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This paper establishes a mathematical model that can represent the conflicting effects of two pedestrian streams that have an oblique intersecting angle in a large crowd. In a previous paper, a controlled experiment in which two streams of pedestrians were asked to walk in designated directions was used to model the bidirectional pedestrian stream of certain intersecting angles. In this paper, the writers revisit that problem and apply the Bayesian inference method to calibrate an improved model with the controlled experiment data. Pedestrian movement data are also collected from a busy crosswalk by using a video observation approach. The two sets of data are used separately to calibrate the proposed model. With the calibrated model, the relationship between speed, density, and flow is studied in both the reference and conflicting streams, and a prediction is made regarding how these factors affected the interactions of moving pedestrian streams. It is found that the speed of one stream not only decreases with its total density, but also decreases with the ratio of its flow relative to the total flow, i.e., the speed of the pedestrians decreases if their stream changes from the major to minor stream. It is also observed that the maximum disruption that was induced by pedestrian flow from an intersecting angle occurs when the angle is approximately 135°. [ABSTRACT FROM AUTHOR]

This paper proposes a new model for investigating the allocation of new lines in a competitive transit network in which transit operations are subject to demand uncertainty and scale economies. Scale economies imply that the operating cost of each operator per unit of transit line decreases with the number of lines operated. The proposed model explicitly considers the interactions among three types of players: transit authority, transit operators, and transit passengers. The transit authority aims to maximize the total social welfare for a given confidence level (or probabilistic guarantee) by optimizing the allocation of new lines to bidding operators. For a given allocation scheme, each of the operators determines the associated frequencies and fares to maximize its own profit at a certain confidence level while accounting for the responses of transit passengers to their strategies. The proposed line allocation model is formulated as a robust 0-1 integer programming problem that can be solved by an implicit enumeration algorithm. A numerical example is presented to illustrate the effects on the transit system of the allocation of new lines, the scale economies, the level of variation in passenger demand, and the risk attitude of transit operators toward uncertainty. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Gridlock is defined when traffic comes to a complete halt inducing huge delays. If a work zone on a two-lane two-way highway is set up, in which one of the traffic lanes is closed for maintenance road works, the remaining lane has to be controlled to serve the two-way traffic alternatively. The study objective is to optimize the traffic signal controls across two closely spaced work zones to prevent a gridlock, which can occur easily if upstream and downstream signals are not well coordinated. When vehicle queues build up in the middle sections between two work zones and further expand to occupy the single available lanes in both directions, the two-way traffic is then blocked and no vehicle can leave from the queues generating a gridlock. To address this problem, spatial queues are important parameters that must be explicitly analyzed. The cell transmission model, which is known to be a robust mathematical tool for the modeling of queue dynamics, is adopted in this study. A signal cell is used to represent each traffic signal control, the exit flow capacity of which is defined in accordance with the signal plan. A set of linear constraints is established to relate all of the model parameters and variables. The objective function is taken as the total number of vehicles in the critical section between the two work zones. The minimization of this objective function can effectively obviate the occurrence of a gridlock. The optimization problem is formulated as a Binary-Mixed-Integer-Linear-Program that can be solved by the standard branch-and-bound technique. Numerical examples are given to demonstrate the effectiveness of the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we develop a model of bidirectional pedestrian streams with an oblique intersecting angle that represents the crossing interaction of pedestrians moving in different directions on a walking facility. We formulate the model based on Drake’s model in the traffic flow literature, and calibrate it using results from a set of controlled experiments in which two groups of pedestrians were asked to walk in different directions and cross on designated walkways with different levels of pedestrian flow and different intersecting angles. Their movements were video recorded, and macroscopic quantities such as speed, density, and flow were extracted to calibrate the model of bidirectional pedestrian streams. All of the parameters of the calibrated model are statistically significant at the 0.1% level. [ABSTRACT FROM AUTHOR]

We propose a macroscopic model of lane-changing that is consistent with car-following behavior on a two-lane highway. Using linear stability theory, we find that lane-changing affects the stable region and the propagation speeds of the first-order and second-order waves. In analyzing a small disturbance, our model effectively reproduces certain non-equilibrium traffic-flow phenomena-small disturbance instability, stop-and-go waves, and local clusters that are affected by lane-changing. The model also gives the flow-density relationships in terms of the actual flow rate, the lane-changing rate, and the difference between the potential flow rate (the flow rate that would have occurred without lane-changing) and the actual flow rate. The relationships between the actual flow rate and traffic density and between the lane-changing rate and traffic density follow a reverse-lambda shape, which is largely consistent with observed traffic phenomena. [ABSTRACT FROM AUTHOR]

This paper deals with the effects of traffic bottlenecks using an extended Lighthill-Whitham-Richards (LWR) model. The solution structure is analytically indicated by the study of the Riemann problem characterized by a discontinuous flux. This leads to a typical solution describing a queue upstream of the bottleneck and its width and height, and informs the design of a δ-mapping algorithm. More significantly, it is found that the kinetic model is able to reproduce stop-and-go waves for a triangular fundamental diagram. Some simulation examples, which are in agreement with the analytical solutions, are given to support these conclusions. [ABSTRACT FROM AUTHOR]

Consider a general, heterogeneous geographical space with a set of competitive facilities, where the customers' demand locations from each of the facilities are continuously dispersed over the area. The total demand generated from a particular location in the space is fixed, but the demands from this location to the set of competitive facilities are subject to a distribution function with respect to the relative transportation costs to these facilities. Furthermore, we take into account congested transportation cost in characterizing customer choices. Congestion effect is explicitly built into our model by using a flow-dependent and location-dependent transportation cost function. The routing behavior of customers over the space and the user equilibrium choices of facilities are modeled by constructing a spatial user equilibrium flow pattern. The problem is formulated as a combined distribution and assignment model. An iterative algorithm between the distribution function for the choice of facilities and a mixed finite element method for route choices is proposed to solve the resulting continuous facility location problem. A numerical example is given to demonstrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

We consider a heterogeneous two-dimensional space where a given set of competitive facilities is located. Customers are assumed to be scattered continuously over the space, and each customer is assumed to choose a facility to minimize individual total cost of receiving service. The total cost consists of both the congested travel time to the facility and a cost associated with the congestion externality at the facility. Furthermore, customer demand at any location is assumed to be a function of the total cost of receiving service. Given these assumptions, it is of interest to estimate the market areas and market shares captured by each competitive facility. This problem is formulated here as a calculus of variations problem, and its optimality conditions are shown to be equivalent to the spatial customer choice equilibrium conditions with elastic demand and market externality. The model is solved by an efficient finite element method and illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

This paper proposes a cellular automata model of pedestrian flow that defines a cost potential field, which takes into account the costs of travel time and discomfort, for a pedestrian to move to an empty neighboring cell. The formulation is based on a reconstruction of the density distribution and the underlying physics, including the rule for resolving conflicts, which is comparable to that in the floor field cellular automaton model. However, we assume that each pedestrian is familiar with the surroundings, thereby minimizing his or her instantaneous cost. This, in turn, helps reduce the randomness in selecting a target cell, which improves the existing cellular automata modelings, together with the computational efficiency. In the presence of two pedestrian groups, which are distinguished by their destinations, the cost distribution for each group is magnified due to the strong interaction between the two groups. As a typical phenomenon, the formation of lanes in the counter flow is reproduced. [ABSTRACT FROM AUTHOR]