Mathematics of Parking: Varying Parking Rate

In the classical parking problem, unit intervals (“car lengths”) are placed uniformly at random without overlapping. The process terminates saturation, i.e. until no more can be stowed. this paper, we present a generalization of problem in which with an exponential distribution rate parameter $$\lambda $$ . We show that mathematical expectation number saturation satisfies certain integral equation. Using Laplace transforms and Tauberian theorems, investigate asymptotic behavior function describe way to compute corresponding limits for large Then, derive another equation derivative use it above small help some results equations. also converge uniform case as vanishes, yielding well-known Renyi constant. Finally, reveal variance saturation.