Hong Kam Lo

NETWORK WITH DEGRADABLE LINKS: CAPACITY ANALYSIS AND DESIGN

Abstract This study developed an approach to model network performance when its link capacities are subject to stochastic degradations, as in the form of day-to-day traffic incidents, which cause travel time variability. We postulate that drivers would select routes to lower their travel time variabilities, just as they would to lower their mean travel times. Over time, commuters learn the routes’ travel time variabilities based on past experiences, factor such variabilities into their route choice considerations, and settle into a long-term equilibrium pattern. We characterize this route choice behavior in the face of uncertain travel times with the notion of probabilistic user equilibrium (PUE). This study then defined and formulated PUE with a reliability approach. We developed a nonlinear mathematical program to study the tradeoff between the maximum flow a network can carry and the extent of satisfying the PUE reliability constraints. As an analytical model, this formulation demonstrates certain interesting properties. The formulation can be used to analyze existing networks or to improve them by link capacity modifications. Numerical studies for a 19-link example are provided to show its performance and properties.

A cell-based variational inequality formulation of the dynamic user optimal assignment problem

This paper developed a cell-based dynamic traffic assignment formulation that follows the ideal dynamic user optimal (DUO) principle through a variational inequality approach. To improve the accuracy of dynamic traffic modeling, this formulation encapsulates a network version of the Cell Transmission Model (CTM). Moreover, this formulation satisfies the first-in-first-out (FIFO) conditions through the CTM. For solutions, we employed an alternating direction method developed for co-coercive variational inequality problems. We set up two scenarios to evaluate the properties of this formulation, in the areas of traffic dynamics and the ideal DUO principle. The results showed that the formulation was capable of capturing dynamic phenomena, such as shockwaves, queue formation and dissipation. Moreover, the results demonstrated that this cell-based formulation produced solutions that precisely followed the ideal DUO principle.

Dynamic network traffic control

This study developed a dynamic traffic control formulation designated as dynamic intersection signal control optimization (DISCO). Traffic in DISCO is modeled after the cell-transmission model (CTM), which is a convergent numerical approximation to the hydrodynamic model of traffic flow. It considers the entire fundamental diagram and captures traffic phenomena such as shockwaves and queue dynamics. As a dynamic approach, the formulation derives dynamic timing plans for time-variant traffic patterns. We solved DISCO based on a genetic algorithm (GA) approach and applied it to a traffic black spot in Hong Kong that is notorious for severe congestion. For performance comparisons, we also applied TRANSYT to the same scenarios. The Results showed that DISCO outperformed TRANSYT for all the scenarios tested especially in congested traffic. For the congested scenarios, DISCO could reduce delay by as much as 33% when compared with TRANSYT. Even for the uncongested scenarios, DISCOs delays could be smaller by as much as 23%.

Traffic equilibrium problem with route-specific costs: formulation and algorithms

Using a new gap function recently proposed by Facchinei and Soares [Facchinei, F., Soares, J., 1995. Testing a new class of algorithms for nonlinear complementarity problems. In: Giannessi, F., Maugeri, A. (Eds.), Variational Inequalities and Network Equilibrium Problems. Plenum Press, New York], we convert the nonlinear complementarity problem (NCP) formulation for the traffic equilibrium problem to an equivalent unconstrained optimization. This equivalent formulation uses both route flows and the minimum origin-destination travel costs as the decision variables. Two unique features of this formulation are that: (i) it can model the traffic assignment problem with a general route cost structure; (ii) it is smooth, unconstrained, and that every stationary point of the minimization corresponds to a global minimum. These properties permit a number of efficient algorithms for its solution. Two solution approaches are developed to solve the proposed formulation. Numerical results using a route-specific cost structure are provided and compared with the classic traffic equilibrium problem, which assumes an additive route cost function.

Dynamic traffic assignment: properties and extensions

Dynamic Traffic Assignment (DTA) is long recognized as a key component for network planning and transport policy evaluations as well as for real-time traffic operation and management. How traffic is encapsulated in a DTA model has important implications on the accuracy and fidelity of the model results. This study compares and contrasts the properties of DTA modelled with point queues versus those with physical queues, and discusses their implications. One important finding is that with the more accurate physical queue paradigm, under certain congested conditions, solutions for the commonly adopted dynamic user optimal (DUO) route choice principle just do not exist. To provide some initial thinking to accommodate this finding, this study introduces the tolerance-based DUO principle. This paper also discusses its solution existence and uniqueness, develops a solution heuristic, and demonstrates its properties through numerical examples. Finally, we conclude by presenting some prospective future research directions.

Modeling transfer and non-linear fare structure in multi-modal network

In metropolitan areas where multi-modal trips are common, modeling transfers is an important issue. The existing approach of connecting multi-modal networks, without attending to the number or kinds of transfers, cannot fully describe actual behavior. In addition, the common practice of non-linear transit fare structures imposes certain modeling difficulties on the assignment approach. In this study, we develop a formulation to overcome these two difficulties, namely the number and kinds of transfers are explicitly considered and non-linear fare structures accommodated. Through a state augmentation technique, we transform a multi-modal network to one we call state-augmented multi-modal (SAM) network. Once formulated, the SAM network behaves like a simple network and can be combined with traffic assignment or network analysis procedures. A numerical example is provided to illustrate this approach.

Solving non-additive traffic assignment problems: A descent method for co-coercive variational inequalities

Abstract This paper developed a descent direction of the merit function for co-coercive variational inequality (VI) problems. The descent approach is closely related to Fukushimas method for strongly monotone VI problems and Hes method for linear VI problems, and can be viewed as an extension for the more general case of co-coercive VI problems. This extension is important for route-based traffic assignment problems as the associated VI is often neither strongly monotone nor linear. This study then implemented the solution method for traffic assignment problems with non-additive route costs. Similar to projection-based methods, the computational effort required per iteration of this solution approach is modest. This is especially so for traffic equilibrium problems with elastic demand, where the solution method consists of a function evaluation and a simple projection onto the non-negative orthant.

A methodology for sustainable traveler information services

The provision of traveler information services in the form of route planning and guidance (RPG) often involves three parties: service providers, users, and the traffic management agency. Each of these parties has distinctive objectives that are often in conflict with each other. This study developed a mixed-equilibrium model to consider the implementation of RPG services. We modeled the market penetration of RPG services in an elastic manner and developed a methodology to study the tradeoff among these conflicting objectives. The goal is to seek solutions that can sustain. This model can also be used to investigate the sensitivity of government policies on these services. Numerical results of a small network are provided to illustrate the behavior of this model.

A MACROSCOPIC TAXI MODEL FOR PASSENGER DEMAND, TAXI UTILIZATION AND LEVEL OF SERVICES

In most urban areas taxi services are subject to various types of regulation such as entry restriction and price control. However, effective intervention depends on generating and using suitable information on the demand-supply equilibrium of the taxi market. This paper develops a simultaneous equation system of passenger demand, taxi utilization and level of services based on a taxi service situation found in the urban area of Hong Kong over the last ten years. A set of variables is introduced including number of licensed taxis, taxi fare, disposable income, occupied taxi journey time as exogenous variables and daily taxi passenger demand, passenger waiting time, taxi availability, taxi utilization and average taxi waiting time as endogenous variables. These variables are coupled together through a system of nonlinear simultaneous equations whose parameters are estimated from survey data. The simultaneous equation system can be used to obtain useful regulatory information to assist with the decisions concerning the restriction over the number of taxi licenses and the fixing of the taxi fare structure as well as a range of service quality control.

A cell-based dynamic traffic assignment model: Formulation and properties

This paper developed a cell-based dynamic traffic assignment (DTA) formulation that follows the ideal dynamic user optimal (DUO) principle. Through defining an appropriate gap function, we transformed a formulation based on the nonlinear complementarity problem to an equivalent mathematical program. To improve the accuracy of dynamic traffic modelling, this formulation encapsulates a network version of the cell transmission model (CTM). We set up four scenarios to evaluate the properties of this formulation, in the aspects of traffic dynamics, traffic interactions across multiple links, and the ideal DUO principle. This formulation produced outputs that are in agreement with what the results ought to be. Namely, the formulation is able to capture dynamic traffic phenomena, such as shock-waves, queue formation, and dissipation. Moreover, it is capable of capturing dynamic traffic interactions across multiple links. Both of these characteristics are inherent from the underlying traffic model adopted in this formulation. The results also demonstrate that this cell-based formulation follows the ideal DUO principle.