In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

Modeling crowd evacuation of a building based on seven methodological approaches

The route choice of pedestrians during evacuation under conditions of both good and zero visibility is investigated using a group of experiments conducted in a classroom, and a microscopic pedestrian model with discrete space representation. Observation of the video recordings made during the experiments reveals several typical forms of behavior related to preference for destination, effect of capacity, interaction between pedestrians, following behavior and evacuation efficiency. Based on these forms of behavior, a microscopic pedestrian model with discrete space representation is developed. In the model, two algorithms are proposed to describe the movement of pedestrians to a destination under conditions of both good and zero visibility, respectively. Through numerical simulations, the ability of the model to reproduce the behavior observed in the experiments is verified. The study is helpful for devising evacuation schemes and in the design of internal layouts and exit arrangements in buildings that are similar to the classroom.

Route choice in pedestrian evacuation under conditions of good and zero visibility: Experimental and simulation results

Limited pedestrian behavior models shed light on the case at signalized crosswalk, where pedestrian behavior is characterized by group or individual evasion with surrounding pedestrians, collision avoidance with conflicting vehicles, and response to signal control and crosswalk boundary. This study fills this gap by developing a microscopic simulation model for pedestrian behavior analysis at signalized intersection. The social force theory has been employed and adjusted for this purpose. The parameters, including measurable and non-measurable ones, are either directly estimated based on observed dataset or indirectly derived by maximum likelihood estimation. Last, the model performance was confirmed in light of individual trajectory comparison between estimation and observation, passing position distribution at several cross-sections, collision avoidance behavior with conflicting vehicles, and lane-formation phenomenon. The simulation results also concluded that the model enables to visually represent pedestrian crossing behavior as in the real world.

Application of social force model to pedestrian behavior analysis at signalized crosswalk

This article provides an in-depth review of the state-of-the-art and describes methodological advances in the design and evaluation of road network pricing schemes. A number of paradigm shifts from the two polar cases of the marginal social cost pricing of road traffic congestion and revenue-maximizing road toll pricing are analyzed, as induced by the need to address realistic design complexities and constraints. The crucial role of the joint consideration of pricing strategies with optimal capacity provision and several network management measures is manifested and an integrated evaluation framework is suggested to incorporate a wide range of road pricing impacts into the scheme design process.

Design and evaluation of road pricing: state-of-the-art and methodological advances

A modified floor field model is proposed to simulate pedestrian evacuation in rooms with internal obstacles and multiple exits. The modifications lie in developing a method to calculate the static floor field for every lattice site, which is determined by the most feasible distance to an exit, and employing a logit-based discrete choice principle to govern the exit selection. Simulation results show that the evacuation time is sensitive to the exit position and some model parameters. For pedestrians unfamiliar with the exit location, additional doors may not be necessary and can cause a negative effect on evacuation time. It is also found that unfamiliarity with the room's inner configuration and blindly following others will lead to an increase of the evacuation time.

Static floor field and exit choice for pedestrian evacuation in rooms with internal obstacles and multiple exits.

We present a mobile lattice gas model for simulating the pedestrian evacuation process in a public building, through combining the advantages of the lattice gas model and the social force model. In our model, the interaction force between every two pedestrians and that between a pedestrian and the building wall are determined by the distance and the pedestrian’s moving step size. Simulation results show that the proposed model can capture the basic characteristics of pedestrian evacuation and generate the average evacuation times reasonably when an emergency incident occurs in the building.

A mobile lattice gas model for simulating pedestrian evacuation

Considering the fact that the interaction among pedestrians in a high-density crowd is asymmetric, accumulative and transferable, we present a modified floor field cellular automata model for simulating the pedestrian evacuation. In this model, the space for evacuation is discretized into smaller cells, every pedestrian is allowed to occupy multiple cells and the interaction among pedestrians is characterized by their own inertia and the forces received or to be imposed on others. By numerical simulation the effects of the pedestrian movement manner and the model parameters on evacuation efficiency are investigated. The results obtained by our modified model are compared with those by the original floor field model.

http://iopscience.iop.org/article/10.1088/1751-8113/41/38/385104/pdf

A modified floor field cellular automata model for pedestrian evacuation simulation

We develop a microscopic pedestrian-simulation model in which pedestrian positions are updated at discrete time steps. At each time step, each pedestrian probabilistically selects a direction of movement from a predetermined set according to a logit-type function that considers the dynamics of other pedestrians around, and then selects a step size that satisfies a certain distribution. We perform a number of field experiments on real intersecting pedestrian flows with four different angles. We then validate and calibrate the model using sample data on the deviation angles, step velocities, and velocity–density relations obtained from the experiments.

Ren-Yong Guo

Papers

Static floor field and exit choice for pedestrian evacuation in rooms with internal obstacles and multiple exits.

A mobile lattice gas model for simulating pedestrian evacuation

A modified floor field cellular automata model for pedestrian evacuation simulation

A microscopic pedestrian-simulation model and its application to intersecting flows

Child behavior during evacuation under non-emergency situations: Experimental and simulation results