 1^. 2 ,x - 1 2 ] ) whose distance from the first car is ( 1 2 ). If there remains an empty interval of length ≧ 1 on the street then a third car is parked, its center being uniformly distributed over the set of points whose distance from the cars already parked and the ends of the street is ( 1 2 ). The process continues until there remains no empty interval of length ≧ 1. We denote by N x the total number of cars parked and extend the definition of N x to all x ≧ 0 by putting N x = 0 for 0 ≦ x < 1.