William H. K. Lam

Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues

Abstract This paper considers a simultaneous route and departure (SRD) time choice equilibrium assignment problem in network with queues. The problem is modeled on discrete-time basis and formulated as an equivalent “zero-extreme value” minimization problem, in which the first-in-first-out (FIFO) behavior at intersection is guaranteed by proper formulation of the dynamic link travel times. A heuristic solution algorithm is proposed, which simulates a normal day-to-day dynamic system by a route/time-swapping process, thereby reaching to an extreme point of the minimization problem. The existence of discrete-time dynamic user-equilibrium (UE) solutions is investigated. The iteration-to-iteration stability of the proposed algorithm is discussed, together with numerical results on two example networks.

A STOCHASTIC USER EQUILIBRIUM ASSIGNMENT MODEL FOR CONGESTED TRANSIT NETWORKS

This paper proposes a stochastic user equilibrium assignment model for congested transit networks, together with a solution algorithm. A mathematical programming problem is formulated, that is equivalent to the stochastic user equilibrium assignment model for congested transit system. When the transit link capacity constraints are reached, it is proven that the Lagrange multipliers of the mathematical programming problem are equivalent to the equilibrium passenger overload delays in the congested transit network. The proposed model can simultaneously predict how passengers will choose their optimal routes and estimate the total passenger travel cost in a congested transit network. Numerical examples are used to illustrate the applications of the proposed model.

ESTIMATION OF AN ORIGIN-DESTINATION MATRIX WITH RANDOM LINK CHOICE PROPORTIONS: A STATISTICAL APPROACH

The use of statistical modeling in the estimation of Origin-Destination (OD) matrix from traffic counts is reviewed. In particular, statistical models that consider explicitly the presence of measurement and sampling errors in the observed link flows are discussed. This paper proposes treating the link choice proportions as random variables. Accordingly, new statistical models are formulated and the corresponding Maximum Likelihood Estimator and Bayesian Estimator of the OD matrix are developed. The accuracies of these estimators are compared with those obtained by previous methods.

An activity-based time-dependent traffic assignment model

This paper presents a conceptual activity-based and time-dependent traffic assignment model. The temporal utility profiles of activities are employed to formulate the temporal activity choice behavior of individuals as a multinomial logit model. Route choice behavior is then described as the ideal dynamic user equilibrium condition. The combined activity/route choice condition is formulated as a time-dependent variational inequality problem, which is solved by a heuristic solution algorithm based on the space-time expanded networks.

A CAPACITY RESTRAINT TRANSIT ASSIGNMENT WITH ELASTIC LINE FREQUENCY

Abstract This paper proposes a new formulation for the capacity restraint transit assignment problem with elastic line frequency, in which the line frequency is related to the passenger flows on transit lines. A stochastic user equilibrium transit assignment model with congestion and elastic line frequency is proposed and the equivalent mathematical programming problem is also formulated. Since the passenger waiting time and the line capacity are dependent on the line frequency, a fixed point problem with respect to the line frequency is devised accordingly. The existence of the fixed point problem has been proved. A solution algorithm for the proposed model is presented. Finally, a numerical example is used to illustrate the application of the proposed model and solution algorithm.

A study of the bi-directional pedestrian flow characteristics at Hong Kong signalized crosswalk facilities

This paper investigates the bi-directional flow characteristics at signalized crosswalk facilities in Hong Kong. Pedestrian flow measurements were conducted at selected signalized crosswalks in Hong Kong urban area with and without the Light Rail Transit (LRT) railway tracks in the median of the carriageway. The pedestrian speed-flow functions for these crosswalk facilities were calibrated. The relationships between the walking speed at capacity and directional distribution of pedestrian flow (or flow ratio) are determined. The effects of different flow ratio on the effective capacity are also investigated. The bi-directional pedestrian flow effects on signalized crosswalk facilities with LRT tracks are found more significant than those without LRT tracks. The result could be used as a basis to improve the assessment of the crosswalks capacity and to determine the design walking speeds under different flow ratios at signalized crosswalks in Hong Kong and in other Asian cities with similar environments.

A STUDY OF CROWDING EFFECTS AT THE HONG KONG LIGHT RAIL TRANSIT STATIONS

This paper investigates the important attributes relating to the crowding effects at the Light Rail Transit (LRT) stations in Hong Kong. With the data collected at two selected LRT stations for studying different crowding effects, the relationships between the dwelling time of trains and the crowding situations at LRT stations are firstly determined, and regression models are established for the dwelling delays of train. In this paper, the degrees of congestion on LRT platforms are also examined. The Level of Service (LOS) concept is applied to study the degrees of congestion on LRT platforms. Finally, the responses of the passengers due to the discomfort at crowded vehicles and congested platforms are investigated, in which stated preference surveys are conducted to study the effects of passenger discomfort at crowded vehicles and congested platforms. The results of this paper could be used as a basis for the platform design and planning of the LRT stations in Hong Kong.

Bidirectional Pedestrian Stream Model with Oblique Intersecting Angle

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 Drakes 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. DOI: 10.1061/ASCETE.1943-5436.0000086 CE Database subject headings: Pedestrians; Two-dimensional flow; Traffic flow; Measurement; Experimentation. Author keywords: Pedestrians; Two-dimensional flow; Measurement; Experimentation.

A generalised function for modeling bi-directional flow effects on indoor walkways in Hong Kong

This paper examines the relationships between walking speed and pedestrian flow under various bi-directional flow conditions at indoor walkways in Hong Kong. The effects of bi-directional pedestrian flows are investigated empirically with particular emphasis on their effects on walking time for different directions of flow at pedestrian walkways in Hong Kong. Flow measurements were conducted at selected indoor walkways in urban areas. A generalized walking time function that takes bi-directional flow distributions (or flow ratios) into account is proposed for these pedestrian facilities and calibrated for various flow conditions ranging from free-flow to congested-flow (at-capacity) situations. The bi-directional flow effects on free-flow walking speed, effective capacity and at-capacity walking speed are validated with observed data. It was found that the bi-directional flow ratios have significant impacts on both the at-capacity walking speeds and the maximum flow rates of the selected walkways but not on the free-flow walking speeds. The findings and study methodology provide better insight into the effects of bi-directional pedestrian flow characteristics and will assist engineers/planners in improving the design and operation of pedestrian facilities not only in Hong Kong, but also in other countries as well.

Dynamic User Optimal Traffic Assignment Model for Many to One Travel Demand

A freeway or expressway corridor where all vehicles travel to the same destination such as the city centre is considered in this article, similar to the morning commute problem. A continuous time optimal control model that deals with the dynamic user optimal assignment for multiple origins and single destination is proposed. The splitting rates of traffic flows at each network node are defined as the control variables in this model. The optimality conditions are proved to be equivalent to the dynamic user optimal principle or user equilibrium of instantaneous travel cost. In order not to solve the complicated two-point boundary-value problem with substantial computational times for obtaining the optimal control solution, a steady state-costate solution algorithm is developed that generates an approximate solution to the network optimal control problem. This algorithm exploits advantage of the embedded network structure of the problem and would be computationally efficient. A numerical example with two peak period traffic demands which was drawn from the road network problem between Hong Kong and several adjacent cities of inland China is used to demonstrate the performance of the proposed algorithm.