Analytical investigation of oscillations in intersecting flows of pedestrian and vehicle traffic

Gap acceptance probability model for pedestrians at unsignalized mid-block crosswalks based on logistic regression

Gap acceptance represents a pedestrian's assessment of how safe it may be to use an available gap in traffic flow at a particular point in time. Though walking is a major component of urban mobility, the high rate of fatal interaction with motor vehicle traffic raises safety issues around how pedestrians decide to accept the available gap. This paper explored these interactions by modeling gap acceptance behavior at the midblock crosswalks. Unlike other pedestrian gap acceptance studies that focus on individual psychological and sociological factors that are difficult to control or manage, this study focused on six environmental factors that we considered important and as having the potential to affect the pedestrians' gap acceptance decision at the crosswalks, i.e. gap size, crossing distance, number of waiting pedestrians, waiting time, vehicle traffic volume and position of pedestrian (whether on street kerb or median). Video data was collected on pedestrian gap acceptance from 13 midblock crosswalk locations in Shanghai, China. A Logit model with 96% accuracy was developed to describe and predict the pedestrian gap acceptance behaviors. The results show that gap size and crossing distance have the highest effect on the pedestrian gap acceptance decision. Pedestrians waiting at the kerbside could confidently accept gaps (with a 95% probability) when the gap is longer than 2.2s, 5.9s, and 9.6s under the condition that the crossing distance is 4 m (one lane), 7.5 m (two lanes), and 11 m (three lanes), respectively while pedestrians waiting at the median could confidently accept gaps when the gap is longer than 1.6s, 5.3s, and 8.5s respectively under the same conditions. The recommendations on improving the crossing safety are proposed accordingly.

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.

Game theory in models of pedestrian room evacuation

We analyze the pedestrian evacuation of a rectangular room with a single door considering a lattice gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational choices and is affected by conflicts between two or more agents that want to advance to the same position. Such conflicts are solved according to certain rules closely related to the concept of strategies in game theory, cooperation and defection. We consider game rules analogous to those from the Prisoner's Dilemma and Stag Hunt games, with payoffs associated to the probabilities of the individuals to advance to the selected site. We find that, even when defecting is the rational choice for any agent, under certain conditions, cooperators can take advantage from mutual cooperation and leave the room more rapidly than defectors.

Coarse-grained particle model for pedestrian flow using diffusion maps

Interacting particle systems constitute the dynamic model of choice in a variety of application areas. A prominent example is pedestrian dynamics, where good design of escape routes for large buildings and public areas can improve evacuation in emergency situations, avoiding exit blocking and the ensuing panic. Here we employ diffusion maps to study the coarse-grained dynamics of two pedestrian crowds trying to pass through a door from opposite sides. These macroscopic variables and the associated smooth embeddings lead to a better description and a clearer understanding of the nature of the transition to oscillatory dynamics. We also compare the results to those obtained through intuitively chosen macroscopic variables.

Evacuation of pedestrians from a single room by using snowdrift game theories

Game theory is introduced to simulate the complicated interaction relations among the conflicting pedestrians in a pedestrian flow system, which is defined on a square lattice with the parallel update rule. Modified on the traditional lattice gas model, each pedestrian can move to not only an empty site, but also an occupied site. It is found that each individual chooses its neighbor randomly and occupies the site with the probability W(x→y)=1/1+exp[-(P(x)-U(x))/κ], where P(x) is the x's payoff representing his personal energy, and U(x) is the average payoff of its neighborhood indicating the potential well energy if he stays. Two types of pedestrians are considered, and they interact with their neighbors following the payoff matrix of snowdrift game theory. The cost-to-benefit ratio r=c/(2b-c) (where b is the perfect payoff and c is the labor cost) represents the fear index of the pedestrians in this model. It is found that there exists a moderate value of r leading to the shortest escape time, and the situation for large values of r is better than that for small ones in general. In addition, the pedestrian flow system always arrives at a consistent state in which the two types of walkers have the same number and evolve by the same law irrespectively of the parameters, which can be interpreted as the self-organization effect of pedestrian flow. It is also proven that the time point of the onset of the steady state is unrelated to the scale of the pedestrians and the square lattice. Meanwhile, the system exhibits different dynamics before reaching the consistent state: the number of the two types of walkers oscillates when P(C)>0.5 (i.e., probability to change the present strategy), while no oscillation happens for P(C)≤0.5. Finally, it is shown that a smaller density of pedestrians ρ induces a shorter average escape time.

Theoretical investigation of synchronous totally asymmetric exclusion processes on lattices with multiple-input-single-output junctions

In this paper, we investigate the dynamics of synchronous totally asymmetric exclusion processes on lattices with a multiple-input-single-output (MISO) junction, which consists of m subchains for the input and one main chain for the output. A MISO junction is a type of complex geometry that is relevant to many biological processes as well as vehicular and pedestrian traffic flow. A mean-field approach is developed to deal with the junction that connects the subchains and the main chain. Theoretical results for stationary particle currents, density profiles, and a phase diagram have been obtained. It is found that the phase boundary moves toward the left in the phase diagram with an increase of the number of subchains. The nonequilibrium stationary states, stationary-state phases, and phase boundaries are determined by the boundary conditions of the system as well as by the number of subchains. The density profiles obtained from computer simulations show very good agreement with our theoretical analysis.

Dynamics of crowd disasters: an empirical study

Many observations of the dynamics of pedestrian crowds, including various self-organization phenomena, have been successfully described by simple many-particle models. For ethical reasons, however, there is a serious lack of experimental data regarding crowd panic. Therefore, we have analyzed video recordings of the crowd disaster in Mina/Makkah during the Hajj in 1426H on 12 January 2006. They reveal two subsequent, sudden transitions from laminar to stop-and-go and "turbulent" flows, which question many previous simulation models. While the transition from laminar to stop-and-go flows supports a recent model of bottleneck flows [D. Helbing, Phys. Rev. Lett. 97, 168001 (2006)], the subsequent transition to turbulent flow is not yet well understood. It is responsible for sudden eruptions of pressure release comparable to earthquakes, which cause sudden displacements and the falling and trampling of people. The insights of this study into the reasons for critical crowd conditions are important for the organization of safer mass events. In particular, they allow one to understand where and when crowd accidents tend to occur. They have also led to organizational changes, which have ensured a safe Hajj in 1427H.

Analytical approach to continuous and intermittent bottleneck flows

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.