Towards a variational principle for motivated vehicle motion

We deal with the problem of deriving the microscopic equations governing the individual car motion based on the assumptions about the strategy of driver behavior. We suppose the driver behavior to be a result of a certain compromise between the will to move at a speed that is comfortable for him under the surrounding external conditions, comprising the physical state of the road, the weather conditions, etc., and the necessity to keep a safe headway distance between the cars in front of him. Such a strategy implies that a driver can compare the possible ways of his further motion and so choose the best one. To describe the driver preferences we introduce the priority functional whose extremals specify the driver choice. For simplicity we consider a single-lane road. In this case solving the corresponding equations for the extremals we find the relationship between the current acceleration, velocity and position of the car. As a special case we get a certain generalization of the optimal velocity model similar to the "intelligent driver model" proposed by Treiber and Helbing.Comment: 6 pages, RevTeX

The effect of temperature on the life cycle of Drosophila nebulosa

It is the purpose of this research to study the effect of temperature on the life cycle of D. nebulosa. D. nebulosa is considered a stenothermal species from a warm environment and has been reported in Texas and Florida, the West Indies, Mexico, Central America, and as far south as Brazil. According to the hypothesis of Hunter (1964), the capacity of this species for adaptation to different temperatures would not be expected to be as great as that of a eurythermal species. Stenothermal species are relatively limited by the environmental temperature, and therefore, one would expect a marked decrease in the length of the life cycle with increasing temperatures. On the other hand, eurythermal species are relatively independent of the environmental temperature, soa relatively less decrease in the length of the life cycle with increasing temperature would be expected

Complex Dynamics of Bus, Tram and Elevator Delays in Transportation System

It is necessary and important to operate buses and trams on time. The bus schedule is closely related to the dynamic motion of buses. In this part, we introduce the nonlinear maps for describing the dynamics of shuttle buses in the transportation system. The complex motion of the buses is explained by the nonlinear-map models. The transportation system of shuttle buses without passing is similar to that of the trams. The transport of elevators is also similar to that of shuttle buses with freely passing. The complex dynamics of a single bus is described in terms of the piecewise map, the delayed map, the extended circle map and the combined map. The dynamics of a few buses is described by the model of freely passing buses, the model of no passing buses, and the model of increase or decrease of buses. The nonlinear-map models are useful to make an accurate estimate of the arrival time in the bus transportation

Anisotropic effect on two-dimensional cellular automaton traffic flow with periodic and open boundaries

By the use of computer simulations we investigate, in the cellular automaton of two-dimensional traffic flow, the anisotropic effect of the probabilities of the change of the move directions of cars, from up to right ($p_{ur}$) and from right to up ($p_{ru}$), on the dynamical jamming transition and velocities under the periodic boundary conditions in one hand and the phase diagram under the open boundary conditions in the other hand. However, in the former case, the first order jamming transition disappears when the cars alter their directions of move ($p_{ur}\neq 0$ and/or $p_{ru}\neq 0$). In the open boundary conditions, it is found that the first order line transition between jamming and moving phases is curved. Hence, by increasing the anisotropy, the moving phase region expand as well as the contraction of the jamming phase one. Moreover, in the isotropic case, and when each car changes its direction of move every time steps ($p_{ru}=p_{ur}=1$), the transition from the jamming phase (or moving phase) to the maximal current one is of first order. Furthermore, the density profile decays, in the maximal current phase, with an exponent $\gamma \approx {1/4}$.}Comment: 13 pages, 22 figure

Optimizing Traffic Lights in a Cellular Automaton Model for City Traffic

We study the impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nagel-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets. Starting from a simple synchronized strategy we show that the capacity of the network strongly depends on the cycle times of the traffic lights. Moreover we point out that the optimal time periods are determined by the geometric characteristics of the network, i.e., the distance between the intersections. In the case of synchronized traffic lights the derivation of the optimal cycle times in the network can be reduced to a simpler problem, the flow optimization of a single street with one traffic light operating as a bottleneck. In order to obtain an enhanced throughput in the model improved global strategies are tested, e.g., green wave and random switching strategies, which lead to surprising results.Comment: 13 pages, 10 figure

Dynamical Phase Transition in One Dimensional Traffic Flow Model with Blockage

Effects of a bottleneck in a linear trafficway is investigated using a simple cellular automaton model. Introducing a blockage site which transmit cars at some transmission probability into the rule-184 cellular automaton, we observe three different phases with increasing car concentration: Besides the free phase and the jam phase, which exist already in the pure rule-184 model, the mixed phase of these two appears at intermediate concentration with well-defined phase boundaries. This mixed phase, where cars pile up behind the blockage to form a jam region, is characterized by a constant flow. In the thermodynamic limit, we obtain the exact expressions for several characteristic quantities in terms of the car density and the transmission rate. These quantities depend strongly on the system size at the phase boundaries; We analyse these finite size effects based on the finite-size scaling.Comment: 14 pages, LaTeX 13 postscript figures available upon request,OUCMT-94-

Solvable Optimal Velocity Models and Asymptotic Trajectory

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine $T$ and $v_B$ (the backward velocity of the pattern), the global parameters associated with vehicles' collective motion in a congested flow, in terms of parameters such as the sensitivity $a$, which appeared in the original coupled equations.Comment: 25 pages, 15 eps figures, LaTe

Experiences with a simplified microsimulation for the Dallas/Fort Worth area

We describe a simple framework for micro simulation of city traffic. A medium sized excerpt of Dallas was used to examine different levels of simulation fidelity of a cellular automaton method for the traffic flow simulation and a simple intersection model. We point out problems arising with the granular structure of the underlying rules of motion.Comment: accepted by Int.J.Mod.Phys.C, 20 pages, 14 figure

Determination of Interaction Potentials in Freeway Traffic from Steady-State Statistics

Many-particle simulations of vehicle interactions have been quite successful in the qualitative reproduction of observed traffic patterns. However, the assumed interactions could not be measured, as human interactions are hard to quantify compared to interactions in physical and chemical systems. We show that progress can be made by generalizing a method from equilibrium statistical physics we learned from random matrix theory. It allows one to determine the interaction potential via distributions of the netto distances s of vehicles. Assuming power-law interactions, we find that driver behavior can be approximated by a forwardly directed 1/s potential in congested traffic, while interactions in free traffic are characterized by an exponent of approximately 4. This is relevant for traffic simulations and the assessment of telematic systems.Comment: For related work see http://www.helbing.or

A Cellular Automaton Model for Bi-Directionnal Traffic

We investigate a cellular automaton (CA) model of traffic on a bi-directional two-lane road. Our model is an extension of the one-lane CA model of {Nagel and Schreckenberg 1992}, modified to account for interactions mediated by passing, and for a distribution of vehicle speeds. We chose values for the various parameters to approximate the behavior of real traffic. The density-flow diagram for the bi-directional model is compared to that of a one-lane model, showing the interaction of the two lanes. Results were also compared to experimental data, showing close agreement. This model helps bridge the gap between simplified cellular automata models and the complexity of real-world traffic.Comment: 4 pages 6 figures. Accepted Phys Rev