Related papers: On friendship and cyclic parking functions
Many models account for the traffic flow of road users but few take the details of local interactions into consideration and how they could deteriorate into safety-critical situations. Building on the concept of sensorimotor control, we…
A parking function of length n is a sequence (b_1, b_2,..., b_n) of nonnegative integers whose nondecreasing rearrangement (a_1, a_2,...,a_n) has the property that a_i < i for every i. A well-known result about parking functions is that the…
Intrinsic location functional is a large class of random locations containing locations that one may encounter in many cases, e.g., the location of the path supremum/infimum over a given interval, the first/last hitting time, etc. It has…
For vehicle sharing schemes, where drop-off positions are not fixed, we propose a pricing scheme, where the price depends in part on the distance between where a vehicle is being dropped off and where the closest shared vehicle is parked.…
Vehicle-sharing systems -- such as bike-, car-, or motorcycle-sharing systems -- have become increasingly popular in big cities in recent years. On the one hand, they provide a cheaper and environmentally friendlier means of transportation…
Recently, the authors extended the notion of parking functions to parking sequences, which include cars of different sizes, and proved a product formula for the number of such sequences. We here give a refinement of that result involving…
This paper studies the cooperative driving of connected and automated vehicles (CAVs) at conflict areas (e.g., non-signalized intersections and ramping regions). Due to safety concerns, most existing studies prohibit lane change since this…
Accidental symmetries in effective field theories can be established by computing and comparing Hilbert series. This invites us to study them with the tools of invariant theory. Applying this technology, we spotlight three classes of…
Modeling of headway/spacing between two consecutive vehicles has many applications in traffic flow theory and transport practice. Most known approaches only study the vehicles running on freeways. In this paper, we propose a model to…
In this paper, we investigate a parking process on a uniform random rooted plane tree with $n$ vertices. Every vertex of the tree has a parking space for a single car. Cars arrive at independent uniformly random vertices of the tree. If the…
For $0\leq k\leq n-1$, we introduce a family of $k$-skeletal paths which are counted by the $n$-th Catalan number for each $k$, and specialize to Dyck paths when $k=n-1$. We similarly introduce $k$-skeletal parking functions which are…
We develop a circular-street argument, in the style of Pollak, to obtain a new proof that there are $C_n = \frac{1}{n+1}\binom{2n}{n}$ weakly increasing parking functions of length $n \geq 1$, where $C_n$ is the $n$th Catalan number.
Merging at highway on-ramps while interacting with other human-driven vehicles is challenging for autonomous vehicles (AVs). An efficient route to this challenge requires exploring and exploiting knowledge of the interaction process from…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
Parking occupancy in the area is defined by three major parameters - the rate of cars arrivals, the dwell time of already parked cars, and the willingness of drivers who are searching but yet did not find a vacant parking spot, to continue…
Anticipation in traffic means that drivers estimate their leaders' velocities for future timesteps. In the article a specific stochastic car--following model with non--unique flow--density relation is investigated with respect to…
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…
In this paper, we complete the enumeration of the number of parking functions of length $n$ avoiding, in the sense defined by Qiu and Remmel, a permutation of length 3, answering several questions of Adeniran and Pudwell. Additionally, we…
In this paper we analyze the spatial distribution of elements around points of interest. Based on a spatial exclusion principle we model the system by means of a Fermi-Dirac distribution defined by two easily interpretable parameters. By…
We give an exact enumerative formula for the minimal acyclic deterministic finite automata. This formula is obtained from a bijection between a family of generalized parking functions and the transitions functions of acyclic automata.