Resonance, criticality, and emergence in city traffic investigated in cellular automaton models

Pedestrian flow in two dimensions: Optimal psychological stress leads to less evacuation time and decongestion

Collective motion is an innate ability of all living systems, which depends on physiological and psychosocial factors in the case of humans. Such a collective organization is becoming of great interest in collective motion in human crowds. Using a cellular automaton (CA) simulation model, we demonstrate that emergency egress from a two-dimensional corridor with optimal stress leads to less evacuation time and efficient mass evacuations. We study how three types of stress (i.e., mild stress, optimal stress, and anxiety) described in the literature have a significant impact on the collective dynamics. We found that low-stress levels could decrease the evacuation time in an entire occupied room since agents choose alternative routes rather than the shortest path to the exit and display cooperative behavior. Therefore, the combination of mild and optimal stress can lead to efficient evacuations. Also CA simulations may be used to find safer and more efficient ways to conduct mass evacuation procedures.

Simulations suggest that navigation software may not be as efficient as expected for city traffic

We suggest a theoretical framework to study the dynamics of an open city, with cars entering at a certain rate and leaving as they reach their destinations. In particular, we assess through simulations some unexpected consequences of the massive use of GPS (global positioning system) navigation systems in the overall dynamics. One of our main interest is to identify what type of measurements would be the most relevant for an experimental study of this system, specifically, the ones useful for city traffic administrators. To do so, we solve the microdynamics using a cellular automaton model considering three different navigation strategies based on the minimization of the individual paths (unweighted strategy) or travel times (weighted strategies). Although the system is inherently stochastic, we found in our simulations an equivalent saddle-node bifurcation for all strategies where the input rate acts as a bifurcation parameter. There is also evidence of additional bifurcations for travel time minimization based strategies. Although we found that weighted strategies are more efficient in terms of car motion, there is a destabilization phenomenon that makes, in an unexpected way, a variation of the unweighted strategy more optimal at certain densities from the fuel efficiency of the overall city traffic point of view. These results bring new insight into the intrinsic dynamics of cities and the perturbations that individual traffic routing can produce on the city as a whole.

Modeling interacting city traffic with finite acceleration and braking capacities

Understanding the fundamental interactions in the complex behavior of one car moving in a sequence of traffic lights necessarily implies the inclusion of finite braking and accelerating capabilities. This characteristic is usually not considered in the standard cellular automaton models, where car interactions are the main concern. Therefore, here we develop a model which includes interactions and finite braking and accelerating capabilities, filling the gap between a standard cellular automaton model that considers car interactions but infinite braking and accelerating capabilities and the continuous one car model that includes finite braking and accelerating capabilities but does not consider, as the name indicates, car interactions. The proposed new model bridge these two seemingly different approaches in an effort to investigate how the traffic jams are produced. We found that, in the appropriate limits, we can reproduce the complex behavior of the one car continuous model and the dynamics close to the resonance induced by the interacting cars, forced by the traffic lights. In the processes of introducing car interactions, we observe how the average velocity decreases to finally obtain traffic jams, which are an emergent state in which the traffic lights control the generation of pulses of cars but do not control its average speed. This model is expected to improve our understanding of the complexity that appears in city traffic situations, as the finite braking and accelerating capabilities are necessary to describe the vehicle dynamics, the control strategy of traffic light synchronization, the motion of buses in segregated lights, and the whole urban design.

The Stochastic Transport Dynamics of a Conserved Quantity on a Complex Network

The stochastic dynamics of conserved quantities is an emergent phenomena observed in many complex systems, ranging from social and to biological networks. Using an extension of the Ehrenfest urn model on a complex network, over which a conserved quantity is transported in a random fashion, we study the dynamics of many elementary packets transported through the network by means of a master equation approach and compare with the mean field approximation and stochastic simulations. By use of the mean field theory, it is possible to compute an approximation to the ensemble average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the master equation. However, the master equation gives a more complete description of the stochastic system and provides a probabilistic view of the occupation number at each node. Of particular relevance is the standard deviation of the occupation number at each node, which is not uniform for a complex network. We analyze and compare different network topologies (small world, scale free, Erdos-Renyi, among others). Given the computational complexity of directly evaluating the asymptotic, or equilibrium, occupation number probability distribution, we propose a scaling relation with the number of packets in the network, that allows to construct the asymptotic probability distributions from the network with one packet. The approximation, which relies on the same matrix found in the mean field approach, becomes increasingly more accurate for a large number of packets.

Signal optimization in urban transport: A totally asymmetric simple exclusion process with traffic lights

We consider the exclusion process on a ring with time-dependent defective bonds at which the hopping rate periodically switches between zero and one. This system models main roads in city traffics, intersecting with perpendicular streets. We explore basic properties of the system, in particular dependence of the vehicular flow on the parameters of signalization as well as the system size and the car density. We investigate various types of the spatial distribution of the vehicular density, and show existence of a shock profile. We also measure waiting time behind traffic lights, and examine its relationship with the traffic flow.

Phase transitions and optimal transport in stochastic roundabout traffic

We study traffic in a roundabout model, where the dynamics along the interior lane of the roundabout are described by the totally asymmetric simple exclusion process (TASEP). Vehicles can enter the interior lane or exit from it via S intersecting streets with given rates, and locally modified dynamics at the junctions take into account that collisions of entering vehicles with vehicles approaching the entrance point from the interior lane should be avoided. A route matrix specifies the probabilities for vehicles to arrive from and to exit to certain intersecting streets. By subdividing the interior lane into segments between consecutive intersecting streets with effective entrance and exit rates, a classification of the stationary roundabout traffic in terms of TASEP multiphases is given, where each segment can be in either the low-density, high-density, or maximum current TASEP phase. A general methodology is developed, which allows one to calculate the multiphases and optimal throughput conditions based on a mean-field treatment. Explicit analytical results from this treatment are derived for equivalent interesting streets. The results are shown to be in good agreement with kinetic Monte Carlo simulations.

Generalization of the Ehrenfest urn model to a complex network

The Ehrenfest urn model is extended to a complex directed network, over which a conserved quantity is transported in a random fashion. The evolution of the conserved number of packets in each urn, or node of the network, is illustrated by means of a stochastic simulation. Using mean-field theory we were able to compute an approximation to the ensemble-average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the stochastic simulation. Using this analytic approximation we are able to find the asymptotic dynamical state of the system and the time scale to approach the equilibrium state, for different networks. The study is extended to large scale-free and small-world networks, in which the relevance of the connectivity distribution and the topology of the network for the distribution of time scales of the system is apparent. This analysis may contribute to the understanding of the transport properties in real networks subject to a perturbation, e.g., the asymptotic state and the time scale required to approach it.

Regular transport dynamics produce chaotic travel times

In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

Totally asymmetric simple exclusion process with a time-dependent boundary: interaction between vehicles and pedestrians at intersections

Interaction between vehicles and pedestrians is seen in many areas such as crosswalks and intersections. In this paper, we study a totally asymmetric simple exclusion process with a bottleneck at a boundary caused by an interaction. Due to the time-dependent effect originating from the speed of pedestrians, the flow of the model varies even if the average hopping probability at the last site is the same. We analyze the phenomenon by using two types of approximations: extended two-cluster approximation and isolated rarefaction wave approximation. The approximate results capture intriguing features of the model. Moreover, we discuss the situation where vehicles turn right at the intersection by adding a traffic light at the boundary condition. The result suggests that pedestrian scrambles are valid to eliminate traffic congestion in the right-turn lane.