Per-site occupancy in the discrete parking problem

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• 作者：Seva Shneer^a ; ^{v.shneer@hw.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Peter M. van de Ven^b ; ^{ven@cwi.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generating functions ; Jamming density ; Parking problem ; Wireless networks
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：120
• 期：Complete
• 页码：141-146
• 全文大小：375 K

文摘

We consider the classical discrete parking problem, in which cars arrive uniformly at random on any two adjacent sites out of md5=8f1d0ea913780a83a963f95673f0a498" title="Click to view the MathML source">n$n$ sites on a line. An arriving car parks if there is no overlap with previously parked cars, and leaves otherwise. This process continues until there is no more space available for cars to park, at which point we may compute the jamming density md5=3a35cc4efbbdbb5cb03c3f35a19f5c88" title="Click to view the MathML source">E_n/n$E_n/n$, which represents the expected fraction of occupied sites. We extend the classical results by not just considering the total expected number of cars parked, but also the probability of each site being occupied by a car. This we then use to provide an alternative derivation of the jamming density.