Related papers: A second row Parking Paradox

In this paper, we consider the problem of identifying patterns of interest in colored strings. A colored string is a string where each position is assigned one of a finite set of colors. Our task is to find substrings of the colored string…

The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA). Unfortunately, there exists no one-dimensional two-state CA which classifies binary…

We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on the bus is fixed. The customers arriving at station i wait for…

Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…

We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of…

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…

A bottleneck situation in one-lane traffic-flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal…

We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…

This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by…

We consider a swarm of mobile robots evolving in a bidimensional Euclidean space. We study a variant of the crash-tolerant gathering problem: if no robot crashes, robots have to meet at the same arbitrary location, not known beforehand, in…

A special type of binomial splitting process is studied. Such a process can be used to model a high-dimensional corner parking problem, as well as the depth of random PATRICIA tries (a special class of digital tree data structures). The…

We show that the spacing distribution between parked cars can be obtained as a solution of certain linear distributional fixed point equation. The results are compared with the data measured on the streets of Hradec Kralove. We also discuss…

Nesetril and Ossona de Mendez introduced the notion of first order convergence as an attempt to unify the notions of convergence for sparse and dense graphs. It is known that there exist first order convergent sequences of graphs with no…

We consider the stabilization of an unstable discrete-time linear system that is observed over a channel corrupted by continuous multiplicative noise. Our main result shows that if the system growth is large enough, then the system cannot…

The problem of reservation in a large distributed system is analyzed via a new mathematical model. A typical application is a station-based car-sharing system which can be described as a closed stochastic network where the nodes are the…

Deep reinforcement learning algorithms typically act on the same set of actions. However, this is not sufficient for a wide range of real-world applications where different subsets are available at each step. In this thesis, we consider the…

We compute the correlation function in the equilibrium version of R\'enyi's {\sl parking problem}. The correlation length is found to diverge as $2^{-1}\pi^{-2}(1-\rho)^{-2}$ when $\rho\nearrow1$ (maximum density) and as…

We consider a controlled double-ended queue consisting of two classes of customers, labeled sellers and buyers. The sellers and buyers arrive in a trading market according to two independent renewal processes. Whenever there is a seller and…

Let P be a set of n points in the plane, not all on a line. We show that if n is large then there are at least n/2 ordinary lines, that is to say lines passing through exactly two points of P. This confirms, for large n, a conjecture of…

The Braess paradox can be observed in road networks used by selfish users. It describes the counterintuitive situation in which adding a new, per se faster, origin-destination connection to a road network results in increased travel times…