Car Parking Problem Research Articles

Park Tag

A major challenge for modern cities is how to maximize the productivity and reliability of urban infrastructure, such as minimizing road congestion by making better use of the limited car parking facilities that are available. We approach a special system for smart parking reservation in a commercial car parking area in an urban environment. This system is mainly designed to avoid unnecessary time conception to find an empty slot in a car parking area. By the same case we can also save more than 80 percentage of fuel wastage in a car parking area to finds the empty parking slot. Car parking problem is a major contributor and has been, still a major problem with increasing vehicle size in the luxurious segment and confined parking spaces in urban cities.

An analytic approach to maximize entropy for computing equilibrium densities of k-mers on linear chains

The irreversible adsorption of polyatomic (or k-mers) on linear chains is related to phenomena such as the adsorption of colloids, long molecules, and proteins on solid substrates. This process generates jammed or blocked final states. In the case of k = 2, the binomial coefficient computes the number of final states. By the canonical ensemble, the Boltzmann–Gibbs–Shannon entropy function is obtained by using Stirling’s approximation, and its equilibrium density ρ eq,2 is its maximum at the thermodynamic limit with value ρ eq,2 ≈ 0.822 991 17. Moreover, since at the same energy we have several possible configurations, we obtain the state probability density. Maximizing the entropy, it converges to a Gaussian distribution as L → ∞.In this article, we generalize this analysis to k > 2 to maximize the entropy and to get the equilibrium densities ρ eq,k . We first develop a complete combinatorial analysis to get the generalized recurrence formula (GRF) for counting all blocked configuration states on a chain of length L with fixed k, which corresponds to a generalized truncated Fibonacci sequence. The configuration states for allocating N k-mers is related with the general binomial coefficient . Since Stirling’s approximation cannot be used for GRF, we numerically compute the state probability density and approximate ρ eq,k and σ eq,k for large k-mers with high precision for k-mers up to k = 1, 000, 000. We highlight that ρ eq,k decreases from k = 2, …, 8 reaching a minimum at k = 9 and then increases with an asymptotic value ρ eq,∞ = 0.9285685. We compared with jamming densities obtained by RSA and at k ≈ 16, both curves intersect and ergodicity is not broken since ρ jam,k ≈ ρ eq,k . In the case of , it grows similarly with asymptotic value . Since the similar behavior for large values, we found the limit relationship as L → ∞ for any k. Finally, as k → ∞, we get the Gaussian distribution for the continuous blocked irreversible adsorption or equivalent to the irreversible blocked car parking problem.

Paris car parking problem for partially oriented discorectangles on a line.

The random sequential adsorption (RSA) of identical elongated particles (discorectangles) on a line ("Paris car parking problem") was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The possible orientations of the discorectanles were restricted between θ∈[-θ_{m};θ_{m}] while the aspect ratio (length-to-width ratio) for the discorectangles was varied within the range ɛ∈[1;100]. Additionally, the limiting case ɛ=∞ (i.e., widthless sticks) was considered. We observed that the RSA deposition for the problem under consideration was governed by the formation of rarefied holes (containing particles oriented along a line) surrounded by comparatively dense stacks (filled with almost parallel particles oriented in the vertical direction). The kinetics of the changes of the order parameter and the packing density are discussed. Partial ordering of the discorectangles significantly affected the packing density at the jamming state, φ_{j}, and shifted the cusps in the φ_{j}(ɛ) dependencies. This can be explained by the effects on the competition between the particles' orientational degrees of freedom and the excluded volume effects.

A combinatorial approach for discrete car parking on random labelled trees

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.

Car Parking Problem in Urban Areas, Causes and Solutions

Car parking is a major problem in urban areas in both developed and developing countries. Following the rapid incense of car ownership, many cities are suffering from lacking of car parking areas with imbalance between parking supply and demand which can be considered the initial reason for metropolis parking problems. This imbalance is partially due to ineffective land use planning and miscalculations of space requirements during first stages of planning. Shortage of parking space, high parking tariffs, and traffic congestion due to visitors in search for a parking place are only a few examples of everyday parking problems. The paper examines car parking problem in the city; its different causes and conventional - yet non-successful - approaches. Modern technology has produced a variety of new solutions and techniques in this respect. The paper reviews new planning trends and creative technological solutions which can help alleviate the strain of the problem. Because car parking solutions are not an end in itself, but rather a means of achieving larger community goals in order to improve urban transportation and make cities more livable and efficient, the paper also discusses the environmental impacts which should be taken into considerations for solutions proposed.

Dynamic control of intelligent parking guidance using neural network predictive control

Abstract The parking problem is a very important issue in city life because many citizens waste a large amount of energy and time trying to find suitable parking lots. To resolve this problem, various intelligent parking guidance systems have been introduced. However, the method of operating an intelligent parking guidance system remains in the infant stage. For successful operation, it is important to develop an effective method that assesses and selects the best parking lot in a real-time environment. In this vein, this study proposes a neural network-based predictive control approach that finds suitable weights for multiple factors dynamically so that the best performance of the intelligent parking guidance system can be achieved. The proposed method can enhance the performance of an intelligent parking guidance system via dynamic control in selecting the best parking lot. To evaluate the proposed approach, simulation tests and comparison with a traditional model have been conducted. As a result, the proposed approach provides a robust solution in an efficient manner under diverse parking environments. With the proposed approach, from the public interest viewpoint, the car parking problem can be approached more effectively.

Revisiting parallel car parking problem

Among many physical and mechanical engineering problems, parallel car parking has drawn the attention of many researchers as it shows how methods of Lie algebra and differential geometry can be applied elegantly to explain the behavior of such a system. In this paper we have reviewed some aspects of this problem in this context and analyse the stability and controllability of such a system by some unconventional integrators like Kahan and Lie trotter integrator. At the same time we have also given the results obtained through conventional Runge Kutta integrator to see a comparison.

Correcting binding parameters for interacting ligand-lattice systems.

Binding of ligands to macromolecules is central to many functional and regulatory biological processes. Key parameters characterizing ligand-macromolecule interactions are the stoichiometry, inducing the number of ligands per macromolecule binding site, and the dissociation constant, quantifying the ligand-binding site affinity. Both these parameters can be obtained from analyses of classical saturation experiments using the standard binding equation that offers the great advantage of mathematical simplicity but becomes an approximation for situations of interest when a ligand binds and covers more than one single binding site on the macromolecule. Using the framework of car-parking problem with latticelike macromolecules where each ligand can cover simultaneously several consecutive binding sites, we showed that employing the standard analysis leads to underestimation of binding parameters, i.e., ligands appear larger than they actually are and their affinity is also greater than it is. Therefore, we have derived expressions allowing to determine the ligand size and true binding parameters (stoichiometry and dissociation constant) as a function of apparent binding parameters retrieved from standard saturation experiments.

Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles.

Random sequential adsorption (RSA) of particles of a particular shape is used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the observed algebraic time dependence of the asymptotic jamming coverage ∼t^{-ν} as t→∞. However, the exact value of the exponent ν is not known apart from the simplest case of the RSA of monodisperse spheres adsorbed on a line (Renyi's seminal "car parking problem"), where ν=1 can be derived analytically. Empirical simulation studies have conjectured on a case-by-case basis that for general nonspherical particles, ν=1/(d+d[over ˜]), where d denotes the dimension of the domain, and d[over ˜] the number of orientational degrees of freedom of a particle. Here, we solve this long-standing problem analytically for the d=1 case-the "Paris car parking problem." We prove, in particular, that the scaling exponent depends on the particle shape, contrary to the original conjecture and, remarkably, falls into two universality classes: (i)ν=1/(1+d[over ˜]/2) for shapes with a smooth contact distance, e.g., ellipsoids, and (ii)ν=1/(1+d[over ˜]) for shapes with a singular contact distance, e.g., spherocylinders and polyhedra. The exact solution explains, in particular, why many empirically observed scalings fall in between these two limits.

Intelligent Parking System

The searching of parking burns a lot of barrels of the world’s oil every day. Car parking problem is a major contributor in congestion of traffic and has been, still a major problem with increasing vehicle size in the luxurious segment and also confines parking spaces in urban cities. The rapid growth in the number of vehicles worldwide is intensifying the problem of the lack of parking space. As the global population continues to urbanize, without a well-planned, convenience-driven retreat from the car, these problems will worsen in many countries. The current unmanaged car parks and transportation facilities make it difficult to accommodate the increasing number of vehicles in a proper, convenient manner so it is necessary to have an efficient and smart parking system. Smart parking management systems are capable of providing extreme level of convenience to the drivers. In this paper, a proposed web App system, named “Park Easy” is based on the usage of smart phones, sensors monitoring techniques with a camera which is used as a sensor to take photos to show the occupancy of cars parks. By implementing this system, the utilization of parking spaces will increase. It allocates available parking space to a given driver to park their vehicle, renew the availability of the parking space when the car leaves and compute the charges due. Smart parking App, “Park Easy”, will also enable most important techniques to provide all the possible shortage route for parking from any area of the city mainly, it helps to predict accurately and sense spot/vehicle occupancy in real-time.

Emerging quasi-0D states at vanishing total entropy of the 1D hard sphere system: A coarse-grained similarity to the car parking problem

A coarse-grained system of one-dimensional (1D) hard spheres (HSs) is created using the Delaunay tessellation, which enables one to define the quasi-0D state. It is found from comparing the quasi-0D and 1D free energy densities that a frozen state due to the emergence of quasi-0D HSs is thermodynamically more favorable than fluidity with a large-scale heterogeneity above crossover volume fraction of $\phi_c=e/(1+e)=0.731\cdots$, at which the total entropy of the 1D state vanishes. The Delaunay-based lattice mapping further provides a similarity between the dense HS system above $\phi_c$ and the jamming limit in the car parking problem.

Voronoi cell patterns: Theoretical model and applications

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We use our model to describe the Voronoi cell patterns of several systems. Specifically, we study the island nucleation with irreversible attachment, the 1D car-parking problem, the formation of second-level administrative divisions, and the pattern formed by the Paris Métro stations.

Reversing Control of a Car with a Trailer Using the Driver Assistance System

Passive trailer systems provide a variety of advantages in delivery and transportation applications. The transportation capacity of the truck with multiple trailers can be increased in proportion to the number of trailers. The cost of the car with trailers is much lower than the cost of multiple cars. However, the major drawback of the trailer system is that the control problem is difficult. We concentrate on the motion control problem of “pushing” trailers because pushing is much more difficult than “pulling”. In this paper, it is shown how the car with passive trailers can be easily controlled by the use of the proposed driver assist system and the motion control scheme. Since the keypad is the only additional device for the driver assist system, the proposed scheme can be implemented with the conventional trucks without many hardware modifications. The manual control strategy of pushing is established. The kinematic design of the passive trailer is adopted from the prior work (Park and Chung, 2004). The kinematic configuration design of the car with trailers is proposed for pushing control. The usefulness of the proposed scheme is experimentally verified with the small scale car with trailer system for the car parking problem. The parking control requires forward and reverse motion in narrow environment. It is shown that even beginners can easily control the pushing motion with the proposed scheme.

Adsorption behavior of large plasmids on the anion-exchange methacrylate monolithic columns

The objective of this study was to investigate the behavior of large plasmids on the monolithic columns under binding and nonbinding conditions. The pressure drop measurements under nonbinding conditions demonstrated that the flow velocities under which plasmid passing monolith became hindered by the monolithic pore structure depended on the plasmid size as well as on the average monolith pore size; however, they were all very high exceeding the values encountered when applying CIM monolithic columns at their maximal flow rate. The impact of the ligand density and the salt concentration in loading buffer on binding capacity of the monolith for different sized plasmids was examined. For all plasmids the increase of dynamic binding capacity with the increase of salt concentration in the loading solution was observed reaching maximum of 7.1 mg/mL at 0.4 M NaCl for 21 kbp, 12.0 mg/mL at 0.4 M NaCl for 39.4 kbp and 8.4 mg/mL at 0.5 M NaCl for 62.1 kbp. Analysis of the pressure drop data measured on the monolithic column during plasmid loading revealed different patterns of plasmid binding to the surface, showing “car-parking problem” phenomena under certain conditions. In addition, layer thickness of adsorbed plasmid was estimated and at maximal dynamic binding capacity it matched calculated plasmid radius of gyration. Finally, it was found that the adsorbed plasmid layer acts similarly as the grafted layer responding to changes in solution's ionic strength as well as mobile phase flow rate and that the density of plasmid layer depends on the plasmid size and also loading conditions.

A Second-row Parking Paradox

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 nearest neighbors are not occupied yet. It can reach the first line if it is not obstructed by cars already parked in the second line (screening). b) The car parks according to the same rules, but parking in the first line can not be obstructed by parked cars in the second line (no screening). In both models, a car that can not park in the first line will attempt to park in the second line. If it is obstructed in the second line as well, the attempt is discarded. We show that both models are solvable in terms of finite-dimensional ODEs. We compare numerically the limits of first and second line densities, with time going to infinity. While it is not surprising that model a) exhibits an increase of the density in the second line from the first line, more remarkably this is also true for model b), albeit in a less pronounced way.

Modeling of Spacing Distribution of Queuing Vehicles at Signalized Junctions Using Random-Matrix Theory

The modeling of headway/spacing between two consecutive vehicles in a queue has many applications in traffic flow theory and transport practice. Most known approaches have only studied vehicles on freeways. This paper presents a model for the spacing distribution of queuing vehicles at a signalized junction based on random-matrix theory. The spacing distribution of a Gaussian symplectic ensemble (GSE) fits well with recently measured spacing distribution data. These results are also compared with measured spacing distribution observed for the car parking problem. Vehicle stationary queuing and vehicle parking have different spacing distributions due to different driving patterns.

Simulation Studies for Random Sequential Adsorption in Narrow Slit: Two-Dimensional Parking Model

largest gap between two successive rods is less than the length of a rod, the parking is full or jamming. During the RSA process, particles are deposited at random positions, one at each time step, with the restriction that overlapping with pre-deposited particles is forbidden. An important nontrivial property of the RSA model is that this irreversible process reaches the jamming limit at large time, and, as a non-Markovian chain sequence, the saturated jamming state depends on the initial configuration. In contrast, the equilibrium fluids exhibit the Markovian stochastic properties, in which the final state has no memory effect from the initial state. The main features observed in the onedimensional car parking problem persist in various systems of higher-order dimensions. The fundamental and application of the RSA process on this subject has been the central topic of reviews 2 and books. 3 The qualitative and quantitative relevance of higher dimensional RSA has been demonstrated in various research areas including proteins, colloidal particles, polymer chains, granular materials, etc. 4 Very recently, by employing both numerical and theoretical methods, Torquato and his coworkers 5 have made the systematic investigation for the RSA packing in Euclidean space over six hyper-dimensional systems. Except for the one-dimensional case, there is no exact analytic solution to the RSA problem because the complicated form of the probability density involved in two or more dimensional systems imposes the non-trivial generalization of the theoretical formalism in statistical thermodynamics. When the system dimensionality of the substrate becomes higher, one can often obtain the detailed structures and kinetics of the RSA model using the computer simulation method. As an extremely useful diagnostic approach, simulation results can provide essentially exact data for precisely defined model systems. 6

Parking in the City

Our aim is to describe the spacing distribution between cars parked parallel to the curb somewhere in the center of a city. We will assume that the street is long enough to enable a parallel parking of many cars. Moreover we assume that there are no driveways or side streets in the segment of interest and that the street is free of any kind of marked parking lots or park meters. So the drivers are not biased to park at some particular positions. On the contrary: they are free to park the car anywhere provided they find and empty space to do it. In addition we assume that there are no cars parked permanently on the street (i.e. we assume that the majority of the cars leaves the street during the night). The standard way to describe such random parking is the continuous version of the random sequential adsorption model known also as the “random car parking problem” — see [1, 2] for review. It is a well-studied process where the cars are parked without overlapping onto randomly chosen positions. All cars have the same length l0 and all parking attempts are regarded as independent. Let us assume that the street has a length L A l0. The particular parking attempt goes as follows: choose a random position x on the street. If the interval (x−l0/2, x+l0/2)

Gap-size distribution functions of a random sequential adsorption model of segments on a line

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 the jamming state structure. In particular, we studied the effect of the size ratio on the mean-gap size, the gap-size dispersion, gap-size skewness, and gap-size kurtosis at the jamming state. We also analyzed the above quantities for the four possible segment-to-segment gap types. We ranged the values of the size ratio from one to twenty. In the limit of a size ratio of one, one recovers the classical car-parking problem. We observed that at low size ratios the jamming state is constituted by short streaks of small and large segments, while at high values of the size ratio the jamming state structure is formed by long streaks of small segments separated by a single large segment. This view of the jamming state structure as a function of the size ratio is supported by the various measured quantities. The present work can help provide insight, for example, on how to minimize the interparticle distance or minimize fluctuations around the mean particle-to-particle distance.

Modelling gap-size distribution of parked cars using random-matrix theory

We apply the random-matrix theory to the car-parking problem. For this purpose, we adopt a Coulomb gas model that associates the coordinates of the gas particles with the eigenvalues of a random matrix. The nature of interaction between the particles is consistent with the tendency of the drivers to park their cars near to each other and in the same time keep a distance sufficient for manoeuvring. We show that the recently measured gap-size distribution of parked cars in a number of roads in central London is well represented by the spacing distribution of a Gaussian unitary ensemble.