Related papers: Subset Parking Functions
Consider the following simple parking process on $\Lambda_n := \{-n, \ldots, n\}^d,d\ge1$: at each step, a site $i$ is chosen at random in $\Lambda_n$ and if $i$ and all its nearest neighbor sites are empty, $i$ is occupied. Once occupied,…
In a scenario of growing usage of park-and-ride facilities, understanding and predicting car park occupancy is becoming increasingly important. This study presents a model that effectively captures the occupancy patterns of park-and-ride…
Let $(A_u : u \in \mathbb{B})$ be i.i.d.~non-negative integers that we interpret as car arrivals on the vertices of the full binary tree $ \mathbb{B}$. Each car tries to park on its arrival node, but if it is already occupied, it drives…
Models of parking in which cars are placed randomly and then move according to a deterministic rule have been studied since the work of Konheim and Weiss in the 1960s. Recently, Damron, Gravner, Junge, Lyu, and Sivakoff introduced a model…
We consider the inversion enumerator I_n(q), which counts labeled trees or, equivalently, parking functions. This polynomial has a natural extension to generalized parking functions. Substituting q = -1 into this generalized polynomial…
With the increasing availability of transaction data collected by digital parking meters, paid curbside parking can be advantageously modeled as a network of interdependent queues. In this article we introduce methods for analyzing a…
In parking problems, a given number of cars enter a one-way street sequentially, and try to park according to a specified preferred spot in the street. Various models are possible depending on the chosen rule for collisions, when two cars…
The aim of this work is to extend to a general $S_m\times S_n$-module context the Grossman-Bizley paradigm that allows the enumeration of Dyck paths in a $m\times n$-rectangle. We obtain an explicit formula for the the "bi-Frobenius"…
Smart city research envisions a future in which data-driven solutions and sustainable infrastructure work together to define urban living at the crossroads of urbanization and technology. Within this framework, smart parking systems play an…
In 2000, it was demonstrated that the set of $x$-parking functions of length $n$, where $x$=($a,b,...,b$) $\in \mathbbm{N}^n$, is equivalent to the set of rooted multicolored forests on [$n$]=\{1,...,$n$\}. In 2020, Yue Cai and Catherine H.…
In smart cities, it is common practice to define a maximum length of stay for a given parking space to increase the space's rotativity and discourage the usage of individual transportation solutions. However, automatically determining…
We present a queuing model of parking dynamics and a model-based prediction method to provide real-time probabilistic forecasts of future parking occupancy. The queuing model has a non-homogeneous arrival rate and time-varying service time…
We study subadditive functions of the random parking model previously analyzed by the second author. In particular, we consider local functions $S$ of subsets of $\mathbb{R}^d$ and of point sets that are (almost) subadditive in their first…
We propose and study a data-driven framework for identifying traffic congestion functions (numerical relationships between observations of traffic variables) at global scale and segment-level granularity. In contrast to methods that…
With the number of vehicles continuously increasing, parking monitoring and analysis are becoming a substantial feature of modern cities. In this study, we present a methodology to monitor car parking areas and to analyze their occupancy in…
Finding an available on-street parking spot is a relevant problem of day-to-day life. In recent years, cities such as Melbourne and San Francisco deployed sensors that provide real-time information about the occupation of parking spots.…
We consider two variations of the discrete car parking problem where at every vertex of the integers a car arrives with rate one, now allowing for parking in two lines. a) The car parks in the first line whenever the vertex and all of its…
In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the…
The classical parking functions, counted by the Cayley number (n+1)^(n-1), carry a natural permutation representation of the symmetric group S_n in which the number of orbits is the n'th Catalan number. In this paper, we will generalize…
This paper introduces a comprehensive approach to optimize parking efficiency for connected and Automated vehicle (CAVs) fleets. We present a multi-vehicle parking simulator, equipped with hierarchical path planning and collision avoidance…