Robert Herman

Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterials

An extension of a recent framework for analyzing the time-dependent departure pattern arising in an idealized situation of a pool of commuters going from a single origin to a single destination along a unique route is presented. Congestion along this route is represented using elementary traffic flow theoretic relationships; time-varying patterns of basic traffic variables are derived under user equilibrium conditions, along with the corresponding time-dependent departure pattern of system users. After demonstrating the basic model in the single-route context, an additional dimension of choice is introduced by considering the joint departure time and route choice decisions of users. Results are derived in a simplified two-route context and numerical illustrations provided.

Network traffic flow theory: microscopic simulation experiments on supercomputers

Abstract Microscopic simulation experiments are conducted to investigate traffic behavior in urban networks and support the development of network-level traffic flow relations. Previous use of microscopic traffic simulation has been limited by computational resources to small networks. Supercomputers largely alleviate such limitations and allow more elaborate and realistic simulations of traffic in large networks. This paper provides computational experience in simulating large-scale urban traffic networks on a CRAY supercomputer. In addition to the computational results, the experiments address the effect of intersection traffic control on the two-fluid characterization of vehicular flow in congested networks. Evidence is provided from larger networks that supports conclusions reached in earlier work using smaller test networks.

The Influence of Stops on Vehicle Fuel Consumption in Urban Traffic

A simple linear relation between fuel consumption per unit distance, (phi) and trip time per unit distance T , (phi) = k 1 + k 2 T is established for the fuel data collected in Austin and Dallas, Texas, and Matamoros, Mexico. The qualities of traffic service in these cities are compared through the study of the spread of the data points along the (phi), T trend, showing that the Matamoros data in general have higher (phi) and T values. The fuel consumption model (phi) = k 1 + k 2 T is improved by the addition of a term proportional to (Delta) N s ( T ), the deviation of the number of stops for a given datum point from the average number of stops associated with the trip time interval into which the datum point falls. It is shown in the resulting new model, (phi) = k 1 + k 2 T + k 3 (Delta) N s , that since T and (Delta) N s are virtually uncorrected, the values of k 1 and k 2 in the simpler model remain unchanged. A discussion of the physical interpretation of the model parameters is presented. In addition, an analysis of data obtained in central London shows that k 1 depends almost entirely on vehicle mass. It is also shown that the value of the parameter k 3 is approximately given by the product of the warmed-up idle fuel flow and the average stop duration.

Technology, human interaction, and complexity: reflections on vehicular traffic science

This paper is based on the second Philip McCord Morse Lecture given May 14, 1991, at the TIMS/ORSA Joint National Meeting in Nashville. It traces the authors involvement in the development of vehicular traffic science over the last 35 years. After some historical background, the paper discusses highlights of this work: developing and testing car-following theory, traffic theory for multilane highways, the behavior of traffic in towns, the relationship of trip decisions to traffic-system dynamics, and fuel consumption in urban areas. Throughout these discussions, particular attention is paid to the role of complexity and collective effects. The paper continues with comments on the importance of viewing traffic in the context of the overall infrastructure as well as its technology and environment. It concludes with some reflections on the state of the scientific enterprise in our society.

Sampling strategies for two-fluid model parameter estimation in urban networks

The basic postulate of the two-fluid theory of town traffic relates the average speed of moving vehicles to the fraction of moving vehicles in a street network; both representing averages over all vehicles in the network. Data collection to provide estimates of the model parameters to-date has consisted of sampling the network with a test car, replicating (as closely as possible) the trip histories of randomly selected vehicles in the network. Because the two-fluid model is nonlinear, it cannot be simultaneously applied at the individual vehicle level and the network level, as is shown in this article. However, due to the practical difficulties in collecting data for all the vehicles in the network, several potential sampling strategies are identified and are evaluated with computer simulation. The simulation experiments suggest that aggregating the trip histories of 10 to 20 test vehicles over 10 to 15 minutes yields parameter estimates very close to the true value.

Trip time-stop time studies of extreme driver behaviors

The focus of the present study has been to investigate the extent to which drivers with “extreme” modes of behavior deviate from the “normal” (chase-car) trend in a given city. The experiment consisted of collecting trip time-stop time data in the Central Business District (CBD) of Roanoke, Virginia, using three vehicles circulating simultaneously in the area. While one of the three vehicles was engaged in the chase-car mode, the other two vehicles were driven aggressively or conservatively. Similar data were also collected in the Austin, Texas, CBD. Using the data for each driver type, three two-fluid trends are established for the Roanoke CBD: an aggressive, a normal (chase-car), and a conservative trend. On a trip time-stop time diagram, while the conservative and aggressive trends are essentially parallel, the conservative trend approaches the normal trend at off-peak periods. The aggressive trend, on the other hand, approaches the normal trend at peak periods. The differences among the trends, however, are by and large statistically significant. Similar results have been obtained in Austin—despite uncertainties at high levels of demand, where the normal trend may cross the aggressive trend. The results also underline the importance of common data collection techniques when comparing the quality of traffic service of various cities using the two-fluid model approach. In assessing the statistical significance of differences among the two-fluid trends of various city networks, the potential impact of driver behavioral variations must be considered.

Interaction of trip decisions and traffic systems dynamics

Abstract A major difficulty in the study of large-scale complex systems involving human decision-making with non-linear collective effects is that of obtaining pertinent data at the desired level of detail. A controlled experiment involving real commuters in a hypothetical computer simulated traffic system is described as an alternative approach of conducting observational studies to support the modelling of such complex dynamic interactive decision systems. An overview of the principal characteristics of the traffic systems evolution obtained in this experiment is presented. Also illustrated are the features of a proposed behavioral framework where users are viewed as boundedly rational seekers of a satisfactory choice outcome.

EFFECT OF CONFIGURATION ON THE BINDING OF AN ELECTRON TO A FIXED LINEAR ELECTRIC QUADRUPOLE

Abstract A quantum mechanical investigation has been made of the binding of an electron to a finite linear electric quadrupole in two configurations, one of which has two positive charges, each of charge + q , symmetrically placed about a negative charge -2 q , and the other has the signs of the charges reversed. When the expectation value of the Hamiltonian is minimized in a variational calculation using Gaussian wave functions and then set to equal zero, the solution of the resulting equation gives the value of the minimum quadrupole moment required to assure the existence of a bound state. It has been found that the ratio of minimum quadrupole moments required to bind an electron for the first and second configurations is 7.9.

Traffic dynamics through human interaction: Reflections on some complex problems

Abstract A brief essay based on a discussion of some highlights in the development of traffic flow theory over the last thirty-five years. Of especial interest are flow and stability in single-lane car following, collective effects in a kinetic theory of vehicular traffic on multi-lane highways and in a two-fluid model of traffic in urban street networks. Remarks are made concerning modeling and the remarkable simplifications that often arise from collective effects. It is pointed out that vehicular traffic is an excellent example of a system involving human interaction with consequent behavioral effects that have been effectively described in mathematical terms.

ROADWAY-VEHICLE INTERACTION, PHYSICAL INDEXES, AND HUMAN JUDGMENT OF RIDE QUALITY

Present serviceability index (PSI) modeling has been an important subject for decades. Other dynamic indexes characterizing a roadway such as the international roughness index (IRI), averaged rectified slope (ARS), and averaged rectified speed (ARV) have been proposed and studied. However, the roles played by these indexes in the interaction between road, vehicle, and human ratings have not been made clear. A unified physical model linking the static profile of a roadway and the dynamic response of a vehicle to the profile to the serviceability index of the roadway is presented here. Analytical expressions for jerk index, acceleration index, ARV, ARS, and IRI are derived from the developed model in terms of the physical parameters for roadways and the dynamic characteristics of a vehicle. Then a linear relation between the PSI and the logarithm of the jerk index is proposed. Using the jerk index computed from field profile data, the linear functional form for the PSI is verified, and regression R2 values higher than 0.94 are obtained for various types of pavements. The same analysis is performed for other dynamic indexes, and the R2 values are found to be approximately in the range from 0.70 to 0.80. These results indicate that the theoretical model correctly predicts and explains the human rating of ride quality and that the jerk experienced by raters in a moving vehicle dictates the ratings. Moreover, the relationship of the static parameters of roadway profiles with human ratings is discussed using the conventional approach.