Mean Field Theory for Pedestrian Outflow through an Exit

An average pedestrian flow through an exit is one of the most important index in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model by using cellular automaton, is extended by taking into account a realistic behavior of pedestrians around the exit. The model is studied by both numerical simulations and cluster analysis to obtain a theoretical expression of an average pedestrian flow through the exit. It is found quantitatively that the effect of exit door width, a wall, and pedestrian's mood of competition or cooperation significantly influence the average flow. The results show that there is suitable width of the exit and position according to pedestrian's mood.Comment: 9 pages, 16 figure

A New Expression of Soliton Solution to the Ultradiscrete Toda Equation

A new type of multi-soliton solution to the ultradiscrete Toda equation is proposed. The solution can be transformed into another expression of solution in a perturbation form. A direct proof of the solution is also given.Comment: 13 page

A stochastic cellular automaton model for traffic flow with multiple metastable states

A new stochastic cellular automaton (CA) model of traffic flow, which includes slow-to-start effects and a driver's perspective, is proposed by extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density relation of this model shows multiple metastable branches near the transition density from free to congested traffic, which form a wide scattering area in the fundamental diagram. The stability of these branches and their velocity distributions are explicitly studied by numerical simulations.Comment: 11 pages, 20 figures, submitted for publicatio

Two-dimensional Burgers Cellular Automaton

A two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform dependent variables into discrete ones. Some exact solutions of the CA, such as shock wave solutions, are studied in detail.Comment: Latex2.09, 17 pages including 7 figure

Max-Plus Algebra for Complex Variables and Its Application to Discrete Fourier Transformation

A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number of complex variables. As an application, the max-plus transformation is applied to the discrete Fourier transformation. Stretched coordinates are introduced to obtain the max-plus transformation whose imaginary part coinsides with a phase of the discrete Fourier transformation

Hysteresis phenomenon in deterministic traffic flows

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow model being a straightforward generalization to the well known Nagel-Schreckenberg model covers also a more recent slow-to-start model as a special case. The model has two distinct ergodic (unmixed) phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the ``free-flowing'' (or ``gaseous'') phase. When the density exceeds the second critical value the model produces large, persistent, well-defined traffic jams, which correspond to the ``jammed'' (or ``liquid'') phase. Between the two critical values each of these phases may take place, which can be interpreted as an ``overcooled gas'' phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the life-time of individual traffic jams for a given configuration of particles.Comment: 22 pages, 6 figures, corrected and improved version, to appear in the Journal of Statistical Physic

Introduction of Frictional and Turning Function for Pedestrian Outflow with an Obstacle

In this paper, two important factors which affect the pedestrian outflow at a bottleneck significantly are studied in detail to analyze the effect of an obstacle set up in front of an exit. One is a conflict at an exit when pedestrians evacuate from a room. We use floor field model for simulating such behavior, which is a well-studied pedestrian model using cellular automata. The conflicts have been taken into account by the friction parameter. However, the friction parameter so far is a constant and does not depend on the number of the pedestrians conflicting at the same time. Thus, we have improved the friction parameter by the frictional function, which is a function of the number of the pedestrians involved in the conflict. Second, we have newly introduced the cost of turning of pedestrians at the exit. Since pedestrians have inertia, their walking speeds decrease when they turn, and the pedestrian outflow decreases. The validity of the extended model, which includes the frictional function and the turning function, is verified by both a mean field theory and experiments. In our experiments, the pedestrian flow increases when we put an obstacle in front of an exit. The analytical results clearly explains the mechanism of the effect of the obstacle, i.e., the obstacle blocks pedestrians moving to the exit and decreases the average number of pedestrians involved in the conflict. We have also found that an obstacle works more effectively when we shift it from the center since pedestrians go through the exit with less turning

Bubble burst as jamming phase transition

Recently research on bubble and its burst attract much interest of researchers in various field such as economics and physics. Economists have been regarding bubble as a disorder in prices. However, this research strategy has overlooked an importance of the volume of transactions. In this paper, we have proposed a bubble burst model by focusing the transactions incorporating a traffic model that represents spontaneous traffic jam. We find that the phenomenon of bubble burst shares many similar properties with traffic jam formation by comparing data taken from US housing market. Our result suggests that the transaction could be a driving force of bursting phenomenon.Comment: 9 pages,12 figure

Modeling the desired direction in a force-based model for pedestrian dynamics

We introduce an enhanced model based on the generalized centrifugal force model. Furthermore, the desired direction of pedestrians is investigated. A new approach leaning on the well-known concept of static and dynamic floor-fields in cellular automata is presented. Numerical results of the model are presented and compared with empirical data.Comment: 14 pages 11 figures, submitted to TGF'1