We consider two analogues of a discrete version of the famous car parking problem of Rényi for trees, which are also known under the term random sequential adsorption. For both models, the blocking model, where cars arrive sequentially at the nodes and only park if the site and all neighbouring nodes are free, and the dimer model, where cars arrive sequentially at the edges and only park if both endnodes are free, we provide a detailed analysis of the number of occupied nodes in a randomly chosen labelled tree of a certain size. In particular, by introducing a combinatorial approach and an analytic combinatorics treatment, we show exact and asymptotic results for the first moments and thus characterize the jamming density, i.e., the limiting ratio of the mean number of occupied nodes to the total number of nodes in the tree; moreover, we state distributional results and a central limit theorem.

我们考虑树木的Rényi著名停车场问题的离散版本的两个类似物，这在术语“随机顺序吸附”下也众所周知。对于这两种模型，分别是阻塞模型和阻塞模型，在阻塞模型中，汽车依次到达节点，并且仅在站点和所有相邻节点空闲时停车；在二聚体模型中，汽车依次到达边缘，并且在两个端节点都空闲时，停车提供对特定大小的随机选择的带标签树中占用节点数的详细分析。特别是，通过引入组合方法和解析组合方法，我们显示了第一刻的精确和渐近结果，从而表征了干扰密度，即，平均占用节点数与节点中节点总数的极限比。那个树; 此外，