Link Travel Time Estimation in Double-Queue-Based Traffic Models

Double queue concept has gained its popularity in dynamic user equilibrium (DUE) modeling because it can properly model real traffic dynamics. While directly solving such double-queue-based DUE problems is extremely challenging, an approximation scheme called first-order approximation was proposed to simplify the link travel time estimation of DUE problems in a recent study without evaluating its properties and performance. This paper focuses on directly investigating the First-In-First-Out property and the performance of the first-order approximation in link travel time estimation by designing and modeling dynamic network loading (DNL) on single-line stretch networks. After model formulation, we analyze the First-In-First-Out (FIFO) property of the first-order approximation. Then a series of numerical experiments is conducted to demonstrate the FIFO property of the first-order approximation, and to compare its performance with those using the second-order approximation, a point queue model, and the cumulative inflow and exit flow curves. The numerical results show that the first-order approximation does not guarantee FIFO and also suggest that the second-order approximation is recommended especially when the link exit flow is increasing. The study provides guidance for further study on proposing new methods to better estimate link travel times

A nonlinear equation system approach to the dynamic stochastic user equilibrium simultaneous route and departure time choice problem

postprin

The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems

postprin

An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance

Different from traditional methods, this paper formulates the logit-based stochastic dynamic user optimal (SDUO) route choice problem as a fixed point (FP) problem in terms of intersection movement choice probabilities, which contain travelers’ route information so that the realistic effects of physical queues can be captured in the formulation when a physical-queue traffic flow model is adopted, and that route enumeration and column generation heuristics can be avoided in the solution procedure when efficient path sets are used. The choice probability can be either destination specific or origin–destination specific, resulting into two formulations. To capture the effect of physical queues in these FP formulations, the link transmission model is modified for the network loading and travel time determination. The self-regulated averaging method (SRAM) was adopted to solve the FP formulations. Numerical examples were developed to illustrate the properties of the problem and the effectiveness of the solution method. The proposed models were further used to evaluate the effect of information quality and road network improvement on the network performance in terms of total system travel time (TSTT) and the cost of total vehicle emissions (CTVE). Numerical results show that providing better information quality, enhancing link outflow capacity, or constructing a new road can lead to poor network performance.postprin

Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness

We present a continuous-time link-based kinematic wave model (LKWM) for dynamic traffic networks based on the scalar conservation law model. Derivation of the LKWM involves the variational principle for the Hamilton-Jacobi equation and junction models defined via the notions of demand and supply. We show that the proposed LKWM can be formulated as a system of differential algebraic equations (DAEs), which captures shock formation and propagation, as well as queue spillback. The DAE system, as we show in this paper, is the continuous-time counterpart of the link transmission model. In addition, we present a solution existence theory for the continuous-time network model and investigate continuous dependence of the solution on the initial data, a property known as well-posedness. We test the DAE system extensively on several small and large networks and demonstrate its numerical efficiency.Comment: 39 pages, 14 figures, 2 tables, Transportmetrica B: Transport Dynamics 201

Modeling Choice Problems with Heterogeneous User Preferences in the Transportation Network

Users of transportation systems need to make a variety of different decisions for their trips in the network, while their objective is to keep the generalized costs of their own trips minimized. In the transportation network, there is a diversity of different factors that can influence the decisions of the users, while the relative importance of these factors varies among the heterogeneous users with different trip purposes. Nonetheless, the cumulative result of the individual decisions of the users seeking to minimize their costs according to their own preferences leads to the user equilibrium condition in which no one can reduce his/her cost by changing his/her decision. In this research, we adapt the concept of the efficient frontier from portfolio theory (Markowitz, 1952) in finance in order to model the bicriterion choice behavior of users with heterogeneous preferences in transportation networks. We show that the efficient frontier has a set of primary properties that remains general in different problems. Thus, the primary properties of the efficient frontier can be employed to analytically model and solve different bicriterion choice problems in transportation. For the first application, we use these properties to propose an analytical model for the morning commute problem when there is a heterogeneity associated with preferences of the users (Vickrey, 1969; Daganzo, 1985). A dynamic pricing strategy is also proposed to optimize the bottleneck by minimizing the total cost for users. In addition to the morning commute problem, Vickrey’s congestion theory is also shown to have applications in modeling and optimizing the operation of the demand responsive transit (DRT) system with time-dependent demand and state-dependent capacity as queueing systems. The efficiency of the DRT system can be improved by implementing a dynamic pricing strategy. The analytical solution of the morning commute problem can be also extended for modeling and pricing the DRT system when there is a heterogeneity associated with the preferences of the DRT service users. For another application of the efficient frontier in modeling choice problems in transportation, we propose a traffic assignment model to account for the heterogeneity in sensitivity of the users to travel time reliability in a network under travel time variability. However, the proposed model can have wide applications in modeling the equilibrium condition of different multicriterion choice problems in transportation

Consistent anticipatory route guidance

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2000.Includes bibliographical references (p. 241-251).Anticipatory route guidance consists of messages, based on traffic network forecasts, that assist drivers' path choice decisions. Guidance is consistent when the forecasts on which it is based are verified after drivers react to it. This thesis addresses the formulation and development of solution algorithms for the consistent anticipatory route guidance generation (RGG) problem. The thesis proposes a framework for the problem, involving a set of time-dependent variables and their relationships. Variables are network conditions, path splits and guidance messages. Relationships are the network loading map, transforming path splits into network conditions; the guidance map, transforming network conditions into guidance messages; and the routing map, transforming guidance messages into path splits. The basic relationships can be combined into three alternative composite maps that model a guidance problem. Consistent guidance corresponds to a fixed point of a composite map. With stochastic maps, RGG model outputs are stochastic process realizations. In this case, the consistency fixed point corresponds to stationarity of the RGG solution process. Numerical methods for fixed point computation were examined, focusing on approaches that are rigorous and applicable to large-scale problems. Methods included Gibbs sampling for highly stochastic maps; generalizations of functional iteration for deterministic maps; and the MSA and Polyak iterate averaging method for "noisy" (deterministic plus disturbance) maps. A guidance-oriented dynamic traffic simulator was developed to experiment with RGG solution methods. Computational tests using the simulator investigated the use of Gibbs sampling to compute general stochastic process outputs; and examined the performance of the averaging methods under different model formulations, problem settings and degrees of stochasticity. Gibbs sampling successfully generated realizations from the stationary solution process of a fully stochastic model, but entails considerable computational effort. For noisy problems, the MSA found fixed points in all cases considered. Polyak averaging converged between two and four times faster than the MSA in low or moderate stochasticity problems, and performed comparably to the MSA in other problems. Formulations involving path-level variables converged more quickly than those involving link-level variables.by Jon Alan Bottom.Ph.D

Modelling Traffic Congestion as a Spreading Phenomenon

The spread of traffic jams in urban networks has long been viewed as a complex spatio-temporal phenomenon that often requires computationally intensive microscopic models for analysis purposes. This dissertation presents frameworks to describe the dynamics of congestion propagation and dissipation of traffic in cities using a simple contagion process, inspired by those used to model infectious disease spread in a population. Specifically, we model the spread of congestion in urban networks by adapting a classical epidemic model to include a propagation and dissipation mechanism dependent on time-varying travel demand and consistent with the fundamentals of network traffic flow theory. We describe the dynamics of congestion spread using two macroscopic new parameters (propagation rate β and recovery rate μ) embedded within a system of ordinary differential equations, similar to the well-known susceptible-infected-recovered (SIR) model. For simplicity, we initially assumed the topological distribution of road networks to be homogeneous. The proposed contagion-based dynamics are verified through empirical multi-city analysis. In addition to the simplistic homogeneous SIR approach, we also explored the significance of the degree of heterogeneity in urban street networks using both empirical and simulation-based traffic data. However, this approach inherently assumes an undirected network with uniform recovery rate compared to a road network, which usually displays directed flow and topological reliance on congestion recovery. Keeping in view of these constraints, we proposed a modification to the heterogeneous mean-field model to describe the spreading process of congestion in urban street networks. A practical application of the proposed model is also tested in this dissertation in the context of signal optimisation using cycle length as a controlling function. The experiments helped quantify the characteristic differences between two widely used traffic assignment models, i.e. Dynamic User Equilibrium (DUE) and Stochastic Route Choice (SRC). Comparison has been made at two levels: link-level flows and network-level congestion patterns. Furthermore, we explored an alternative approach for congestion dynamic modelling, namely the "Reaction-Diffusion (RD) model", with a similar concept as our proposed frameworks but at link-level. This model, with its complexity, requires higher computation time with detailed link-level information of congestion dynamics