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We settle a conjecture of B\'ona regarding the log-concavity of a certain statistic on parking functions by utilizing recent log-concavity results on matroids. This result allows us to also prove that connected, labeled graphs graded by…

In this paper, we mainly study two notions of pattern avoidance in parking functions. First, for any collection of length 3 patterns, we compute the number of parking functions of size $n$ that avoid them under the first notion. This is…

The notion of parking sequences is a new generalization of parking functions introduced by Ehrenborg and Happ. In the parking process defining the classical parking functions, instead of each car only taking one parking space, we allow the…

Autonomous vehicles currently suffer from a time-inefficient driving style caused by uncertainty about human behavior in traffic interactions. Accurate and reliable prediction models enabling more efficient trajectory planning could make…

Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been…

Nowadays, traffic monitoring systems have access to real time data, e.g. through GPS devices. We propose a new traffic model able to take into account these data and, hence, able to describe the effects of unpredictable accidents. The well…

The parking-lot model provides a qualitative description of the main features of the phenomenology of granular compaction. We derive here approximate kinetic equations for this model, equations that are based on a $2-$parameter…

This article mediates an mathematical insight to the theory of vehicular headways measured on signalized crossroads. Considering both, mathematical and empirical substances of the socio-physical system studied, we firstly formulate several…

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…

We performed extensive simulations accompanied by a detailed study of a two-segment size random sequential model on the line. We followed the kinetics towards the jamming state, but we paid particular attention to the characterization of…

Urban traffic congestion, exacerbated by inefficient parking management and cruising for parking, significantly hampers mobility and sustainability in smart cities. Drivers often face delays searching for parking spaces, influenced by…

Double parking that often negatively affects traffic operations and safety is not a new phenomenon on urban streets. This study proposes a novel data-driven integrated framework for estimating the actual frequency of double parking so that…

We illustrate the experimental, empirical, approach to mathematics (that contrary to popular belief, is often rigorous), by using parking functions and their "area" statistic, as a case study. Our methods are purely finitistic and…

Parking in large metropolitan areas is often a time-consuming task with further implications toward traffic patterns that affect urban landscaping. Reducing the premium space needed for parking has led to the development of automated…

This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is crucial to find…

Machine Learning (ML) methods have become a useful tool for tackling vehicle routing problems, either in combination with popular heuristics or as standalone models. However, current methods suffer from poor generalization when tackling…

The effects of real-time provision of travel-time information on the behaviour of drivers are considered. The model of Marecek et al. [arXiv:1406.7639, Int. J. Control 88(10), 2015] is extended to consider uncertainty in the response of a…

I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the…

We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…

We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…